Formalization of Physics Problems
A.Y. 2026/2027
Learning objectives
The course aims to provide students with fundamental knowledge of classical physics, focusing particularly on mechanics, rigid body dynamics, and elements of dimensional and statistical analysis. It is designed to develop analytical skills, mathematical modelling, and problem-solving abilities using methods typical of physics, with applications relevant to the field of computer science, such as numerical simulation and game physics. The course also seeks to encourage a critical approach to solving complex problems and the ability to integrate theoretical and practical knowledge.
Expected learning outcomes
Upon completion of the course, students will be able to understand the fundamental principles of classical physics and apply mathematical tools to solve physical, including complex, problems. They will be able to tackle Fermi-type problems, develop numerical models, and connect physics to computer science applications such as simulation and game physics, integrating both theoretical and practical knowledge in the analysis of physical phenomena.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Fermi problems and the physical approach to problem solving.
Mathematical background: vectors, derivatives, integrals, ordinary differential equations (ODEs).
Kinematics of the material point: basic definitions, velocity, acceleration, Galilean relativity. Basic motions (uniform, uniformly accelerated, uniform circular motion).
Dynamics of the material point: Newton's laws, free fall, projectile motion, harmonic oscillator, inclined plane, friction, viscous motion. Work, energy, conservation theorems, momentum, and collisions.
Dynamics of rigid bodies: centre of mass, torque, moments of inertia, dynamic equations, conservation laws. Applications in game physics.
(Optional) Numerical simulation of Newtonian dynamics: integration methods (Taylor, Runge-Kutta), basic algorithms, examples of simulations, collision detection, simplifications for complex rigid bodies, applications in game physics.
(Optional) Elements of fluid mechanics: statics (Stevino, Archimedes), dynamics (Bernoulli, laminar flow, Reynolds number), hydrodynamic effects on aircraft, balls, cars. Introduction to fluid simulation and dimensional analysis in hydrodynamics.
Basics of probability: Bernoulli trials, binomial distribution, random walk, Poisson processes.
Basics of statistical thermodynamics: entropy and information.
Mathematical background: vectors, derivatives, integrals, ordinary differential equations (ODEs).
Kinematics of the material point: basic definitions, velocity, acceleration, Galilean relativity. Basic motions (uniform, uniformly accelerated, uniform circular motion).
Dynamics of the material point: Newton's laws, free fall, projectile motion, harmonic oscillator, inclined plane, friction, viscous motion. Work, energy, conservation theorems, momentum, and collisions.
Dynamics of rigid bodies: centre of mass, torque, moments of inertia, dynamic equations, conservation laws. Applications in game physics.
(Optional) Numerical simulation of Newtonian dynamics: integration methods (Taylor, Runge-Kutta), basic algorithms, examples of simulations, collision detection, simplifications for complex rigid bodies, applications in game physics.
(Optional) Elements of fluid mechanics: statics (Stevino, Archimedes), dynamics (Bernoulli, laminar flow, Reynolds number), hydrodynamic effects on aircraft, balls, cars. Introduction to fluid simulation and dimensional analysis in hydrodynamics.
Basics of probability: Bernoulli trials, binomial distribution, random walk, Poisson processes.
Basics of statistical thermodynamics: entropy and information.
Prerequisites for admission
There are no formal prerequisites. However, a basic knowledge of mathematical analysis (e.g. functions, derivatives, integrals) is recommended to facilitate understanding of the topics covered.
Teaching methods
The course is delivered through lectures combining theoretical explanations with problem-solving sessions. Interactive teaching tools, are used to encourage active student participation. Some classes adopt a reverse teaching approach, where students themselves present parts of the course content under the guidance of the instructor.
Teaching Resources
The teaching materials mainly consist of lecture slides and notes prepared in previous academic years, available online through platforms such as MyAriel. The slides include references and suggestions for further reading in various textbooks.
During the lecture period, students who are occasionally absent may access recorded video lectures to catch up on missed topics.
During the lecture period, students who are occasionally absent may access recorded video lectures to catch up on missed topics.
Assessment methods and Criteria
The exam consists of a written test with open-ended problems aimed at assessing problem-solving skills and the application of theoretical concepts. The written test is conducted in open-book mode, allowing students to consult notes, textbooks, and course materials.
The oral examination is optional for students who achieve a passing grade in the written test and can be used either to explore specific topics in physics or to present a modelling project on physical phenomena (including simulations or code development).
For students whose written test result is close to the passing threshold, the oral examination becomes mandatory and is intended to address any gaps identified in the written exam.
The final grade is expressed in thirtieths. No differences are foreseen between attending and non-attending students.
The oral examination is optional for students who achieve a passing grade in the written test and can be used either to explore specific topics in physics or to present a modelling project on physical phenomena (including simulations or code development).
For students whose written test result is close to the passing threshold, the oral examination becomes mandatory and is intended to address any gaps identified in the written exam.
The final grade is expressed in thirtieths. No differences are foreseen between attending and non-attending students.
PHYS-03/A - Experimental Physics of Matter and Applications - University credits: 3
PHYS-04/A - Theoretical Physics of Matter, Models, Mathematical Methods and Applications - University credits: 3
PHYS-04/A - Theoretical Physics of Matter, Models, Mathematical Methods and Applications - University credits: 3
Lessons: 48 hours
Professor:
Stabile Alberto
Professor(s)