Astrophysics and Cosmology

Educational objectives

GENERAL OBJECTIVES:
The course aims to describe the basics of optics for application of sky observations. At the end of the course, students will gain a deep knowledge of the impact of aberrations and diffraction in the final performance of a telescope by a quantitative evaluation. Students will be able to put into practice what they have learned during the course by working in teams by using an optical design and optimization commercial program.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know and to strengthen the basics of geometrical, physical and gaussian optics.
OF 2) To understand how to recover and to quantify the defects present in telescope’s images and how to treat them.
OF 3) To know the main figures of merit to compare and to evaluate between them different instruments.

B - Application skills
OF 4) To be able to apply what has been acquired by drawing, optimising and analysing the performance of a chosen telescope with the academic licence of one of the most used optics code.
OF 5) To be able to work in a team by sharing the activities, search of data and analysis.

D - Communication skills
OF 7) To know how to communicate the main logical steps of their study and how it has been faced by reporting to the other students the results.

E - Ability to learn
OF 8) Have the ability to consult web sites and papers to integrate what has been learned during the course and to recover all the necessary information to study an optical instrument.
OF 9) Have the ability to evaluate autonomously the performane of one specific optical instrument.

Educational objectives

GENERAL OBJECTIVES::
Providing a knowledge of astrophysical problems connected to the study of the gravitational
potential. Such knowledge will leads the students to understand the calculation of a density profile
starting from the gravitational potential and viceversa. Particular attention will be addressed to
calculation of gravitational potential of a generic distribution of matter by a development in series
of Legendre Polynomials.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of homogeneous spheroids
OF 2) To understand the procedures underlying the calculation of the gravitational potential of any
matter distribution by development in spherical harmonics.
B - Application skills
OF 3) To be able to calculate a development in spherical harmonics.
C - Autonomy of judgment
OF 4) To be able to integrate the knowledge acquired in order to apply them in the more general
context connected with gravitational waves and cosmology
D - Communication skills
E - Ability to learn
OF 5) Have the ability to consult scientific articles in order to independently investigate some topics
introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to deepen the knowledge of theoretical aspects of the theory of gravity and of its most important applications in astrophysics: phenomenology of gravitational wave sources, neutron
stars and black hole structure and properties.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the quadrupole formalism and to understand how gravitational radiation reaction affects the evolution of a compact binary system and of a rotating compact star
OF 2) To understand which quantities can be measured using the detection of gravitational waves
OF 3) To know the final stages of stellar evolution as a function of the mass, which is the structure of a whith dwarf and how can it be determined. To understand the concept of critical mass.
OF 4) To know how the equations of Thermodynamics have to be modified in General Relativity.
OF 5) To know how the structure of a neutron star can be determined using the theory of General Relativity
OF 6) To understand the complex phenomenology associated to the motion of bodies and light around a rotating black hole, and some of the astrophysical phenomena involved in these processes.
OF 7) To know how the Einstein equations can be derived using a variational approach.
OF 8) To know how to derive the geodesic equations for a Kerr black hole, discuss their properties in the equatorial plane, both for massive and massless particles.
OF 9) To understand the process of extraction of energy by a rotating black hole
(Penrose's process).

B - Application skills
OF 10) To be able to apply the quadrupole formalism to determine the gravitational waveforms emitted by source in the regime of weak field and slow motion. In particular, to be able to compute the gravitational waveforms emitted by binary systems formed by black holes and neutron stars, and by rotating neutron stars.
OF 11) To be able to compute, for assigned equations of state of nuclear matter, the inner structure of a neutron star, by integrating Einstein's equations, finding the mass and radius of the star.
OF 12) To be able to discuss the mass-radius or mass-central density diagrams for a star, identifying the instability regions.
…
C - Autonomy of judgment
OF 13) To be able to integrate the knowledge acquired in advanced Theoretical Physics courses, such as Quantum Gravity, Alternative Theories of Gravity, String Theory
OF 14) To be able to integrate the knowledge acquired in advanced Relativistic Astrophysics courses

D - Communication skills

E - Ability to learn
OF 15) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
OF 1) To know the observational foundations of standard cosmological model
OF 2) To know the observable predictions of possible deviations from the standard cosmological
model
OF 3) To develop a proper language to discuss topics of modern observational cosmology and the
definitions of related observable quantities.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 4) To know the fundamental laws of cosmology and develop the language needed to illustrate
them
OF 5) To know how physical quantities associated to cosmology are correlated to directly
measurable quantities
OF 6) To understand the meaning of a report on comsological constraints extracted from combined
observations of different cosmological probes
B - Application skills
OF 7) To plan a cosmological measurement as function of the basic observational and instrumental
parameters involved (e.g. resolution, noise, depth and volume of a survey)
OF 8) To be able to comparatively assess the quality and the effectiveness of different datasets or
strategies in constraining specific cosmological parameters
C - Autonomy of judgment
OF 9) To be able to evaluate the consistency of cosmological results extracted from independent
observations
OF 10) To critically assess and design strategies for systematics control and mitigation in
cosmological measurements
D - Communication skills
OF 11) To be able to clearly and effectively present a comological measurement, from the science
case to the description of the observing strategy, down to the discussion of the expected or available
results
E - Ability to learn
OF 12) To be able to consult an advanced cosmology textbook or a published article on a specific
topic in the field

Educational objectives

GENERAL OBJECTIVES: The course aims to teach the student mainly the theory of structures formation, both in the early stages of linear evolution and in the most advanced phases. At the same time, statistical methods will be analyzed to compare theoretical predictions with observational data. Finally, the student will learn the main elements of gravitational lensing, both the theoretical aspects and its use in astrophysics and cosmology

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the equations that regulate the growth of density perturbations in different cosmological scenarios
OF 2) To understand the role of the radiative, baryonic and dark matter components in the formation of cosmic structures
OF 3) To know the statistical properties of Gaussian stochastic fields and in particular those of the perturbation power spectrum
OF 4) To know the spherical collapse model and the role of numerical simulations in cosmology
OF 5) To know the statistical methods used in the analysis of collapsed objects
OF 6) To know the equations that determine the deflection of light by massive objects, in particular those concerning the formation of multiple images and the distortion of background sources
…
B - Application skills
OF 7) To be able to deduce the properties of the large-scale structure of the Universe as a function of the different dynamic components and different types of primordial spectrum
OF 8) To be able to apply statistical methods to data analysis of different cosmological probes
OF 9) To be able to deduce the properties of collapsed structures from those of the density field in linear regime using the Press-Schechter formalism
OF 10) To be able to apply the lensing equations in the case of the main astrophysical and cosmological applications

C - Autonomy of judgment
OF 11) To be able to integrate the concepts acquired in order to apply them in the more general context of cosmology and extra-galactic astrophysics

D - Communication skills
OF 12) To know how to communicate concepts and ideas in the cosmology field with an appropriate mathematical language and formalism

E - Ability to learn
OF 13) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course

Educational objectives

GENERAL OBJECTIVES:
Providing a knowledge of astrophysical problems connected to equilibrium and stability of selfgravitating systems. Knowledge of basic statistical mechanics forstudying distribution functions to apply to ravitational equilibrium models. Analysis of formation and dynamical evolution of some astrophysical systems and calculation of equilibrium configurations with particular attention to stability problem in dynamic and thermodynamic regime. Analysis of gravothermal catastrophe by Lynden-Bell and Wood model and relationship with evolution of globular clusters.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of a collisional system.
OF 2) To understand the mechanisms underlying the formation and evolution of some astrophysical systems.
OF 3) Understanding the mechanisms connected with the phenomenon of the gravothermal catastrophe.

B - Application skills
OF 4) To be able to calculate the equilibrium configurations of a self-gravitating system.

C - Autonomy of judgment
OF 5) To be able to integrate the knowledge acquired in order to apply them in the more general context linked to the equilibrium and stability of stars and star clusters.

D - Communication skills

E - Ability to learn
OF 6) Have the ability to consult scientific articles in order to independently investigate some topics introduced during the course.

Educational objectives

A - Knowledge and understanding
OF 1) Starting from a general analysis of the chemical composition present in the solar system, the course will show how and where the various nuclear species have been synthesized over the lifetime of the Universe.
B - Application skills
OF 2) The student will acquire the ability to interpret correctly the observed trends of the various nuclear species as a function of the metallicity (age) as well as understand which are the current problems the community is facing to solve still puzzling abundances, like those of the r process nuclei
OF 3) The student will acquire the knowledge necessary to follow numerically the evolution of a large number of nuclear species.
C - Autonomy of judgment
OF 4) The student will be able to read professional papers in the field of the chemical evolution of the universe as well as follow seminars in the field.
D - Communication skills
OF 5) Discussion about different topics will be encouraged during the course, so that the student will learn to express his/her ideas and to discuss with others different aspects of the chemical evolution of the universe
E - Ability to learn
OF 6) The student will be asked to critically read scientific papers on the subject
OF 7) At the end of the course the student will be able to develop a personal project aimed to understand the production site of any nucleus

Educational objectives

GENERAL OBJECTIVES:
The course is aimed at the study of high energy cosmic sources (neutron stars and black holes in particular), their extreme astrophysical environments and their electromagnetic and gravitational emission mechanisms. The course includes cutting edge research topics in this field, descriptions of instrumentation and observing techniques. Students acquire skills in the physics of the sources, in their identification in relation to the emission processes, in carrying out approximate calculations and in the study and understanding of original research papers. Through the preparation and presentation of a short essay the students enhance their critical and communication skills.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowing the basic physics behind compact objects (white dwarfs, neutron stars and black holes), their energy release mechanisms and their production of electromagnetic and gravitational radiation.
OF 2) Knowing the different classes of high-energy sources and the models interpreting their properties.
OF 3) Understanding open problems in this field of research.
B - Application skills
OF 4) Being able to carry out estimates and calculations in high energy astrophysics.
C - Autonomy of judgment
OF 5) Developing critical skills in the comparison between observations and the theory and models interpreting them.
D - Communication skills
OF 6) Being able to prepare and present an original work, a short essay, on a subject related to the topics of the course.
E - Ability to learn
OF 7) Being able to carry out bibliographic searches, to independently study books and original research papers to deepen the understanding of the topics covered by the course.

Educational objectives

GENERAL OBJECTIVES:
This module provides an introduction to the topics of detection and characterisation of planets orbiting stars other than the Sun. Current theories of planetary formation and evolution are also reviewed. Until 20 years ago, planets of our Solar System were the only known bodies orbiting a star. Today we know that on average every star in the Galaxy has at least one planet. Exoplanets present a diversity in their physical parameters that it is not observed in the Solar System. This present new challenges to modern Astrophysics in order to answer questions about planet formation and evolution, and about the uniqueness of our Solar System in the Galaxy.
This module is for those students interested in acquiring an understanding of the field through the knowledge of observational and data analysis techniques used, the interpretation of the experimental evidences, and by reviewing current theories of planet formation and evolution.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To introduce the theoretical concepts of planet formation and evolution
OF 2) To describe our Solar System as a reference case
OF 3) To discuss current research in exoplanetary science
OF 4) To describe the main challenges arising from exoplanetary observations
OF 5) To introduce observational and statistical methods applied to the detection of exoplanets and remote sensing of their atmospheres
OF 6) To describe the current and future astronomical facilities for the detection and characterisation of the exoplanet population in the Solar System neighborhood

B - Application skills
OF 7) Ability to understand and apply the most common data and scientific analysis techniques used in the field
OF 8) Ability to understand and critically evaluate scientific literature
C - Autonomy of judgment
OF 9) To be able to integrate the knowledge acquired in order to apply them in the more general context of planetary sciences.
D - Communication skills
OF 10) To be able to review scientific literature to peers
E - Ability to learn
OF 11) Ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES
The course aims to describe the formation and evolution of galaxies in the more general context of the standard cosmological model for structure formation. At the end of the course, students will gain a deep knowledge of the physical processes governing properties of galaxies, active galactic nuclei, intergalactic medium, and their evolution with redshift.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamental equations of structure formation in the non-linear regime
OF 2) To understand the physical processes that govern gas cooling and star formation
OF 3) To know the properties of the interstellar and intergalactic medium
OF 4) To know the properties of active galactic nuclei and their relation with their host galaxy

B - Application skills
OF 4) To deduce the evolutionary behavior of a galaxy from the knowledge of the physical laws that determine its evolution

C - Autonomy of judgment
OF 5) To be able to integrate the knowledge acquired in order to apply them in the more general context of the evolution of cosmic structures

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

GENERAL OBJECTIVES:
The course aims to describe the basics of optics for application of sky observations. At the end of the course, students will gain a deep knowledge of the impact of aberrations and diffraction in the final performance of a telescope by a quantitative evaluation. Students will be able to put into practice what they have learned during the course by working in teams by using an optical design and optimization commercial program.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know and to strengthen the basics of geometrical, physical and gaussian optics.
OF 2) To understand how to recover and to quantify the defects present in telescope’s images and how to treat them.
OF 3) To know the main figures of merit to compare and to evaluate between them different instruments.

B - Application skills
OF 4) To be able to apply what has been acquired by drawing, optimising and analysing the performance of a chosen telescope with the academic licence of one of the most used optics code.
OF 5) To be able to work in a team by sharing the activities, search of data and analysis.

D - Communication skills
OF 7) To know how to communicate the main logical steps of their study and how it has been faced by reporting to the other students the results.

E - Ability to learn
OF 8) Have the ability to consult web sites and papers to integrate what has been learned during the course and to recover all the necessary information to study an optical instrument.
OF 9) Have the ability to evaluate autonomously the performane of one specific optical instrument.

Educational objectives

GENERAL OBJECTIVES:
OF 1) To know the observational foundations of standard cosmological model
OF 2) To know the observable predictions of possible deviations from the standard cosmological
model
OF 3) To develop a proper language to discuss topics of modern observational cosmology and the
definitions of related observable quantities.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 4) To know the fundamental laws of cosmology and develop the language needed to illustrate
them
OF 5) To know how physical quantities associated to cosmology are correlated to directly
measurable quantities
OF 6) To understand the meaning of a report on comsological constraints extracted from combined
observations of different cosmological probes
B - Application skills
OF 7) To plan a cosmological measurement as function of the basic observational and instrumental
parameters involved (e.g. resolution, noise, depth and volume of a survey)
OF 8) To be able to comparatively assess the quality and the effectiveness of different datasets or
strategies in constraining specific cosmological parameters
C - Autonomy of judgment
OF 9) To be able to evaluate the consistency of cosmological results extracted from independent
observations
OF 10) To critically assess and design strategies for systematics control and mitigation in
cosmological measurements
D - Communication skills
OF 11) To be able to clearly and effectively present a comological measurement, from the science
case to the description of the observing strategy, down to the discussion of the expected or available
results
E - Ability to learn
OF 12) To be able to consult an advanced cosmology textbook or a published article on a specific
topic in the field

Educational objectives

GENERAL OBJECTIVES: The course aims to teach the student mainly the theory of structures formation, both in the early stages of linear evolution and in the most advanced phases. At the same time, statistical methods will be analyzed to compare theoretical predictions with observational data. Finally, the student will learn the main elements of gravitational lensing, both the theoretical aspects and its use in astrophysics and cosmology

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the equations that regulate the growth of density perturbations in different cosmological scenarios
OF 2) To understand the role of the radiative, baryonic and dark matter components in the formation of cosmic structures
OF 3) To know the statistical properties of Gaussian stochastic fields and in particular those of the perturbation power spectrum
OF 4) To know the spherical collapse model and the role of numerical simulations in cosmology
OF 5) To know the statistical methods used in the analysis of collapsed objects
OF 6) To know the equations that determine the deflection of light by massive objects, in particular those concerning the formation of multiple images and the distortion of background sources
…
B - Application skills
OF 7) To be able to deduce the properties of the large-scale structure of the Universe as a function of the different dynamic components and different types of primordial spectrum
OF 8) To be able to apply statistical methods to data analysis of different cosmological probes
OF 9) To be able to deduce the properties of collapsed structures from those of the density field in linear regime using the Press-Schechter formalism
OF 10) To be able to apply the lensing equations in the case of the main astrophysical and cosmological applications

C - Autonomy of judgment
OF 11) To be able to integrate the concepts acquired in order to apply them in the more general context of cosmology and extra-galactic astrophysics

D - Communication skills
OF 12) To know how to communicate concepts and ideas in the cosmology field with an appropriate mathematical language and formalism

E - Ability to learn
OF 13) 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) Knowledge of the features of cosmic rays
OF 2) Knowledge of the nature and properties of the elementary particles
OF 3) Knowledge of the nature and features of collisons
OF 4) Knowledge of the trasport equations of primary and secondary cosmic rays in the
atmosphere and the development of showers
OF 5) Understand the differential flux and mass composition of the primary cosmic rays
OF 6) Knowledge of the problem of the ultra high energy cosmic rays
OF 7) Knowledge of the the first and second order Fermi acceleration mechanism
B – Application skills
OF 8) Be able to deduce the basic issues of astroparticle physics starting by using the
observational techniques
OF 9) Be able to apply the propagation of ultra high energy particles such as protons, photons,
neeutrinos and heavy nuclei
OF 10) Be able to apply the first and second order Fermi acceleration mechanism
OF 11) Be able to deduce the limits of the observational techniques in use in the different
esperiments
C - Autonomy of judgment
OF 12) Be able to evaluate the nature of the different interacting particles in a specif process
OF 13) Be able to evaluate the observational methodologies for the different experiments
OF 14) Be able to evaluate every aspect of the system
OF 15) Be able to suggest the techniques to perform a scientific evaluation of the system
D - Communication skills
OF 16) Know how to describe the nature of physical processes to workers without scientific
training
OF 17) Know how to communicate physical techniques for a complete study of the system
E - Ability to learn
OF 18) Have the ability to consult scientific literature and physical methods
OF 19) Have the ability to evaluate technical descriptions for specific physical processes

Educational objectives

A - Knowledge and understanding
OF 1) Starting from the experimental bases of gravitation, and the theoretical implications, the course focusses on gravitational wave detection. Two interlaces aspects will be illustrated, the experimental apparuses and data analysis technicques.
OF 2) This will give students the necessary preparation for a rigorous application of the acquired notions, not only for the topics inherent to the course, but for the broadest and more general field of experimental physics of fundamental interactions.
B - Application skills
OF 3) The student will be able to correctly interpret the experimental issues and the avancement of the apparatuses.
OF 4) The student will be able to apply techniques/metods of data analysis
C - Autonomy of judgment
OF 5) Thanks to the lesson attendance, and the persistent interaction with the lecturer, the student will develop an adequate autonomy of judgment and will critically analyze the acquired information.
D - Communication skills
OF 6) The acquisition of adequate skills and tools for communication will be verified both during the
lessons and during the final exam, contributing to the development of clear communication skills by the student.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve a broad range of data analysis issues.
OF 8) Ther student will be able to conceive and develop an experimental/theoretical project,
starting from the data acquisition, through the analysis of the collected data and outlining some conclusions via the related post-processing.

Educational objectives

GENERAL OBJECTIVES:
The course aims at studying the use of space instrumentation for astrophysical measurements. It focuses on the space environment, its adavantages and disadvantages for astrophysical measurements, the characteristics of space vectors, space missions and instrumentation for the payloads. Finally studies the differnet phases and the development of a space mission for astrophysics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know advntages and disadvantages of the space environment for astrophysical use.
OF 2) To know the main classes of space vectors and their capabilities for astrophysical use.
OF 3) To know the theory of orbits and their perturbations.
OF 4) To know methods and instruments for attitude contro and space cryogenic and their use to optimize the performance of astronomical instrumentation in space.
OF 5) To know the generalities of space payloads, the design methods and the phases of a space program.
B - Application skills
OF 6) To be able to evaluate the best vector, orbit and space mission for a given space astrophysics measurement.
OF 7) To be able to program the development of a space mission for a given space astrophysics measurement.
C - Autonomy of judgment
OF 8) To be able to decide if a giv en astrophysical measurement has to be carried out from space.
OF 9) To be able to evaluate the best way to carry out a space-based astrophysics measurement.
D - Communication skills
OF 10) To be able to describe a space-based astrophysics project.
OF 11) To be able to describe the characteristics and functions of scientific space instrumentation.
E - Ability to learn
OF 12) To be able to understand the characteristics of space systems.

Educational objectives

GENERAL OBJECTIVES:
Providing a knowledge of astrophysical problems connected to equilibrium and stability of selfgravitating systems. Knowledge of basic statistical mechanics forstudying distribution functions to apply to ravitational equilibrium models. Analysis of formation and dynamical evolution of some astrophysical systems and calculation of equilibrium configurations with particular attention to stability problem in dynamic and thermodynamic regime. Analysis of gravothermal catastrophe by Lynden-Bell and Wood model and relationship with evolution of globular clusters.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of a collisional system.
OF 2) To understand the mechanisms underlying the formation and evolution of some astrophysical systems.
OF 3) Understanding the mechanisms connected with the phenomenon of the gravothermal catastrophe.

B - Application skills
OF 4) To be able to calculate the equilibrium configurations of a self-gravitating system.

C - Autonomy of judgment
OF 5) To be able to integrate the knowledge acquired in order to apply them in the more general context linked to the equilibrium and stability of stars and star clusters.

D - Communication skills

E - Ability to learn
OF 6) Have the ability to consult scientific articles in order to independently investigate some topics introduced during the course.

Educational objectives

A - Knowledge and understanding
OF 1) Starting from a general analysis of the chemical composition present in the solar system, the course will show how and where the various nuclear species have been synthesized over the lifetime of the Universe.
B - Application skills
OF 2) The student will acquire the ability to interpret correctly the observed trends of the various nuclear species as a function of the metallicity (age) as well as understand which are the current problems the community is facing to solve still puzzling abundances, like those of the r process nuclei
OF 3) The student will acquire the knowledge necessary to follow numerically the evolution of a large number of nuclear species.
C - Autonomy of judgment
OF 4) The student will be able to read professional papers in the field of the chemical evolution of the universe as well as follow seminars in the field.
D - Communication skills
OF 5) Discussion about different topics will be encouraged during the course, so that the student will learn to express his/her ideas and to discuss with others different aspects of the chemical evolution of the universe
E - Ability to learn
OF 6) The student will be asked to critically read scientific papers on the subject
OF 7) At the end of the course the student will be able to develop a personal project aimed to understand the production site of any nucleus

Educational objectives

GENERAL OBJECTIVES:
The course aims to describe the basics of optics for application of sky observations. At the end of the course, students will gain a deep knowledge of the impact of aberrations and diffraction in the final performance of a telescope by a quantitative evaluation. Students will be able to put into practice what they have learned during the course by working in teams by using an optical design and optimization commercial program.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know and to strengthen the basics of geometrical, physical and gaussian optics.
OF 2) To understand how to recover and to quantify the defects present in telescope’s images and how to treat them.
OF 3) To know the main figures of merit to compare and to evaluate between them different instruments.

B - Application skills
OF 4) To be able to apply what has been acquired by drawing, optimising and analysing the performance of a chosen telescope with the academic licence of one of the most used optics code.
OF 5) To be able to work in a team by sharing the activities, search of data and analysis.

D - Communication skills
OF 7) To know how to communicate the main logical steps of their study and how it has been faced by reporting to the other students the results.

E - Ability to learn
OF 8) Have the ability to consult web sites and papers to integrate what has been learned during the course and to recover all the necessary information to study an optical instrument.
OF 9) Have the ability to evaluate autonomously the performane of one specific optical instrument.

Educational objectives

GENERAL OBJECTIVES::
Providing a knowledge of astrophysical problems connected to the study of the gravitational
potential. Such knowledge will leads the students to understand the calculation of a density profile
starting from the gravitational potential and viceversa. Particular attention will be addressed to
calculation of gravitational potential of a generic distribution of matter by a development in series
of Legendre Polynomials.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of homogeneous spheroids
OF 2) To understand the procedures underlying the calculation of the gravitational potential of any
matter distribution by development in spherical harmonics.
B - Application skills
OF 3) To be able to calculate a development in spherical harmonics.
C - Autonomy of judgment
OF 4) To be able to integrate the knowledge acquired in order to apply them in the more general
context connected with gravitational waves and cosmology
D - Communication skills
E - Ability to learn
OF 5) Have the ability to consult scientific articles in order to independently investigate some topics
introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course aims at studying the use of space instrumentation for astrophysical measurements. It focuses on the space environment, its adavantages and disadvantages for astrophysical measurements, the characteristics of space vectors, space missions and instrumentation for the payloads. Finally studies the differnet phases and the development of a space mission for astrophysics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know advntages and disadvantages of the space environment for astrophysical use.
OF 2) To know the main classes of space vectors and their capabilities for astrophysical use.
OF 3) To know the theory of orbits and their perturbations.
OF 4) To know methods and instruments for attitude contro and space cryogenic and their use to optimize the performance of astronomical instrumentation in space.
OF 5) To know the generalities of space payloads, the design methods and the phases of a space program.
B - Application skills
OF 6) To be able to evaluate the best vector, orbit and space mission for a given space astrophysics measurement.
OF 7) To be able to program the development of a space mission for a given space astrophysics measurement.
C - Autonomy of judgment
OF 8) To be able to decide if a giv en astrophysical measurement has to be carried out from space.
OF 9) To be able to evaluate the best way to carry out a space-based astrophysics measurement.
D - Communication skills
OF 10) To be able to describe a space-based astrophysics project.
OF 11) To be able to describe the characteristics and functions of scientific space instrumentation.
E - Ability to learn
OF 12) To be able to understand the characteristics of space systems.

Educational objectives

This course is focused on the most important
techniques adopted in order to solve system of ordinary differential equations
that describe the physical processes at the base of most of the astrophysical
systems. The students, continuosly followed by the professor, have the
opportunity to develope, by themselves, numerical codes on C++ in
order to test one, or more, numerical schemes described during the lectures.