THREE-DIMENSIONAL MODELING
Course 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
Channel 2
SANDRO DE CECCO
Lecturers' profile
Program - Frequency - Exams
Course program
A) Physical quantities:
- Measurement of a physical quantity: direct measurements and indirect measurements;
- Fundamental quantities and derived quantities.
- Dimensions of a physical quantity; systems of units of measurement.
- Random measurement uncertainties and systematic errors;
- Study of the trend of one quantity as a function of another;
- Graphs and their use; frequency histograms.
B) Statistical analysis of experimental data with classroom exercises.
- Definitions of probability. Conditional probability. Compound and total probability theorems.
Discrete random variables and probability distribution. Continuous random variables and probability density.
Characteristic parameters of a distribution function: expected value and variance.
- Some probability distribution functions: Bernoulli distribution, Poisson distribution,
uniform distribution, Gauss distribution.
- Functions of several random variables and covariance matrix (hint).
- The central limit theorem. Law of large numbers.
- Measurement of a physical quantity as a random variable; definition of measurement uncertainty through variance.
- Propagation of measurement uncertainties in indirect measurements.
- Statistical inference. Estimation of the parameters of a probability distribution function from a population sample; the arithmetic mean, the mean square deviation and their properties.
- Estimation of the parameters of a linear relationship.
- Comparison of observed and expected frequency distributions.
- Hypothesis testing. the Chi2 method.
The laboratory activity includes classical mechanics experiments including: the study of the motion of a body subjected to an elastic force, the study of the motion of a body on an inclined plane, the measurement of the acceleration of gravity with a simple pendulum, counting measurements (Geiger counter); the study of the motion of a body rotating about a fixed axis (flywheel), the torsion pendulum, fluids.
Prerequisites
Knowledge of algebra; trigonometry; basics of differential and integral calculus including: derivatives, integrals and series development of elementary functions; graphing of functions; elementary knowledge of an electronic calculator and an operating system to be able to write simple data processing programs.
Books
F.Bellini, G.D'agostini, A.Messina: "Laboratorio di Meccanica, Dispense" download on course e-learning page
C.Bini "Lezioni di Statistica per la Fisica Sperimentale", Nuova Cultura Editrice.
Frequency
Group exercises and individual practice tests (totaling 36 hours in the laboratory) are mandatory. Only one excused absence will be allowed for group practice. The absent student is still required to participate in the group report.
For the two individual laboratory tests and the statistics test, make-up days will be scheduled during the course period in case of a justified and unavoidable reason (and only in this case). There will be no ordinary individual laboratory or statistics tests in the fall and winter terms.
Exam mode
Laboratory tests have the following weight on the final grade: group tests 30%, individual tests 30%. The evaluation of the laboratory tests is maintained throughout the student's academic career and there is no make-up in the oral examination sessions.
The remaining 40% is contributed by the oral interview consisting of a theoretical part and numerical solving of problems in data analysis and probability'. The student is exempted from the latter part by taking a written test on the way.
The oral examination consists of an interview on the most relevant topics explained in the course. To pass the exam, the student/student must be able to present a topic or repeat a calculation discussed in the course. The student/student will be required to apply the methods learned in exercises or to examples and situations similar to those discussed in the course. The assessment will take into account:
- correctness and completeness of the concepts expounded;
- clarity and rigor of exposition;
- ability to develop theory analytically;
- aptitude in problem solving (method and results).
SANDRO DE CECCO
Lecturers' profile
Program - Frequency - Exams
Course program
A) Physical quantities:
- Measurement of a physical quantity: direct measurements and indirect measurements;
- Fundamental quantities and derived quantities.
- Dimensions of a physical quantity; systems of units of measurement.
- Random measurement uncertainties and systematic errors;
- Study of the trend of one quantity as a function of another;
- Graphs and their use; frequency histograms.
B) Statistical analysis of experimental data with classroom exercises.
- Definitions of probability. Conditional probability. Compound and total probability theorems.
Discrete random variables and probability distribution. Continuous random variables and probability density.
Characteristic parameters of a distribution function: expected value and variance.
- Some probability distribution functions: Bernoulli distribution, Poisson distribution,
uniform distribution, Gauss distribution.
- Functions of several random variables and covariance matrix (hint).
- The central limit theorem. Law of large numbers.
- Measurement of a physical quantity as a random variable; definition of measurement uncertainty through variance.
- Propagation of measurement uncertainties in indirect measurements.
- Statistical inference. Estimation of the parameters of a probability distribution function from a population sample; the arithmetic mean, the mean square deviation and their properties.
- Estimation of the parameters of a linear relationship.
- Comparison of observed and expected frequency distributions.
- Hypothesis testing. the Chi2 method.
The laboratory activity includes classical mechanics experiments including: the study of the motion of a body subjected to an elastic force, the study of the motion of a body on an inclined plane, the measurement of the acceleration of gravity with a simple pendulum, counting measurements (Geiger counter); the study of the motion of a body rotating about a fixed axis (flywheel), the torsion pendulum, fluids.
Prerequisites
Knowledge of algebra; trigonometry; basics of differential and integral calculus including: derivatives, integrals and series development of elementary functions; graphing of functions; elementary knowledge of an electronic calculator and an operating system to be able to write simple data processing programs.
Books
F.Bellini, G.D'agostini, A.Messina: "Laboratorio di Meccanica, Dispense" download on course e-learning page
C.Bini "Lezioni di Statistica per la Fisica Sperimentale", Nuova Cultura Editrice.
Frequency
Group exercises and individual practice tests (totaling 36 hours in the laboratory) are mandatory. Only one excused absence will be allowed for group practice. The absent student is still required to participate in the group report.
For the two individual laboratory tests and the statistics test, make-up days will be scheduled during the course period in case of a justified and unavoidable reason (and only in this case). There will be no ordinary individual laboratory or statistics tests in the fall and winter terms.
Exam mode
Laboratory tests have the following weight on the final grade: group tests 30%, individual tests 30%. The evaluation of the laboratory tests is maintained throughout the student's academic career and there is no make-up in the oral examination sessions.
The remaining 40% is contributed by the oral interview consisting of a theoretical part and numerical solving of problems in data analysis and probability'. The student is exempted from the latter part by taking a written test on the way.
The oral examination consists of an interview on the most relevant topics explained in the course. To pass the exam, the student/student must be able to present a topic or repeat a calculation discussed in the course. The student/student will be required to apply the methods learned in exercises or to examples and situations similar to those discussed in the course. The assessment will take into account:
- correctness and completeness of the concepts expounded;
- clarity and rigor of exposition;
- ability to develop theory analytically;
- aptitude in problem solving (method and results).
Channel 3
LEONETTA BALDASSARRE
Lecturers' profile
Program - Frequency - Exams
Course program
A) Physical quantities:
- Measurement of a physical quantity: direct measures and indirect measures;
- Fundamental quantities and derived quantities.
- Dimensions of a physical quantity; units of measurement systems.
- random uncertainties and systematic errors;
- Study of the dependance of a quantity according to another;
- plots and their use; frequency histograms.
- Design of simple mechanics experiments
B) Statistical analysis of experimental data with exercises in the classroom
- Definitions of probability. Conditional probability. Composite probability theorems and total probability.
Discrete random variables and probability distribution. Continuous random variables and probability density.
Parameters of a probability distribution function: expected value and variance.
- Some probability distribution functions: Bernoulli distribution, Poisson distribution,
uniform distribution, distribution of Gauss.
- Functions of multiple random variables and covariance matrix.
- The central limit theorem. Law of large numbers.
- Measurement of a physical quantity as a random variable; definition of measurement uncertainty through variance.
- Propagation of uncertainties in indirect measures.
- Statistical inference. Estimation of the parameters of a probability distribution function
starting from a sample of the population; the arithmetic mean, the standard deviation and their properties.
- Estimation of the parameters of a linear relation.
- Comparison between observed and predicted frequency distributions.
- Hypothesis testing. the Chi2 method.
The laboratory activity includes experiments of classical mechanics including: the study of motion of a body subjected to an elastic force, the study of the motion of a body on a sloping plane, the measurement of the gravity acceleration with a simple pendulum, counting measurements (Geiger counter); the study of the motion of a rotating body around a fixed axis (flywheel), the torsion pendulum, the fluids.
Prerequisites
Knowledge of algebra; of trigonometry; of the bases of differential and integral calculus including: derivatives, integrals and series expansion of elementary functions; graphical representation of functions; basic knowledge of the computer and an operating system to write simple data processing programs.
Books
Dispense del corso messe a disposizione degli studenti.
C.Bini "Lezioni di Statistica per la Fisica Sperimentale", Nuova Cultura Editrice.
J.R. Taylor “Introduzione all’analisi statistica degli errori”, Zanichelli
P. Fornasini “The Uncertainty in Physical Measurements: An Introduction to Data Analysis in the Physics Laboratory”, Springer
Frequency
The course is divided into lectures and classroom exercises and practical laboratory experiences both in groups and individually which include a written work. As far as practical laboratory experiences are concerned, attendance is compulsory, attendance at frontal lessons is recommended.
Exam mode
The laboratory tests (both group and individual) will account for 50% of the final mark. The evaluation of the laboratory tests is maintained throughout the student's academic career and there is no recovery in the oral exam sessions.
The remaining 50% is contributed by the oral interview articulated on a theoretical and design part of simple experiments and on the numerical resolution of data and probability analysis problems. The student is exempt from the latter part by taking a written test in progress.
LEONETTA BALDASSARRE
Lecturers' profile
Program - Frequency - Exams
Course program
A) Physical quantities:
- Measurement of a physical quantity: direct measures and indirect measures;
- Fundamental quantities and derived quantities.
- Dimensions of a physical quantity; units of measurement systems.
- random uncertainties and systematic errors;
- Study of the dependance of a quantity according to another;
- plots and their use; frequency histograms.
- Design of simple mechanics experiments
B) Statistical analysis of experimental data with exercises in the classroom
- Definitions of probability. Conditional probability. Composite probability theorems and total probability.
Discrete random variables and probability distribution. Continuous random variables and probability density.
Parameters of a probability distribution function: expected value and variance.
- Some probability distribution functions: Bernoulli distribution, Poisson distribution,
uniform distribution, distribution of Gauss.
- Functions of multiple random variables and covariance matrix.
- The central limit theorem. Law of large numbers.
- Measurement of a physical quantity as a random variable; definition of measurement uncertainty through variance.
- Propagation of uncertainties in indirect measures.
- Statistical inference. Estimation of the parameters of a probability distribution function
starting from a sample of the population; the arithmetic mean, the standard deviation and their properties.
- Estimation of the parameters of a linear relation.
- Comparison between observed and predicted frequency distributions.
- Hypothesis testing. the Chi2 method.
The laboratory activity includes experiments of classical mechanics including: the study of motion of a body subjected to an elastic force, the study of the motion of a body on a sloping plane, the measurement of the gravity acceleration with a simple pendulum, counting measurements (Geiger counter); the study of the motion of a rotating body around a fixed axis (flywheel), the torsion pendulum, the fluids.
Prerequisites
Knowledge of algebra; of trigonometry; of the bases of differential and integral calculus including: derivatives, integrals and series expansion of elementary functions; graphical representation of functions; basic knowledge of the computer and an operating system to write simple data processing programs.
Books
Dispense del corso messe a disposizione degli studenti.
C.Bini "Lezioni di Statistica per la Fisica Sperimentale", Nuova Cultura Editrice.
J.R. Taylor “Introduzione all’analisi statistica degli errori”, Zanichelli
P. Fornasini “The Uncertainty in Physical Measurements: An Introduction to Data Analysis in the Physics Laboratory”, Springer
Frequency
The course is divided into lectures and classroom exercises and practical laboratory experiences both in groups and individually which include a written work. As far as practical laboratory experiences are concerned, attendance is compulsory, attendance at frontal lessons is recommended.
Exam mode
The laboratory tests (both group and individual) will account for 50% of the final mark. The evaluation of the laboratory tests is maintained throughout the student's academic career and there is no recovery in the oral exam sessions.
The remaining 50% is contributed by the oral interview articulated on a theoretical and design part of simple experiments and on the numerical resolution of data and probability analysis problems. The student is exempt from the latter part by taking a written test in progress.
- Academic year2025/2026
- CoursePhysics
- CurriculumAstrofisica
- Year1st year
- Semester1st semester
- SSDFIS/01
- CFU3