Physics

Educational objectives

General aim:
to acquire basic knowledge on linear systems, vector spaces, linear maps, symmetric bilinear forms and hermitian forms.

Specific aim
Knowledge and comprehension: successful students will acquire basic notions and results about solvability of linear systems and its geometric interpretation, matrix calculus, vector spaces and linear maps between them, with special focus on endomorphisms of vector spaces and their associate decompositions into eigenspaces.

Applied knowledge and comprehension: successful students will be able to solve linear systems with a finite number of variables, to
recognize mathematical problems that can be codified into vector spaces and linear maps and therefore to solve them;
to manipulate matrices and determine the solvability of a linear system and the invertibility of a linear map by studying its rank and by
computing the determinant of the associated matrix; moreover, he/she will be able to compute the eigenvalues of a linear endomorphism
and to determine the associated decomposition into eigenspaces.

Critical thinking abilities: in this course the student will acquire basic knowledge that will make him/her able to discover analogies between the topics treated in this course and the topics treated in following courses such as Mechanics and Vectorial Analysis.

Communication skills: ability to illustrate the content of the course in the oral exam and in the possible theoretical questions in the written test.

Learning skills: the learnings of these lectures will allow the student to access the study of the following courses of the degree program in Physics.

Educational objectives

General Targets

to get basic tools of Differential and Integral Calculus in one variable, more variables Differential Calculus, linear and some nonlinear ODE’s of first and second degree.

A - Knowledge and understanding
OF 1) Integrals in one variable, Differential Calculus in Rn, techniques of solutions to ODEs
B – Application skills
OF 2) To be able to apply analytical methods to problems of Classical Mechanics
C - Autonomy of judgment
OF 3) To be able to individually solve problems by a rigorous logical/analytic approach (stimulated in exercise sessions
D – Communication skills
OF 4) Effective interaction among students and with prof.
E - Ability to learn
OF 5) Links to concepts arising in upcoming Courses and attention to rigorous way of thinking will provide awareness in consulting books and in individual learning

Educational objectives

Laboratorio di Calcolo (Computational Laboratory) is an introductory course in computer programming and in the numerical methods used in Physics. This course takes a practical approach in teaching fundamental concepts of programming with a strong emphasis on tutorials and laboratory work and is an important vehicle for developing students’ analytical and problem-solving skills. The course aims to provide skills that will be relevant for the students’ academic career. Therefore, the main purpose of the course is not to give a detailed knowledge in whatever are the current leading programming tools on the market, but rather to teach the general principles that are at the basis of any programming language. Programming is a practical subject: the purpose of the course is that of teaching students to write (short) programs that actually work. The important skills which underlie programming are abstract ones. The ability to see patterns and to abstract from specific examples to the more general case is crucial. Being able to think logically so one can predict in advance the behaviour of a system working to a fixed set of rules is essential. These skills are developed through practice, and indeed, the course uses a problem-based learning approach. In addition the course aims at providing good working practices: self-motivation, good time management, thinking and acting rationally, learning how to interact with coworkers. At the end of the course, students will understand computational methods typically employed in physics and will be able to write simple computer programs. They will have a good knowledge of the C language, of the Linux operating system and of Python basic instructions that will be used to improve student’s skills in terms of analysis and description of algorithms needed to solve physics problems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Acquire fundamental concepts and general principles that are at the basis of any programming language
OF 2) Acquire the general principles that underlie any programming language.
OF 3) Understanding the basic architecture of a computer and its functioning.
OF 4) Understand algorithms and computing methods to solve scientific problems

…
B - Application skills
OF 5) Solve logical and/or analytical problems, as well as simple probles of general physics by developing optimal and efficient algorithms
OF 6) Write simple programs in C or Python that actually work.

C - Autonomy of judgment
OF 7) Identify general patterns from specific examples.
OF 8) To be able to integrate the knowledge acquired in order to…

D - Communication skills
OF 13) Interact and collaborate with other students in the problem-solving process through appropriate communication of ideas, insights, and knowledge

E - Ability to learn
OF 15) Have the ability to learn new algorithms for solving scientific problems.
OF 16) Have the ability to learn new programming techniques and languages.

Educational objectives

The goal is to give students the practical ability to use a modern personal computer and perform the basic operations of use (on, off, data and program management), on proprietary OS or open source.

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
OF 1) To describe the fundamental laws of mechanics and their applications to real-world situations.
OF 2) To develop problem-solving skills using an approach which describes physical phenomena by combining methods and mathematical formulae on one hand, and physics intuition on the other hand.
OF 3) To develop mathematical skills required to derive accurate numerical solutions which can be directly compared to real-world situations and measurements.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 4) To know the fundamental laws of mechanics
OF 5) To know the conservation laws in physics and their implications
OF 6) To understand the text of a physics problem
B - Application skills
OF 7) To formalise the solution of a physics problem from the mathematical point of view
OF 8) To solve a physics problem in a coherent way, both from a formal and a quantitative point of view
OF 9) To be able to evaluate the dominant effects in a physics problem
C - Autonomy of judgment
OF 10) To be able to establish whether a relation between physical quantities, or a physical law, is correct from the dimensional point of view
OF 11) To develop quantitative and analytical reasoning skills required to study, model and understand the fundamental principles of mechanics
D - Communication skills
OF 12) To be able to talk about physics using the appropriate terminology
OF 13) To know how to simplify a complex problem, by identifying its most relevant aspects.
E - Ability to learn
OF 14) To be able to consult a physics textbook

Educational objectives

The chemistry course provides a basic overview of the chemistry, structure and reactivity of chemical compounds. All topics are addressed in a simple way as this course is intended for first-year students of different scientific backgrounds. The objective is to encourage students to think and solve chemical problems, teaching general methods that can be used in different chemical contexts.
Specifically, at the end of the course, by means of theoretical and numerical lessons, the student will have a proper knowledge and understanding of basic concepts of General Chemistry. In particular, he will understand the composition, structure and properties of the different states of matter, and the laws the control their transformations. Moreover, students will be able to solve simple numerical exercises on these topics.
The final exam will be passed only if the student has an appropriate critical understanding of the subject. It will be obtained by means of
the personal study of the suggested textbooks and of the theoretical lessons, and by solving appropriate numerical exercises.
The course also aims at improving the communication skills of the student: he should be able to explain, in a simple but rigorous way, basic chemical processes, both in written and oral form, to non-experts. Moreover, the notions acquired in the course should allow him to understand
chemistry textbooks and scientific articles, as needed for his future studies.

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to provide basic notions and skills of differential and integral calculus for functions of several variables that are necessary for the understanding of the main scientific disciplines, with a special attention to the physical sciences.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the principles of differential and integral calculus for functions of several variables
OF 2) To know the theory of vector fields and linear differential forms
OF 3) To understand basic theory of ordinary differential equations

B - Application skills
OF 4) To be able to deal with problems involving scalar functions of several variables (e.g.: optimization, area and volume calculations), vector fields (e.g. work and flux calculations) and differential equations (e.g. resolution and qualitative study).

C - Autonomy of judgment
OF 5) To have essential tools for successive approach to functional analysis, functions of one complex variable, measure theory, quantum mechanics.
OF 6) To be able to autonomously solve new problems, applying mathematical tools to phenomena or processes to be encountered in University studies or subsequent working activities.

D - Communication skills
OF 7) To know how to communicate using properly mathematical language

E - Ability to learn
OF 8) To be able to deepen autonomously some arguments introduced during the course

Educational objectives

GENERAL OBJECTIVES:
The course aims for students to acquire the knowledge of the laws of thermodynamics. Students will understand how these fundamental laws apply to both ideal (ideal gases, ideal machines) and real (real gas model, real thermal machines) systems. With the laboratory experiences, students will apply the laws studied and will acquire practical knowledge on the measurement of thermodynamic quantities (temperature, heat, pressure). They will also acquire practice with the use of vacuum systems and related instrumentation.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the basics of thermodynamics.…
OF 2) To understand thermodynamic systems and their interactions with the surroundings.
OF 3) To learn the correlation between the nature and entropy.
OF 4) To understanding thermodynamics of real systems.
OF 5) To learn the transport phenomena at the molecular level.
…
B - Application skills
OF 6) To be able to deduce the relationship between the fundamental thermodynamic quantities.
OF 7) To be able to solve problems of thermodynamics of ideal and real systems.
OF 8) To be able to apply methods/techniques for the measurements of fundamental quantities.
…
C - Autonomy of judgment
OF 9) To be able to integrate the acquired knowledge in order to subsequently apply it in the more general context for heat engines.

D - Communication skills
OF 10) To know how to communicate the presentation of thermodynamic quantities with their realistic uncertainties.

E - Ability to learn
OF 11) To have the ability to consult and evaluate properly the scientific literature for advanced knowledge on the topics of the course.
OF 12) To be able to conceive and develop a project related to heat engines.

Educational objectives

GENERAL OBJECTIVES:
The course aims to cover the fundamental aspects of Lagrangian and Hamiltonian mechanics. At the end of the course, students should be able to apply the concepts learned to solve Lagrangian/Hamiltonian mechanics problems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of Lagrangian mechanics
OF 2) Know the basics of Hamiltonian mechanics
OF 3) Develop the ability to apply mathematical methods to the modeling of physical systems

B – Application capabilities
OF 4) Know how to describe a constrained mechanical system with a finite number of degrees of freedom in terms of Lagrangian variables, determining the Lagrangian function and the Euler-Lagrange equations
OF 5) Know how to describe a constrained mechanical system with a finite number of degrees of freedom in terms of Hamiltonian variables, determining the Hamiltonian function and the Hamilton equations
OF 6) Know how to study the properties of equilibrium, stability, small oscillations and the main symmetries of a system using the techniques of Lagrangian mechanics
OF 7) Know how to solve simple problems involving canonical transformations in Hamiltonian systems

C - Independence of judgment
OF 8) Be able to integrate the knowledge acquired in Lagrangian Mechanics in order to subsequently apply them in different contexts of Theoretical Physics (Quantum Mechanics, Statistical Mechanics, Field Theory, etc...)
OF 9) Be able to integrate the knowledge acquired in Hamiltonian Mechanics in order to subsequently apply them in different contexts of Theoretical Physics (Quantum Mechanics, Statistical Mechanics, Field Theory, etc...)

D – Communication skills

E - Ability to learn
OF 10) Have the ability to consult advanced textbooks in order to independently delve into some topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course is to teach students the use of computers for solving some fundamental problems in physics. This is achieved by teaching students some advanced elements of the C programming language, along with several algorithms which, although simple, are widely applicable in different contexts.
At the end of the course, students will have acquired a sufficiently in-depth knowledge of the C programming language and other operational tools useful for data analysis and their graphic representation. They will have acquired the skills necessary to solve physics problems of medium difficulty with the computer and to autonomously implement algorithms of a certain complexity.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Advanced elements of C programming (dynamic allocation, struct, recursion)
OF 2) Basic and advanced algorithms for the integration of ordinary differential equations, for the generation of pseudo-random numbers, and for the study of simple stochastic processes (random walk, reticular gas and percolation)
OF 3) Understand a program written in C language
B - Application skills
OF 4) Be able to implement an algorithm in C language
OF 5) Knowing how to solve, with the use of computers, medium difficulty physics problems that are described by differential equations or by a simple stochastic process
OF 6) Being able to find errors in a program written in C language (debugging) and knowing how to correct them
OF 7) Be able to perform, with IT tools, simple data analysis (e.g. performing averages and the calculation of the error for independent measurements), and their graphical representation
C - Autonomy of judgment
OF 8) Knowing how to independently evaluate if a program written in C language correctly executes a given algorithm and if this implementation is efficient
D - Communication skills
OF 9) Knowing how to discuss critically the choices made in the implementation of a given algorithm in a program written in C language
OF 10) Knowing how to present in written form the results of the study of a physical problem carried out numerically using the computer
E - Ability to learn
OF 11) Have the ability to consult the description of a new algorithm or understand a C language program written by others

Educational objectives

GENERAL OBJECTIVES:

- Learning of the foundations of the classical theory of electromagnetism, starting from the experimental observations of electrical and magnetic phenomena and arriving at the complete formulation of classical electrodynamics in terms of Maxwell's equations and in terms of electrodynamic potentials. Introduction to Special Relativity and covariant formulation of Electromagnetism.

- Acquiring of the ability to solve problems in electrodynamics.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

- Demonstrate knowledge and understanding in the field of electromagnetism at post secondary instruction level, also with respect to some cutting-edge topics in modern electromagnetism and relativity, with the support of advanced textbooks.

B - Application skills

- Be able to apply the acquired knowledge in a competent and reflective way; possess adequate skills both to conceive and support arguments, and to solve problems and apply techniques and methods within the field of electromagnetism.

C - Autonomy of judgment

- Develop the ability to autonomously set up, analyze and solve problems of physics.

D - Communication skills

- Communicate ideas, problems and solutions to specialists and non-specialists.

E - Ability to learn

- Develop the skills necessary to undertake further studies with a high degree of autonomy.

Educational objectives

GENERAL OBJECTIVES:
The first objective of the class is the study of the theory of electrical circuits and most common electrical components. The second objective is to acquire the know-how of optimal use of basic electric measurements instrumentation: voltage and current generators, multimeter, oscilloscope.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the theory of DC circuits
OF 2) To know the theory of AC circuits
OF 3) To know the theory of electrical measurements

B - Application skills
OF 4) To be able to solve simple problems with DC and AC circuits
OF 5) To be able to carry out measurements of voltage, current, resistance (multimeter)
OF 6) To be able to carry out measurements of time intervals, voltages and phases (oscilloscope)
OF 7) To be able to estimate and correct for the perturbation induced by the measurement system
C - Autonomy of judgment
OF 8) To be able to evaluate the best way of performing an electrical measurement

D - Communication skills
OF 9) To know how to communicate in written reports the results of the experimental work
OF 10) To know how to discuss the characteristics and functionalities of simple electrical circuits

E - Ability to learn
OF 11) Being able to consult the manuals of the measurement instruments
OF 12) Being able to understand the datasheets of electric components

Educational objectives

PART I
General goals:
The goal of the course is the study and the comprehension of advanced mathematical techniques. The student will acquire the basic concepts of complex
analysis and functional analysis and she/he will be able to apply them to the study of problems in classical (electromagnetism and continuum media) and
quantum physics. The know-how that the student acquires attending this course is indispensable for the Physics courses of the third year.

Specific goals:
Introduction to the fundamental concepts of complex analysis, i) to provide the student with a deep knowledge and understanding of these concepts, and ii) to
allow him/her to successfully apply them in various physical contexts. In particular, the student must be able to use techniques of integration in the complex
domain in all the physical
contexts in which they have applications. In order to achieve these goals, and to help the student to develop the capability i) to communicate the acquired
knowledges, and
ii) to continue the studies autonomously, we plan to involve him (her), during the theoretical lectures and exercises, through general and specific questions
related to the
subject; or through the presentation in depth of some specific subject agreed with the teacher

PART II
General goals:
The goal of the course is the study and the comprehension of advanced mathematical techniques. The student will acquire the basic concepts of complex
analysis and functional analysis and she/he will be able to apply them to the study of problems in classical (electromagnetism and continuum media) and
quantum physics. The know-how that the student acquires attending this course is indispensable for the Physics courses of the third year.

Specific goals:
Introduction to the fundamental concepts of functional analysis, i) to provide the student with a deep knowledge and understanding of these concepts, and ii) to
allow him/her to successfully apply them in various physical contexts. In particular, the student must be able to use the Fourier series, the Fourier and Laplace
transforms, and the distributions in all the physical contexts in which they have applications; in addition the student must be able to work with Hilbert spaces and
with operators on functional spaces of physical interest. In order to achieve these goals, and to help the student to develop the capability i) to communicate the
acquired knowledges, and ii) to continue the studies autonomously, we plan to involve him (her), during the theoretical lectures and exercises, through general
and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher

Educational objectives

To provide students with the basic linguistic skills needed to deal with written scientific communication.

Educational objectives

A - Knowledge and understanding
OF 1) Understanding the physical concepts underlying quantum mechanics.
OF 2) Understanding the mathematical aspects necessary to describe quantum mechanical systems.
OF 3) Knowing the main experimental evidences that led to the crisis of classical mechanics.
OF 4) Knowing the properties of some notable systems such as the harmonic oscillator and the particle in a Coulomb field.

B - Application skills
OF 5) Knowing how to deduce the consequences and physical properties of a system governed by a quantum dynamics.
OF 6) Solving quantum mechanical problems of various kinds.
OF 7) Being able to use different mathematical methods to solve the problems.

C - Autonomy of judgment
OF 8) The student will have to learn how to evaluate the correctness of the logical reasoning used in the solution of problems and in the proofs of theorems.
OF 9) The regular assignment of exercises will encourage the habit of self-assessment.
OF 7) Being able to use different mathematical methods to solve the problems

D - Communication skills
OF 11) The acquisition of adequate skills and tools for communication will be verified during the evaluation tests. The oral and written exams require the student to express herself/himself with scientific language and to follow a rigorous logic in reasoning.

E - Ability to learn
OF 12) The work required for this course stimulates the development of a flexible mentality, useful both for more advanced scientific studies and in the context of various workplaces.

Educational objectives

GENERAL OBJECTIVES:
The first main objective of the course is to introduce the students to the fundamental concepts of Statistical Mechanics (SM). Generally speaking the students must understand how to derive the thermodynamic description of a macroscopic system from its microscopic laws. This knowledge is of obvious relevance for their background in Physics and for the more specialised courses of the next years.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) basic concepts in equilibrium SM and in probability theory
OF 2) computation rules in classical SM (microcanonical, canonical and grand canonical ensembles); equivalence between the different rules and their application to non-interacting systems;
OF 3) Basic concepts and example of interacting systems (Van Der Waals equation).
OF 4) Fundamental concepts and computation rules in Quantum SM; application to the quantum perfect gas, Bose-Einstein and Fermi-Dirac distributions;
OF 5) Thermodynamic properties of quantum bosonic and fermionic systems; high and low temperature limits; Sommerfeld expansion for a Fermionic gas; specific heat in a solid; Debye theory.
OF 6) Brief summary of quantisation of the electromagnetic radiation, black body radiation.
B - Application skills
OF 7) The second objective is to prepare the students to actively solve problems in physics where SM concepts are required. This will happen at first with problems structured with a conceptual scheme similar to the one discussed and applied during the course. However, as their preparation progresses, students are also expected to use SM concepts for solving new problems in different applications.
C - Autonomy of judgment
OF 8) The third and more ambitious objective is to teach the students to think in probabilistic and statistic terms, using concepts and methods from SM as a powerful problem solving tool, both in physics and in different fields (e.g. socio-economic systems, biological systems, medical applications)
D - Communication skills
OF 9) Besides having a clear understanding of the new acquired concepts in SM, the studend should correspondingly acquire the ability to communicate and transmit these concepts in a clear and direct way.
E - Ability to learn
OF 10) The students should become able to read and understand scientific books and articles where SM concepts are involved and should be able to deepen autonomously their knowledge in this field.

Educational objectives

GENERAL OBJECTIVES:
The course describes the basics of nuclear and subnuclear physics through the study of the main discoveries that have contributed to the modern description of particles and their interactions. Relativistic kinematics is used to analyze the production reactions and decays of particles, applying the conservation laws of quantum numbers. The nature of alpha and beta decays is described through non-relativistic mechanics. Finally, the interactions of particles in matter and the operating principles of the detectors for the measurement of energy and momentum and the identification of charged particles are discussed.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowing different types of fundamental interactions between elementary particles
OF 2) Understanding the kinematics of production and decay processes
OF 3) Knowledge of basic nuclear reactions and energy properties
OF 4) Recognize and describe the primary interactions of particles in matter

B - Application skills
OF 5) Compute kinematic properties of decay products and collisions between elementary particles, using the selection rules
OF 6) Calculate the energy lost by elementary particles passing through matter
OF 7) Calculate the probability of decay and interaction in collisions

C - Autonomy of judgment
OF 8) Ability to apply the acquired knowledge to understand the main discoveries in subnuclear physics in the twentieth century
OF 9) Understand the experimental method and the measurements made in some of the most important and famous experiments of the twentieth century

D - Communication skills
OF 10) Ability to discuss, at an elementary level, modern physics as regards the fundamental interactions of particles.

E - Ability to learn
OF 11) Ability to consult scientific articles relative to the measurements covered in the course and understand their methodology and purpose
OF 12) Ability to understand the physics processes of elementary particles treated in the Master's Degree in Physics, using the notions of kinematics and conservation laws of quantum numbers

Educational objectives

The aim of the course is to enable students to enrich the knowledge of curricular courses with topics of their choice.

Educational objectives

GENERAL OBJECTIVES:
The student will acquire knowledge of the fundamental principles and laws of Classical Optics, with regards to general phenomena, such as interference, diffraction and polarization of light. These phenomena will be also investigated in laboratory sessions by using advanced didactic set-ups. The student will learn how to use the basic principles of Optics to solve simple problems related to the knowledge acquired during the course. At the end of the course, the students will develop quantitative reasoning abilities and problem-solving skills, which represent the basis to study, model and understand light propagation and interaction with matter at a fundamental level.
Furthermore, thanks to the laboratory sessions, the student will develop practical ability to use optical set-ups as well as to convey the observations made during the experiments via laboratory reports. A direct interaction with the teacher will be also a plus during the execution of the experiments.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Understand the fundamentals of physical optics (electromagnetic waves)
OF 2) Understand the fundamentals of optics in linear media (isotropic and anisotropic dielectrics)
OF 3) To understand the language of optics
B - Application skills
OF 4) To be able to assemble simple optical experiments
OF 5) To be able to align an optical interferometer
OF 6) To be able to measure optical intensity (photodiodes)
OF 7) To be able to measure and control light polarization states
C - Autonomy of judgment
OF 8) To be able to evaluate the best way of performing an experimental measurement
D - Communication skills
OF 9) To know how to communicate in written reports the results the experimental work
OF 10) To know how to discuss the characteristics and functionalities of simple optical schemes
E - Ability to learn
OF 11) Being able to consult optical components datasheets
OF 12) Being able to design a of simple optical schemeanalog and digital circuits

Educational objectives

GENERAL OBJECTIVES:
The goal of the course is to study the foundations of material’s structure, providing the basis of atomic and molecular physics, with an elementary introduction to solid state physics, starting from knowledge and methods of quantum mechanics. The student, at the end of the course, will acquire basic concepts to determine energy eigenvalues ang eigenstates of atomic and molecular systems unser external fields. The developed know-how will be fundamental for the advanced condensed matter and solid state physics courses.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know foundations of atomic and molecular physics, and basics elements of solid state physics
OF 2) To understand energy spectra and eigenstates of atomic, molecular and solid state systems.
OF 3) Undesratnd principles of light-matter interaction.

B - Application skills
OF 4) Learn how to apply principles of quantum mechanics do describe atoms and molecules.
OF 5) Solve problems related to atomic and molecular spectra
OF 6) To be able to apply perturbative and variational techniques to evaluate eigenvalues and eigenstates at atoms and molecules

C - Autonomy of judgment
OF 7) To be able to apply in the future the acquired skills to the more general context of condensed matter physics

D - Communication skills
OF 8) To know how to communicate the critical steps necessary to solve elementary problems dealing with material structure

E - Ability to learn
OF 10) Have the ability to autonomously consult basic textbooks and in some cases scientific articles to expand the knowledge developed in the course

Educational objectives

GENERAL OBJECTIVES:
The course describes the basics of nuclear and subnuclear physics through the study of the main discoveries that have contributed to the modern description of the atomic nucleus, of elementary particles and their interactions. Relativistic kinematics is used to analyze the production reactions and decays of particles, applying the conservation laws of quantum numbers. The nature of alpha and beta decays is described through non-relativistic mechanics. Finally, the interactions of particles in matter and the operating principles of the detectors for the measurement of energy and momentum and the identification of charged particles are discussed.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowing different types of fundamental interactions between elementary particles
OF 2) Understanding the kinematics of production and decay processes
OF 3) Knowledge of basic nuclear reactions and energy properties
OF 4) Recognize and describe the primary interactions of particles in matter

B - Application skills
OF 5) Compute kinematic properties of decay products and collisions between elementary particles, using the selection rules
OF 6) Calculate the energy lost by elementary particles passing through matter
OF 7) Calculate the probability of decay and interaction in collisions

C - Autonomy of judgment
OF 8) Ability to apply the acquired knowledge to understand the main discoveries in nuclear and subnuclear physics in the twentieth century
OF 9) Understand the experimental method and the measurements made in some of the most important and famous experiments of the twentieth century

D - Communication skills
OF 10) Ability to discuss, at an elementary level, modern physics as regards the nuclear structure and the fundamental interactions of particles.

E - Ability to learn
OF 11) Ability to consult scientific articles relative to the measurements covered in the course and understand their methodology and purpose
OF 12) Ability to understand the physics processes of elementary particles treated in the Master's Degree in Physics, using the notions of kinematics and conservation laws of quantum numbers

Educational objectives

The aim of the course is to enable students to enrich the knowledge of curricular courses with topics of their choice.

Educational objectives

The final exam consists of the presentation of a report on the activities conducted during the stage/thesis. The preparation for this exam implies skills related to the presentation of her/his work, and the capability to discuss and argue with an audience fully aware of the topics presented.

Educational objectives

General aim:
to acquire basic knowledge on linear systems, vector spaces, linear maps, symmetric bilinear forms and hermitian forms.

Specific aim
Knowledge and comprehension: successful students will acquire basic notions and results about solvability of linear systems and its geometric interpretation, matrix calculus, vector spaces and linear maps between them, with special focus on endomorphisms of vector spaces and their associate decompositions into eigenspaces.

Applied knowledge and comprehension: successful students will be able to solve linear systems with a finite number of variables, to
recognize mathematical problems that can be codified into vector spaces and linear maps and therefore to solve them;
to manipulate matrices and determine the solvability of a linear system and the invertibility of a linear map by studying its rank and by
computing the determinant of the associated matrix; moreover, he/she will be able to compute the eigenvalues of a linear endomorphism
and to determine the associated decomposition into eigenspaces.

Critical thinking abilities: in this course the student will acquire basic knowledge that will make him/her able to discover analogies between the topics treated in this course and the topics treated in following courses such as Mechanics and Vectorial Analysis.

Communication skills: ability to illustrate the content of the course in the oral exam and in the possible theoretical questions in the written test.

Learning skills: the learnings of these lectures will allow the student to access the study of the following courses of the degree program in Physics.

Educational objectives

General Targets

to get basic tools of Differential and Integral Calculus in one variable, more variables Differential Calculus, linear and some nonlinear ODE’s of first and second degree.

A - Knowledge and understanding
OF 1) Integrals in one variable, Differential Calculus in Rn, techniques of solutions to ODEs
B – Application skills
OF 2) To be able to apply analytical methods to problems of Classical Mechanics
C - Autonomy of judgment
OF 3) To be able to individually solve problems by a rigorous logical/analytic approach (stimulated in exercise sessions
D – Communication skills
OF 4) Effective interaction among students and with prof.
E - Ability to learn
OF 5) Links to concepts arising in upcoming Courses and attention to rigorous way of thinking will provide awareness in consulting books and in individual learning

Educational objectives

Laboratorio di Calcolo (Computational Laboratory) is an introductory course in computer programming and in the numerical methods used in Physics. This course takes a practical approach in teaching fundamental concepts of programming with a strong emphasis on tutorials and laboratory work and is an important vehicle for developing students’ analytical and problem-solving skills. The course aims to provide skills that will be relevant for the students’ academic career. Therefore, the main purpose of the course is not to give a detailed knowledge in whatever are the current leading programming tools on the market, but rather to teach the general principles that are at the basis of any programming language. Programming is a practical subject: the purpose of the course is that of teaching students to write (short) programs that actually work. The important skills which underlie programming are abstract ones. The ability to see patterns and to abstract from specific examples to the more general case is crucial. Being able to think logically so one can predict in advance the behaviour of a system working to a fixed set of rules is essential. These skills are developed through practice, and indeed, the course uses a problem-based learning approach. In addition the course aims at providing good working practices: self-motivation, good time management, thinking and acting rationally, learning how to interact with coworkers. At the end of the course, students will understand computational methods typically employed in physics and will be able to write simple computer programs. They will have a good knowledge of the C language, of the Linux operating system and of Python basic instructions that will be used to improve student’s skills in terms of analysis and description of algorithms needed to solve physics problems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Acquire fundamental concepts and general principles that are at the basis of any programming language
OF 2) Acquire the general principles that underlie any programming language.
OF 3) Understanding the basic architecture of a computer and its functioning.
OF 4) Understand algorithms and computing methods to solve scientific problems

…
B - Application skills
OF 5) Solve logical and/or analytical problems, as well as simple probles of general physics by developing optimal and efficient algorithms
OF 6) Write simple programs in C or Python that actually work.

C - Autonomy of judgment
OF 7) Identify general patterns from specific examples.
OF 8) To be able to integrate the knowledge acquired in order to…

D - Communication skills
OF 13) Interact and collaborate with other students in the problem-solving process through appropriate communication of ideas, insights, and knowledge

E - Ability to learn
OF 15) Have the ability to learn new algorithms for solving scientific problems.
OF 16) Have the ability to learn new programming techniques and languages.

Educational objectives

The goal is to give students the practical ability to use a modern personal computer and perform the basic operations of use (on, off, data and program management), on proprietary OS or open source.

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
OF 1) To describe the fundamental laws of mechanics and their applications to real-world situations.
OF 2) To develop problem-solving skills using an approach which describes physical phenomena by combining methods and mathematical formulae on one hand, and physics intuition on the other hand.
OF 3) To develop mathematical skills required to derive accurate numerical solutions which can be directly compared to real-world situations and measurements.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 4) To know the fundamental laws of mechanics
OF 5) To know the conservation laws in physics and their implications
OF 6) To understand the text of a physics problem
B - Application skills
OF 7) To formalise the solution of a physics problem from the mathematical point of view
OF 8) To solve a physics problem in a coherent way, both from a formal and a quantitative point of view
OF 9) To be able to evaluate the dominant effects in a physics problem
C - Autonomy of judgment
OF 10) To be able to establish whether a relation between physical quantities, or a physical law, is correct from the dimensional point of view
OF 11) To develop quantitative and analytical reasoning skills required to study, model and understand the fundamental principles of mechanics
D - Communication skills
OF 12) To be able to talk about physics using the appropriate terminology
OF 13) To know how to simplify a complex problem, by identifying its most relevant aspects.
E - Ability to learn
OF 14) To be able to consult a physics textbook

Educational objectives

The chemistry course provides a basic overview of the chemistry, structure and reactivity of chemical compounds. All topics are addressed in a simple way as this course is intended for first-year students of different scientific backgrounds. The objective is to encourage students to think and solve chemical problems, teaching general methods that can be used in different chemical contexts.
Specifically, at the end of the course, by means of theoretical and numerical lessons, the student will have a proper knowledge and understanding of basic concepts of General Chemistry. In particular, he will understand the composition, structure and properties of the different states of matter, and the laws the control their transformations. Moreover, students will be able to solve simple numerical exercises on these topics.
The final exam will be passed only if the student has an appropriate critical understanding of the subject. It will be obtained by means of
the personal study of the suggested textbooks and of the theoretical lessons, and by solving appropriate numerical exercises.
The course also aims at improving the communication skills of the student: he should be able to explain, in a simple but rigorous way, basic chemical processes, both in written and oral form, to non-experts. Moreover, the notions acquired in the course should allow him to understand
chemistry textbooks and scientific articles, as needed for his future studies.

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to provide basic notions and skills of differential and integral calculus for functions of several variables that are necessary for the understanding of the main scientific disciplines, with a special attention to the physical sciences.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the principles of differential and integral calculus for functions of several variables
OF 2) To know the theory of vector fields and linear differential forms
OF 3) To understand basic theory of ordinary differential equations

B - Application skills
OF 4) To be able to deal with problems involving scalar functions of several variables (e.g.: optimization, area and volume calculations), vector fields (e.g. work and flux calculations) and differential equations (e.g. resolution and qualitative study).

C - Autonomy of judgment
OF 5) To have essential tools for successive approach to functional analysis, functions of one complex variable, measure theory, quantum mechanics.
OF 6) To be able to autonomously solve new problems, applying mathematical tools to phenomena or processes to be encountered in University studies or subsequent working activities.

D - Communication skills
OF 7) To know how to communicate using properly mathematical language

E - Ability to learn
OF 8) To be able to deepen autonomously some arguments introduced during the course

Educational objectives

GENERAL OBJECTIVES:
The course aims for students to acquire the knowledge of the laws of thermodynamics. Students will understand how these fundamental laws apply to both ideal (ideal gases, ideal machines) and real (real gas model, real thermal machines) systems. With the laboratory experiences, students will apply the laws studied and will acquire practical knowledge on the measurement of thermodynamic quantities (temperature, heat, pressure). They will also acquire practice with the use of vacuum systems and related instrumentation.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the basics of thermodynamics.…
OF 2) To understand thermodynamic systems and their interactions with the surroundings.
OF 3) To learn the correlation between the nature and entropy.
OF 4) To understanding thermodynamics of real systems.
OF 5) To learn the transport phenomena at the molecular level.
…
B - Application skills
OF 6) To be able to deduce the relationship between the fundamental thermodynamic quantities.
OF 7) To be able to solve problems of thermodynamics of ideal and real systems.
OF 8) To be able to apply methods/techniques for the measurements of fundamental quantities.
…
C - Autonomy of judgment
OF 9) To be able to integrate the acquired knowledge in order to subsequently apply it in the more general context for heat engines.

D - Communication skills
OF 10) To know how to communicate the presentation of thermodynamic quantities with their realistic uncertainties.

E - Ability to learn
OF 11) To have the ability to consult and evaluate properly the scientific literature for advanced knowledge on the topics of the course.
OF 12) To be able to conceive and develop a project related to heat engines.

Educational objectives

GENERAL OBJECTIVES:
The course aims to cover the fundamental aspects of Lagrangian and Hamiltonian mechanics. At the end of the course, students should be able to apply the concepts learned to solve Lagrangian/Hamiltonian mechanics problems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of Lagrangian mechanics
OF 2) Know the basics of Hamiltonian mechanics
OF 3) Develop the ability to apply mathematical methods to the modeling of physical systems

B – Application capabilities
OF 4) Know how to describe a constrained mechanical system with a finite number of degrees of freedom in terms of Lagrangian variables, determining the Lagrangian function and the Euler-Lagrange equations
OF 5) Know how to describe a constrained mechanical system with a finite number of degrees of freedom in terms of Hamiltonian variables, determining the Hamiltonian function and the Hamilton equations
OF 6) Know how to study the properties of equilibrium, stability, small oscillations and the main symmetries of a system using the techniques of Lagrangian mechanics
OF 7) Know how to solve simple problems involving canonical transformations in Hamiltonian systems

C - Independence of judgment
OF 8) Be able to integrate the knowledge acquired in Lagrangian Mechanics in order to subsequently apply them in different contexts of Theoretical Physics (Quantum Mechanics, Statistical Mechanics, Field Theory, etc...)
OF 9) Be able to integrate the knowledge acquired in Hamiltonian Mechanics in order to subsequently apply them in different contexts of Theoretical Physics (Quantum Mechanics, Statistical Mechanics, Field Theory, etc...)

D – Communication skills

E - Ability to learn
OF 10) Have the ability to consult advanced textbooks in order to independently delve into some topics introduced during the course.

Educational objectives

The aim of the course is to enable students to enrich the knowledge of curricular courses with topics of their choice.

Educational objectives

GENERAL OBJECTIVES:

- Learning of the foundations of the classical theory of electromagnetism, starting from the experimental observations of electrical and magnetic phenomena and arriving at the complete formulation of classical electrodynamics in terms of Maxwell's equations and in terms of electrodynamic potentials. Introduction to Special Relativity and covariant formulation of Electromagnetism.

- Acquiring of the ability to solve problems in electrodynamics.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

- Demonstrate knowledge and understanding in the field of electromagnetism at post secondary instruction level, also with respect to some cutting-edge topics in modern electromagnetism and relativity, with the support of advanced textbooks.

B - Application skills

- Be able to apply the acquired knowledge in a competent and reflective way; possess adequate skills both to conceive and support arguments, and to solve problems and apply techniques and methods within the field of electromagnetism.

C - Autonomy of judgment

- Develop the ability to autonomously set up, analyze and solve problems of physics.

D - Communication skills

- Communicate ideas, problems and solutions to specialists and non-specialists.

E - Ability to learn

- Develop the skills necessary to undertake further studies with a high degree of autonomy.

Educational objectives

GENERAL OBJECTIVES:
The first objective of the class is the study of the theory of electrical circuits and most common electrical components. The second objective is to acquire the know-how of optimal use of basic electric measurements instrumentation: voltage and current generators, multimeter, oscilloscope.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the theory of DC circuits
OF 2) To know the theory of AC circuits
OF 3) To know the theory of electrical measurements

B - Application skills
OF 4) To be able to solve simple problems with DC and AC circuits
OF 5) To be able to carry out measurements of voltage, current, resistance (multimeter)
OF 6) To be able to carry out measurements of time intervals, voltages and phases (oscilloscope)
OF 7) To be able to estimate and correct for the perturbation induced by the measurement system
C - Autonomy of judgment
OF 8) To be able to evaluate the best way of performing an electrical measurement

D - Communication skills
OF 9) To know how to communicate in written reports the results of the experimental work
OF 10) To know how to discuss the characteristics and functionalities of simple electrical circuits

E - Ability to learn
OF 11) Being able to consult the manuals of the measurement instruments
OF 12) Being able to understand the datasheets of electric components

Educational objectives

GENERAL OBJECTIVES:
Provide the students with fundamentals concepts in complex and functional analysis as detailed in the program and stimulate the student's ability to find out how they apply to physics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of analytic functions.
OF 2) To understand the nature of the singularities of the analytic functions.
OF 3) To know the properties of Banach and Hilbert spaces.
OF 4) To know Fourier series and transform, and elements of distribution theory.
OF 5) To undestand the proof of those theorems underlying the properties cited above.

B - Application skills
OF 6) To be able to study the behavior of an analytic function.
OF 7) Compute integrals in the complex plane using the residue method.
OF 8) Compute Fourier series and transform, and distributions.

E - Ability to learn
OF 9) To have the ability to consult a textbook whose prerequisites are the fundamental notions of complex analysis and functional analysis.

Educational objectives

To provide students with the basic linguistic skills needed to deal with written scientific communication.

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide a basic knowledge of modern astronomy. After a first part dedicated to the solar system and its planets, the various types of astronomical coordinates and the main methods for determining distances will be illustrated. Much of the course is dedicated to an introduction to stellar classification and evolution, to the study of the electromagnetic spectrum of stars and to the equations of stellar structure. Knowledge will then be provided regarding the structure of our galaxy, the various types of galaxies and their distribution in the universe. The course ends with references to modern cosmology.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the structure and composition of the Solar System.
OF 2) To know the various types of celestial coordinates, the perturbative effects and the various methods for determining distances.
OF 3) To know the basis for stellar evolution and the Hertzprung-Russell diagram.
B - Application skills
OF 4) To deduce the main physical properties of a star from its electromagnetic spectrum
C - Autonomy of judgment
OF 5) To be able to understand current theories regarding the structure and composition of celestial objects.
D - Communication skills

E - Ability to learn
OF 6) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

A - Knowledge and understanding
OF 1) Understanding the physical concepts underlying quantum mechanics.
OF 2) Understanding the mathematical aspects necessary to describe quantum mechanical systems.
OF 3) Knowing the main experimental evidences that led to the crisis of classical mechanics.
OF 4) Knowing the properties of some notable systems such as the harmonic oscillator and the particle in a Coulomb field.

B - Application skills
OF 5) Knowing how to deduce the consequences and physical properties of a system governed by a quantum dynamics.
OF 6) Solving quantum mechanical problems of various kinds.
OF 7) Being able to use different mathematical methods to solve the problems.

C - Autonomy of judgment
OF 8) The student will have to learn how to evaluate the correctness of the logical reasoning used in the solution of problems and in the proofs of theorems.
OF 9) The regular assignment of exercises will encourage the habit of self-assessment.
OF 7) Being able to use different mathematical methods to solve the problems

D - Communication skills
OF 11) The acquisition of adequate skills and tools for communication will be verified during the evaluation tests. The oral and written exams require the student to express herself/himself with scientific language and to follow a rigorous logic in reasoning.

E - Ability to learn
OF 12) The work required for this course stimulates the development of a flexible mentality, useful both for more advanced scientific studies and in the context of various workplaces.

Educational objectives

GENERAL OBJECTIVES:
The first main objective of the course is to introduce the students to the fundamental concepts of Statistical Mechanics (SM). Generally speaking the students must understand how to derive the thermodynamic description of a macroscopic system from its microscopic laws. This knowledge is of obvious relevance for their background in Physics and for the more specialised courses of the next years.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) basic concepts in equilibrium SM and in probability theory
OF 2) computation rules in classical SM (microcanonical, canonical and grand canonical ensembles); equivalence between the different rules and their application to non-interacting systems;
OF 3) Basic concepts and example of interacting systems (Van Der Waals equation).
OF 4) Fundamental concepts and computation rules in Quantum SM; application to the quantum perfect gas, Bose-Einstein and Fermi-Dirac distributions;
OF 5) Thermodynamic properties of quantum bosonic and fermionic systems; high and low temperature limits; Sommerfeld expansion for a Fermionic gas; specific heat in a solid; Debye theory.
OF 6) Brief summary of quantisation of the electromagnetic radiation, black body radiation.
B - Application skills
OF 7) The second objective is to prepare the students to actively solve problems in physics where SM concepts are required. This will happen at first with problems structured with a conceptual scheme similar to the one discussed and applied during the course. However, as their preparation progresses, students are also expected to use SM concepts for solving new problems in different applications.
C - Autonomy of judgment
OF 8) The third and more ambitious objective is to teach the students to think in probabilistic and statistic terms, using concepts and methods from SM as a powerful problem solving tool, both in physics and in different fields (e.g. socio-economic systems, biological systems, medical applications)
D - Communication skills
OF 9) Besides having a clear understanding of the new acquired concepts in SM, the studend should correspondingly acquire the ability to communicate and transmit these concepts in a clear and direct way.
E - Ability to learn
OF 10) The students should become able to read and understand scientific books and articles where SM concepts are involved and should be able to deepen autonomously their knowledge in this field.

Educational objectives

GENERAL OBJECTIVES:
The course is a general introduction to astrophysics. It aims at the description the most important physical mechanisms and phenomena at work in the universe: stellar, interstellar, galactic, extragalactic and cosmological. The focus is on the modelling of astrophysical and cosmological phenomena, and on the use of physical laws in the interpretation of astrophysical and cosmological observations.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the stellar phenomenology and understand it in terms of the different physical mechanisms of energy production. Understand the stellar evolution, as described by the fundamental equations of stellar structure.
OF 2) To know the phenomenology of the insterstellar medium (plasmas, gases, dust) and understand it in terms of physical mechanisma of emission and absorption.
OF 3) To know the phenomenology of the Galaxy and of the galaxies in the universe, and understand it in terms of the physical phenomena at work.
OF 4) To know the cosmological phenomenology, the observables and their use in the development of a physical model of the universe at large scales. To understand the cosmological evolution of the universe in the homogenous isotropic approximation using physics and in particular gravitation.
B - Application skills
OF 5) To be able to explain astrophysical and cosmological measurements, and use them to constrain the physical model of the system under study, understanding its nature.
C - Autonomy of judgment
OF 6) To master the acquired know-how, and use it in the solution of basic problems in astrophysics and cosmology, and in the understanding of the specialized literature.
D - Communication skills

E - Ability to learn
OF 7) To be able to understand specialistic papers in order to deepen the knowledge of particular topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The objectives of this course are to provide the knowledge of the astronomical observation techniques, and of theastronomical instrumentation as well as the choice of the astronomical observables. Furthermore, the course aimsat using, and understanting the characteristics of, astrophysical instrumentation for laboratory classes andradio/optical observations. The student will understand the importance of the calibration and of the noisemitigation techniques through a series of experimental classes both in the laboratory and at the radioastronomy/optical-astronomy facilities on the roofs of the Physics department at Sapienza. Basic concepts ofastronomical optics, electronics, signal theory, cryogenics, interferometry, spectroscopics, polarimetry, will bepresented as well as the state of the art of radio, mm, sub-mm, IR, optical, UV, X, gamma instrumentation.
SPECIFIC OBJECTIVES:
A -Knowledge and understanding
OF 1) Know the fundamentals of astronomical observations
OF 2) To know the fundamentals of the functioning of astrophysical radiation detectors
OF 3) Understand the use of astrophysical radiation detection techniques
B -Application skills
OF 4) Knowing how to deduce the characteristics of an astrophysical observation
OF 5) Solve problems related to noise
OF 6) Be able to apply noise reduction techniques / methods
C -Autonomy of judgment
OF 7) Being able to evaluate the best way to perform a measurement
OF 8) Integrate the acquired knowledge in order to establish the best observational techniqueD -Communication skills
OF 9) Knowing how to communicate the results of one's work in writing in laboratory reports
OF 10) Knowing how to communicate about known and unknown problemsE -Ability to learn
OF 11) Have the ability toconsult electronic components datasheets
OF 12) Have the ability to evaluate the adequacy of an astrophysics instrument
OF 13) Be able to conceive and develop an astronomical project

Educational objectives

GENERAL OBJECTIVES:
The objectives of this course are to provide the knowledge of the astronomical observation techniques, and of theastronomical instrumentation as well as the choice of the astronomical observables. Furthermore, the course aimsat using, and understanting the characteristics of, astrophysical instrumentation for laboratory classes andradio/optical observations. The student will understand the importance of the calibration and of the noisemitigation techniques through a series of experimental classes both in the laboratory and at the radioastronomy/optical-astronomy facilities on the roofs of the Physics department at Sapienza. Basic concepts ofastronomical optics, electronics, signal theory, cryogenics, interferometry, spectroscopics, polarimetry, will bepresented as well as the state of the art of radio, mm, sub-mm, IR, optical, UV, X, gamma instrumentation.
SPECIFIC OBJECTIVES:
A -Knowledge and understanding
OF 1) Know the fundamentals of astronomical observations
OF 2) To know the fundamentals of the functioning of astrophysical radiation detectors
OF 3) Understand the use of astrophysical radiation detection techniques
B -Application skills
OF 4) Knowing how to deduce the characteristics of an astrophysical observation
OF 5) Solve problems related to noise
OF 6) Be able to apply noise reduction techniques / methods
C -Autonomy of judgment
OF 7) Being able to evaluate the best way to perform a measurement
OF 8) Integrate the acquired knowledge in order to establish the best observational techniqueD -Communication skills
OF 9) Knowing how to communicate the results of one's work in writing in laboratory reports
OF 10) Knowing how to communicate about known and unknown problemsE -Ability to learn
OF 11) Have the ability toconsult electronic components datasheets
OF 12) Have the ability to evaluate the adequacy of an astrophysics instrument
OF 13) Be able to conceive and develop an astronomical project

Educational objectives

GENERAL OBJECTIVES:
The student will acquire knowledge of the fundamental principles and laws of Classical Optics, with regards to general phenomena, such as interference, diffraction and polarization of light. These phenomena will be also investigated in laboratory sessions by using advanced didactic set-ups. The student will learn how to use the basic principles of Optics to solve simple problems related to the knowledge acquired during the course. At the end of the course, the students will develop quantitative reasoning abilities and problem-solving skills, which represent the basis to study, model and understand light propagation and interaction with matter at a fundamental level.
Furthermore, thanks to the laboratory sessions, the student will develop practical ability to use optical set-ups as well as to convey the observations made during the experiments via laboratory reports. A direct interaction with the teacher will be also a plus during the execution of the experiments.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Understand the fundamentals of physical optics (electromagnetic waves)
OF 2) Understand the fundamentals of optics in linear media (isotropic and anisotropic dielectrics)
OF 3) To understand the language of optics
B - Application skills
OF 4) To be able to assemble simple optical experiments
OF 5) To be able to align an optical interferometer
OF 6) To be able to measure optical intensity (photodiodes)
OF 7) To be able to measure and control light polarization states
C - Autonomy of judgment
OF 8) To be able to evaluate the best way of performing an experimental measurement
D - Communication skills
OF 9) To know how to communicate in written reports the results the experimental work
OF 10) To know how to discuss the characteristics and functionalities of simple optical schemes
E - Ability to learn
OF 11) Being able to consult optical components datasheets
OF 12) Being able to design a of simple optical schemeanalog and digital circuits

Educational objectives

GENERAL OBJECTIVES:
The goal of the course is to study the foundations of material’s structure, providing the basis of atomic and molecular physics, with an elementary introduction to solid state physics, starting from knowledge and methods of quantum mechanics. The student, at the end of the course, will acquire basic concepts to determine energy eigenvalues ang eigenstates of atomic and molecular systems unser external fields. The developed know-how will be fundamental for the advanced condensed matter and solid state physics courses.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know foundations of atomic and molecular physics, and basics elements of solid state physics
OF 2) To understand energy spectra and eigenstates of atomic, molecular and solid state systems.
OF 3) Undesratnd principles of light-matter interaction.

B - Application skills
OF 4) Learn how to apply principles of quantum mechanics do describe atoms and molecules.
OF 5) Solve problems related to atomic and molecular spectra
OF 6) To be able to apply perturbative and variational techniques to evaluate eigenvalues and eigenstates at atoms and molecules

C - Autonomy of judgment
OF 7) To be able to apply in the future the acquired skills to the more general context of condensed matter physics

D - Communication skills
OF 8) To know how to communicate the critical steps necessary to solve elementary problems dealing with material structure

E - Ability to learn
OF 10) Have the ability to autonomously consult basic textbooks and in some cases scientific articles to expand the knowledge developed in the course

Educational objectives

GENERAL OBJECTIVES:
The objectives of this course are to provide the knowledge of the astronomical observation techniques, and of theastronomical instrumentation as well as the choice of the astronomical observables. Furthermore, the course aimsat using, and understanting the characteristics of, astrophysical instrumentation for laboratory classes andradio/optical observations. The student will understand the importance of the calibration and of the noisemitigation techniques through a series of experimental classes both in the laboratory and at the radioastronomy/optical-astronomy facilities on the roofs of the Physics department at Sapienza. Basic concepts ofastronomical optics, electronics, signal theory, cryogenics, interferometry, spectroscopics, polarimetry, will bepresented as well as the state of the art of radio, mm, sub-mm, IR, optical, UV, X, gamma instrumentation.
SPECIFIC OBJECTIVES:
A -Knowledge and understanding
OF 1) Know the fundamentals of astronomical observations
OF 2) To know the fundamentals of the functioning of astrophysical radiation detectors
OF 3) Understand the use of astrophysical radiation detection techniques
B -Application skills
OF 4) Knowing how to deduce the characteristics of an astrophysical observation
OF 5) Solve problems related to noise
OF 6) Be able to apply noise reduction techniques / methods
C -Autonomy of judgment
OF 7) Being able to evaluate the best way to perform a measurement
OF 8) Integrate the acquired knowledge in order to establish the best observational techniqueD -Communication skills
OF 9) Knowing how to communicate the results of one's work in writing in laboratory reports
OF 10) Knowing how to communicate about known and unknown problemsE -Ability to learn
OF 11) Have the ability toconsult electronic components datasheets
OF 12) Have the ability to evaluate the adequacy of an astrophysics instrument
OF 13) Be able to conceive and develop an astronomical project

Educational objectives

GENERAL OBJECTIVES:
The objectives of this course are to provide the knowledge of the astronomical observation techniques, and of theastronomical instrumentation as well as the choice of the astronomical observables. Furthermore, the course aimsat using, and understanting the characteristics of, astrophysical instrumentation for laboratory classes andradio/optical observations. The student will understand the importance of the calibration and of the noisemitigation techniques through a series of experimental classes both in the laboratory and at the radioastronomy/optical-astronomy facilities on the roofs of the Physics department at Sapienza. Basic concepts ofastronomical optics, electronics, signal theory, cryogenics, interferometry, spectroscopics, polarimetry, will bepresented as well as the state of the art of radio, mm, sub-mm, IR, optical, UV, X, gamma instrumentation.
SPECIFIC OBJECTIVES:
A -Knowledge and understanding
OF 1) Know the fundamentals of astronomical observations
OF 2) To know the fundamentals of the functioning of astrophysical radiation detectors
OF 3) Understand the use of astrophysical radiation detection techniques
B -Application skills
OF 4) Knowing how to deduce the characteristics of an astrophysical observation
OF 5) Solve problems related to noise
OF 6) Be able to apply noise reduction techniques / methods
C -Autonomy of judgment
OF 7) Being able to evaluate the best way to perform a measurement
OF 8) Integrate the acquired knowledge in order to establish the best observational techniqueD -Communication skills
OF 9) Knowing how to communicate the results of one's work in writing in laboratory reports
OF 10) Knowing how to communicate about known and unknown problemsE -Ability to learn
OF 11) Have the ability toconsult electronic components datasheets
OF 12) Have the ability to evaluate the adequacy of an astrophysics instrument
OF 13) Be able to conceive and develop an astronomical project

Educational objectives

The aim of the course is to enable students to enrich the knowledge of curricular courses with topics of their choice.

Educational objectives

The final exam consists of the presentation of a report on the activities conducted during the stage/thesis. The preparation for this exam implies skills related to the presentation of her/his work, and the capability to discuss and argue with an audience fully aware of the topics presented.

Educational objectives

General aim:
to acquire basic knowledge on linear systems, vector spaces, linear maps, symmetric bilinear forms and hermitian forms.

Specific aim
Knowledge and comprehension: successful students will acquire basic notions and results about solvability of linear systems and its geometric interpretation, matrix calculus, vector spaces and linear maps between them, with special focus on endomorphisms of vector spaces and their associate decompositions into eigenspaces.

Applied knowledge and comprehension: successful students will be able to solve linear systems with a finite number of variables, to
recognize mathematical problems that can be codified into vector spaces and linear maps and therefore to solve them;
to manipulate matrices and determine the solvability of a linear system and the invertibility of a linear map by studying its rank and by
computing the determinant of the associated matrix; moreover, he/she will be able to compute the eigenvalues of a linear endomorphism
and to determine the associated decomposition into eigenspaces.

Critical thinking abilities: in this course the student will acquire basic knowledge that will make him/her able to discover analogies between the topics treated in this course and the topics treated in following courses such as Mechanics and Vectorial Analysis.

Communication skills: ability to illustrate the content of the course in the oral exam and in the possible theoretical questions in the written test.

Learning skills: the learnings of these lectures will allow the student to access the study of the following courses of the degree program in Physics.

Educational objectives

General Targets

to get basic tools of Differential and Integral Calculus in one variable, more variables Differential Calculus, linear and some nonlinear ODE’s of first and second degree.

A - Knowledge and understanding
OF 1) Integrals in one variable, Differential Calculus in Rn, techniques of solutions to ODEs
B – Application skills
OF 2) To be able to apply analytical methods to problems of Classical Mechanics
C - Autonomy of judgment
OF 3) To be able to individually solve problems by a rigorous logical/analytic approach (stimulated in exercise sessions
D – Communication skills
OF 4) Effective interaction among students and with prof.
E - Ability to learn
OF 5) Links to concepts arising in upcoming Courses and attention to rigorous way of thinking will provide awareness in consulting books and in individual learning

Educational objectives

Laboratorio di Calcolo (Computational Laboratory) is an introductory course in computer programming and in the numerical methods used in Physics. This course takes a practical approach in teaching fundamental concepts of programming with a strong emphasis on tutorials and laboratory work and is an important vehicle for developing students’ analytical and problem-solving skills. The course aims to provide skills that will be relevant for the students’ academic career. Therefore, the main purpose of the course is not to give a detailed knowledge in whatever are the current leading programming tools on the market, but rather to teach the general principles that are at the basis of any programming language. Programming is a practical subject: the purpose of the course is that of teaching students to write (short) programs that actually work. The important skills which underlie programming are abstract ones. The ability to see patterns and to abstract from specific examples to the more general case is crucial. Being able to think logically so one can predict in advance the behaviour of a system working to a fixed set of rules is essential. These skills are developed through practice, and indeed, the course uses a problem-based learning approach. In addition the course aims at providing good working practices: self-motivation, good time management, thinking and acting rationally, learning how to interact with coworkers. At the end of the course, students will understand computational methods typically employed in physics and will be able to write simple computer programs. They will have a good knowledge of the C language, of the Linux operating system and of Python basic instructions that will be used to improve student’s skills in terms of analysis and description of algorithms needed to solve physics problems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Acquire fundamental concepts and general principles that are at the basis of any programming language
OF 2) Acquire the general principles that underlie any programming language.
OF 3) Understanding the basic architecture of a computer and its functioning.
OF 4) Understand algorithms and computing methods to solve scientific problems

…
B - Application skills
OF 5) Solve logical and/or analytical problems, as well as simple probles of general physics by developing optimal and efficient algorithms
OF 6) Write simple programs in C or Python that actually work.

C - Autonomy of judgment
OF 7) Identify general patterns from specific examples.
OF 8) To be able to integrate the knowledge acquired in order to…

D - Communication skills
OF 13) Interact and collaborate with other students in the problem-solving process through appropriate communication of ideas, insights, and knowledge

E - Ability to learn
OF 15) Have the ability to learn new algorithms for solving scientific problems.
OF 16) Have the ability to learn new programming techniques and languages.

Educational objectives

The goal is to give students the practical ability to use a modern personal computer and perform the basic operations of use (on, off, data and program management), on proprietary OS or open source.

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
OF 1) To describe the fundamental laws of mechanics and their applications to real-world situations.
OF 2) To develop problem-solving skills using an approach which describes physical phenomena by combining methods and mathematical formulae on one hand, and physics intuition on the other hand.
OF 3) To develop mathematical skills required to derive accurate numerical solutions which can be directly compared to real-world situations and measurements.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 4) To know the fundamental laws of mechanics
OF 5) To know the conservation laws in physics and their implications
OF 6) To understand the text of a physics problem
B - Application skills
OF 7) To formalise the solution of a physics problem from the mathematical point of view
OF 8) To solve a physics problem in a coherent way, both from a formal and a quantitative point of view
OF 9) To be able to evaluate the dominant effects in a physics problem
C - Autonomy of judgment
OF 10) To be able to establish whether a relation between physical quantities, or a physical law, is correct from the dimensional point of view
OF 11) To develop quantitative and analytical reasoning skills required to study, model and understand the fundamental principles of mechanics
D - Communication skills
OF 12) To be able to talk about physics using the appropriate terminology
OF 13) To know how to simplify a complex problem, by identifying its most relevant aspects.
E - Ability to learn
OF 14) To be able to consult a physics textbook

Educational objectives

The chemistry course provides a basic overview of the chemistry, structure and reactivity of chemical compounds. All topics are addressed in a simple way as this course is intended for first-year students of different scientific backgrounds. The objective is to encourage students to think and solve chemical problems, teaching general methods that can be used in different chemical contexts.
Specifically, at the end of the course, by means of theoretical and numerical lessons, the student will have a proper knowledge and understanding of basic concepts of General Chemistry. In particular, he will understand the composition, structure and properties of the different states of matter, and the laws the control their transformations. Moreover, students will be able to solve simple numerical exercises on these topics.
The final exam will be passed only if the student has an appropriate critical understanding of the subject. It will be obtained by means of
the personal study of the suggested textbooks and of the theoretical lessons, and by solving appropriate numerical exercises.
The course also aims at improving the communication skills of the student: he should be able to explain, in a simple but rigorous way, basic chemical processes, both in written and oral form, to non-experts. Moreover, the notions acquired in the course should allow him to understand
chemistry textbooks and scientific articles, as needed for his future studies.

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to provide basic notions and skills of differential and integral calculus for functions of several variables that are necessary for the understanding of the main scientific disciplines, with a special attention to the physical sciences.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the principles of differential and integral calculus for functions of several variables
OF 2) To know the theory of vector fields and linear differential forms
OF 3) To understand basic theory of ordinary differential equations

B - Application skills
OF 4) To be able to deal with problems involving scalar functions of several variables (e.g.: optimization, area and volume calculations), vector fields (e.g. work and flux calculations) and differential equations (e.g. resolution and qualitative study).

C - Autonomy of judgment
OF 5) To have essential tools for successive approach to functional analysis, functions of one complex variable, measure theory, quantum mechanics.
OF 6) To be able to autonomously solve new problems, applying mathematical tools to phenomena or processes to be encountered in University studies or subsequent working activities.

D - Communication skills
OF 7) To know how to communicate using properly mathematical language

E - Ability to learn
OF 8) To be able to deepen autonomously some arguments introduced during the course

Educational objectives

GENERAL OBJECTIVES:
The course aims for students to acquire the knowledge of the laws of thermodynamics. Students will understand how these fundamental laws apply to both ideal (ideal gases, ideal machines) and real (real gas model, real thermal machines) systems. With the laboratory experiences, students will apply the laws studied and will acquire practical knowledge on the measurement of thermodynamic quantities (temperature, heat, pressure). They will also acquire practice with the use of vacuum systems and related instrumentation.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the basics of thermodynamics.…
OF 2) To understand thermodynamic systems and their interactions with the surroundings.
OF 3) To learn the correlation between the nature and entropy.
OF 4) To understanding thermodynamics of real systems.
OF 5) To learn the transport phenomena at the molecular level.
…
B - Application skills
OF 6) To be able to deduce the relationship between the fundamental thermodynamic quantities.
OF 7) To be able to solve problems of thermodynamics of ideal and real systems.
OF 8) To be able to apply methods/techniques for the measurements of fundamental quantities.
…
C - Autonomy of judgment
OF 9) To be able to integrate the acquired knowledge in order to subsequently apply it in the more general context for heat engines.

D - Communication skills
OF 10) To know how to communicate the presentation of thermodynamic quantities with their realistic uncertainties.

E - Ability to learn
OF 11) To have the ability to consult and evaluate properly the scientific literature for advanced knowledge on the topics of the course.
OF 12) To be able to conceive and develop a project related to heat engines.

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course is to teach students the use of computers for solving some fundamental problems in physics. This is achieved by teaching students some advanced elements of the C programming language, along with several algorithms which, although simple, are widely applicable in different contexts.
At the end of the course, students will have acquired a sufficiently in-depth knowledge of the C programming language and other operational tools useful for data analysis and their graphic representation. They will have acquired the skills necessary to solve physics problems of medium difficulty with the computer and to autonomously implement algorithms of a certain complexity.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Advanced elements of C programming (dynamic allocation, struct, recursion)
OF 2) Basic and advanced algorithms for the integration of ordinary differential equations, for the generation of pseudo-random numbers, and for the study of simple stochastic processes (random walk, reticular gas and percolation)
OF 3) Understand a program written in C language
B - Application skills
OF 4) Be able to implement an algorithm in C language
OF 5) Knowing how to solve, with the use of computers, medium difficulty physics problems that are described by differential equations or by a simple stochastic process
OF 6) Being able to find errors in a program written in C language (debugging) and knowing how to correct them
OF 7) Be able to perform, with IT tools, simple data analysis (e.g. performing averages and the calculation of the error for independent measurements), and their graphical representation
C - Autonomy of judgment
OF 8) Knowing how to independently evaluate if a program written in C language correctly executes a given algorithm and if this implementation is efficient
D - Communication skills
OF 9) Knowing how to discuss critically the choices made in the implementation of a given algorithm in a program written in C language
OF 10) Knowing how to present in written form the results of the study of a physical problem carried out numerically using the computer
E - Ability to learn
OF 11) Have the ability to consult the description of a new algorithm or understand a C language program written by others

Educational objectives

GENERAL OBJECTIVES:
The course aims to cover the fundamental aspects of Lagrangian and Hamiltonian mechanics. At the end of the course, students should be able to apply the concepts learned to solve Lagrangian/Hamiltonian mechanics problems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of Lagrangian mechanics
OF 2) Know the basics of Hamiltonian mechanics
OF 3) Develop the ability to apply mathematical methods to the modeling of physical systems

B – Application capabilities
OF 4) Know how to describe a constrained mechanical system with a finite number of degrees of freedom in terms of Lagrangian variables, determining the Lagrangian function and the Euler-Lagrange equations
OF 5) Know how to describe a constrained mechanical system with a finite number of degrees of freedom in terms of Hamiltonian variables, determining the Hamiltonian function and the Hamilton equations
OF 6) Know how to study the properties of equilibrium, stability, small oscillations and the main symmetries of a system using the techniques of Lagrangian mechanics
OF 7) Know how to solve simple problems involving canonical transformations in Hamiltonian systems

C - Independence of judgment
OF 8) Be able to integrate the knowledge acquired in Lagrangian Mechanics in order to subsequently apply them in different contexts of Theoretical Physics (Quantum Mechanics, Statistical Mechanics, Field Theory, etc...)
OF 9) Be able to integrate the knowledge acquired in Hamiltonian Mechanics in order to subsequently apply them in different contexts of Theoretical Physics (Quantum Mechanics, Statistical Mechanics, Field Theory, etc...)

D – Communication skills

E - Ability to learn
OF 10) Have the ability to consult advanced textbooks in order to independently delve into some topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:

- Learning of the foundations of the classical theory of electromagnetism, starting from the experimental observations of electrical and magnetic phenomena and arriving at the complete formulation of classical electrodynamics in terms of Maxwell's equations and in terms of electrodynamic potentials. Introduction to Special Relativity and covariant formulation of Electromagnetism.

- Acquiring of the ability to solve problems in electrodynamics.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

- Demonstrate knowledge and understanding in the field of electromagnetism at post secondary instruction level, also with respect to some cutting-edge topics in modern electromagnetism and relativity, with the support of advanced textbooks.

B - Application skills

- Be able to apply the acquired knowledge in a competent and reflective way; possess adequate skills both to conceive and support arguments, and to solve problems and apply techniques and methods within the field of electromagnetism.

C - Autonomy of judgment

- Develop the ability to autonomously set up, analyze and solve problems of physics.

D - Communication skills

- Communicate ideas, problems and solutions to specialists and non-specialists.

E - Ability to learn

- Develop the skills necessary to undertake further studies with a high degree of autonomy.

Educational objectives

GENERAL OBJECTIVES:
The first objective of the class is the study of the theory of electrical circuits and most common electrical components. The second objective is to acquire the know-how of optimal use of basic electric measurements instrumentation: voltage and current generators, multimeter, oscilloscope.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the theory of DC circuits
OF 2) To know the theory of AC circuits
OF 3) To know the theory of electrical measurements

B - Application skills
OF 4) To be able to solve simple problems with DC and AC circuits
OF 5) To be able to carry out measurements of voltage, current, resistance (multimeter)
OF 6) To be able to carry out measurements of time intervals, voltages and phases (oscilloscope)
OF 7) To be able to estimate and correct for the perturbation induced by the measurement system
C - Autonomy of judgment
OF 8) To be able to evaluate the best way of performing an electrical measurement

D - Communication skills
OF 9) To know how to communicate in written reports the results of the experimental work
OF 10) To know how to discuss the characteristics and functionalities of simple electrical circuits

E - Ability to learn
OF 11) Being able to consult the manuals of the measurement instruments
OF 12) Being able to understand the datasheets of electric components

Educational objectives

To provide students with the basic linguistic skills needed to deal with written scientific communication.

Educational objectives

PART I
General goals:
The goal of the course is the study and the comprehension of advanced mathematical techniques. The student will acquire the basic concepts of complex
analysis and functional analysis and she/he will be able to apply them to the study of problems in classical (electromagnetism and continuum media) and
quantum physics. The know-how that the student acquires attending this course is indispensable for the Physics courses of the third year.

Specific goals:
Introduction to the fundamental concepts of complex analysis, i) to provide the student with a deep knowledge and understanding of these concepts, and ii) to
allow him/her to successfully apply them in various physical contexts. In particular, the student must be able to use techniques of integration in the complex
domain in all the physical
contexts in which they have applications. In order to achieve these goals, and to help the student to develop the capability i) to communicate the acquired
knowledges, and
ii) to continue the studies autonomously, we plan to involve him (her), during the theoretical lectures and exercises, through general and specific questions
related to the
subject; or through the presentation in depth of some specific subject agreed with the teacher

PART II
General goals:
The goal of the course is the study and the comprehension of advanced mathematical techniques. The student will acquire the basic concepts of complex
analysis and functional analysis and she/he will be able to apply them to the study of problems in classical (electromagnetism and continuum media) and
quantum physics. The know-how that the student acquires attending this course is indispensable for the Physics courses of the third year.

Specific goals:
Introduction to the fundamental concepts of functional analysis, i) to provide the student with a deep knowledge and understanding of these concepts, and ii) to
allow him/her to successfully apply them in various physical contexts. In particular, the student must be able to use the Fourier series, the Fourier and Laplace
transforms, and the distributions in all the physical contexts in which they have applications; in addition the student must be able to work with Hilbert spaces and
with operators on functional spaces of physical interest. In order to achieve these goals, and to help the student to develop the capability i) to communicate the
acquired knowledges, and ii) to continue the studies autonomously, we plan to involve him (her), during the theoretical lectures and exercises, through general
and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher

Educational objectives

A - Knowledge and understanding
OF 1) Understanding the physical concepts underlying quantum mechanics.
OF 2) Understanding the mathematical aspects necessary to describe quantum mechanical systems.
OF 3) Knowing the main experimental evidences that led to the crisis of classical mechanics.
OF 4) Knowing the properties of some notable systems such as the harmonic oscillator and the particle in a Coulomb field.

B - Application skills
OF 5) Knowing how to deduce the consequences and physical properties of a system governed by a quantum dynamics.
OF 6) Solving quantum mechanical problems of various kinds.
OF 7) Being able to use different mathematical methods to solve the problems.

C - Autonomy of judgment
OF 8) The student will have to learn how to evaluate the correctness of the logical reasoning used in the solution of problems and in the proofs of theorems.
OF 9) The regular assignment of exercises will encourage the habit of self-assessment.
OF 7) Being able to use different mathematical methods to solve the problems

D - Communication skills
OF 11) The acquisition of adequate skills and tools for communication will be verified during the evaluation tests. The oral and written exams require the student to express herself/himself with scientific language and to follow a rigorous logic in reasoning.

E - Ability to learn
OF 12) The work required for this course stimulates the development of a flexible mentality, useful both for more advanced scientific studies and in the context of various workplaces.

Educational objectives

GENERAL OBJECTIVES:
The first main objective of the course is to introduce the students to the fundamental concepts of Statistical Mechanics (SM). Generally speaking the students must understand how to derive the thermodynamic description of a macroscopic system from its microscopic laws. This knowledge is of obvious relevance for their background in Physics and for the more specialised courses of the next years.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) basic concepts in equilibrium SM and in probability theory
OF 2) computation rules in classical SM (microcanonical, canonical and grand canonical ensembles); equivalence between the different rules and their application to non-interacting systems;
OF 3) Basic concepts and example of interacting systems (Van Der Waals equation).
OF 4) Fundamental concepts and computation rules in Quantum SM; application to the quantum perfect gas, Bose-Einstein and Fermi-Dirac distributions;
OF 5) Thermodynamic properties of quantum bosonic and fermionic systems; high and low temperature limits; Sommerfeld expansion for a Fermionic gas; specific heat in a solid; Debye theory.
OF 6) Brief summary of quantisation of the electromagnetic radiation, black body radiation.
B - Application skills
OF 7) The second objective is to prepare the students to actively solve problems in physics where SM concepts are required. This will happen at first with problems structured with a conceptual scheme similar to the one discussed and applied during the course. However, as their preparation progresses, students are also expected to use SM concepts for solving new problems in different applications.
C - Autonomy of judgment
OF 8) The third and more ambitious objective is to teach the students to think in probabilistic and statistic terms, using concepts and methods from SM as a powerful problem solving tool, both in physics and in different fields (e.g. socio-economic systems, biological systems, medical applications)
D - Communication skills
OF 9) Besides having a clear understanding of the new acquired concepts in SM, the studend should correspondingly acquire the ability to communicate and transmit these concepts in a clear and direct way.
E - Ability to learn
OF 10) The students should become able to read and understand scientific books and articles where SM concepts are involved and should be able to deepen autonomously their knowledge in this field.

Educational objectives

GENERAL OBJECTIVES:
The course describes the basics of nuclear and subnuclear physics through the study of the main discoveries that have contributed to the modern description of particles and their interactions. Relativistic kinematics is used to analyze the production reactions and decays of particles, applying the conservation laws of quantum numbers. The nature of alpha and beta decays is described through non-relativistic mechanics. Finally, the interactions of particles in matter and the operating principles of the detectors for the measurement of energy and momentum and the identification of charged particles are discussed.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowing different types of fundamental interactions between elementary particles
OF 2) Understanding the kinematics of production and decay processes
OF 3) Knowledge of basic nuclear reactions and energy properties
OF 4) Recognize and describe the primary interactions of particles in matter

B - Application skills
OF 5) Compute kinematic properties of decay products and collisions between elementary particles, using the selection rules
OF 6) Calculate the energy lost by elementary particles passing through matter
OF 7) Calculate the probability of decay and interaction in collisions

C - Autonomy of judgment
OF 8) Ability to apply the acquired knowledge to understand the main discoveries in subnuclear physics in the twentieth century
OF 9) Understand the experimental method and the measurements made in some of the most important and famous experiments of the twentieth century

D - Communication skills
OF 10) Ability to discuss, at an elementary level, modern physics as regards the fundamental interactions of particles.

E - Ability to learn
OF 11) Ability to consult scientific articles relative to the measurements covered in the course and understand their methodology and purpose
OF 12) Ability to understand the physics processes of elementary particles treated in the Master's Degree in Physics, using the notions of kinematics and conservation laws of quantum numbers

Educational objectives

The aim of the course is to enable students to enrich the knowledge of curricular courses with topics of their choice.

Educational objectives

GENERAL OBJECTIVES:
The student will acquire knowledge of the fundamental principles and laws of Classical Optics, with regards to general phenomena, such as interference, diffraction and polarization of light. These phenomena will be also investigated in laboratory sessions by using advanced didactic set-ups. The student will learn how to use the basic principles of Optics to solve simple problems related to the knowledge acquired during the course. At the end of the course, the students will develop quantitative reasoning abilities and problem-solving skills, which represent the basis to study, model and understand light propagation and interaction with matter at a fundamental level.
Furthermore, thanks to the laboratory sessions, the student will develop practical ability to use optical set-ups as well as to convey the observations made during the experiments via laboratory reports. A direct interaction with the teacher will be also a plus during the execution of the experiments.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Understand the fundamentals of physical optics (electromagnetic waves)
OF 2) Understand the fundamentals of optics in linear media (isotropic and anisotropic dielectrics)
OF 3) To understand the language of optics
B - Application skills
OF 4) To be able to assemble simple optical experiments
OF 5) To be able to align an optical interferometer
OF 6) To be able to measure optical intensity (photodiodes)
OF 7) To be able to measure and control light polarization states
C - Autonomy of judgment
OF 8) To be able to evaluate the best way of performing an experimental measurement
D - Communication skills
OF 9) To know how to communicate in written reports the results the experimental work
OF 10) To know how to discuss the characteristics and functionalities of simple optical schemes
E - Ability to learn
OF 11) Being able to consult optical components datasheets
OF 12) Being able to design a of simple optical schemeanalog and digital circuits

Educational objectives

The aim of the course is to enable students to enrich the knowledge of curricular courses with topics of their choice.

Educational objectives

The final exam consists of the presentation of a report on the activities conducted during the stage/thesis. The preparation for this exam implies skills related to the presentation of her/his work, and the capability to discuss and argue with an audience fully aware of the topics presented.