MATHEMATICAL PHYSICS
Course objectives
Obiettivi generali: to acquire knowledge on the fundamental topics of Mathematical Physics and on the corresponding mathematical methods. Obiettivi specifici: Knowledge and understanding: At the end of the course the student will master the basic elements of dynamical systems theory, the mathematical structure of Hamiltonian formalism and perturbation theory, the basic methods for the study of some aspects of Modern Physics (Statistical Mechanics or Quantum Mechanics) from the point of view of Mathematical Physics. Applying knowledge and understanding: Students who have passed the exam will be able to: i) study the stability of equilibrium points; ii) use the Hamilton-Jacobi method for the determination of first integrals; iii) introduce action-angle variables for an integrable Hamiltonian system; iv) apply perturbation theory to specific physical problems obtaining qualitative and quantitative information on the motion; v) approach a rigorous analysis of some problems of Statistical Mechanics or Quantum Mechanics. Making judgments : Students who have passed the exam will be able to understand a mathematical-physics approach to problems and to analyze similarities and differences with respect to the typical approach of Theoretical Physics.
Channel 1
ALESSANDRO TETA
Lecturers' profile
Program - Frequency - Exams
Course program
Dynamical systems: basic elements on ordinary differential equations, Liouville transport theorem, equilibrium and stability, Lyapunov theorem.
Hamiltonian systems: basic elements on Hamilton's equations, action-angle variables, first order canonical perturbation theory.
Many-body systems: Liouville equation; BBGKY hierarchy; Vlasov equation; Boltzmann equation; kinetic models of viscous friction.
Continuous systems: Euler equation; Navier-Stokes equation; examples and applications.
Prerequisites
Good knowledge of the mathematical concepts discussed in the courses:
Analisi, Geometria, Analisi Vettoriale, Modelli e Metodi Matematici della Fisica.
Good knowledge of the basic notions of Mechanics discussed in the course:
Meccanica Analitica e Relativistica.
Books
Lecture notes available at https://sites.google.com/site/sandroprova/didattica-1/appunti-ed-esercizi
R. Esposito, Appunti dalle lezioni di Meccanica Razionale, ed. Aracne
A. Teta, A Mathematical Primer on Quantum Mechanics, Springer 2018
M. Hirsch and S Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press 1974
A. Fasano and S. Marmi, Analytical Mechanics, Oxford Univ. Press 2006
K. Huang: Statistical Mechanics, Wiley, 1991
A. Chorin, J.E. Marsden: A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, 2000.
P. Buttà, G. Cavallaro, C. Marchioro: Mathematical Models of Viscous Friction, Lecture Notes in Mathematics (Springer), 2015.
Teaching mode
Lectures on the theoretical concepts with classroom exercises
Frequency
Attendance at lessons is essential for a good understanding of the course
Exam mode
The examination consists of an interview on the most relevant topics
presented in the course. To pass the exam, the student must be able to
present arguments and repeat calculations discussed and explained
during the course. The student will be asked to apply the
methods learned during the course to exercises or to examples and
situations similar to those that were discussed in the course.
The evaluation takes into account:
- correctness and completeness of the concepts discussed by the
student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).
Bibliography
V.I. Arnold, Mathematical Methods in Classical Mechanics, second ed., Springer-Verlag
C. Marchioro, M. Pulvirenti: Mathematical Theory of Incompressible Nonviscous Fluids, Springer-Verlag, 1994.
Lesson mode
Lectures (70%) on the theoretical concepts with classroom exercises (30%)
ALESSANDRO TETA
Lecturers' profile
Program - Frequency - Exams
Course program
Dynamical systems: basic elements on ordinary differential equations, Liouville transport theorem, equilibrium and stability, Lyapunov theorem.
Hamiltonian systems: basic elements on Hamilton's equations, action-angle variables, first order canonical perturbation theory.
Many-body systems: Liouville equation; BBGKY hierarchy; Vlasov equation; Boltzmann equation; kinetic models of viscous friction.
Continuous systems: Euler equation; Navier-Stokes equation; examples and applications.
Prerequisites
Good knowledge of the mathematical concepts discussed in the courses:
Analisi, Geometria, Analisi Vettoriale, Modelli e Metodi Matematici della Fisica.
Good knowledge of the basic notions of Mechanics discussed in the course:
Meccanica Analitica e Relativistica.
Books
Lecture notes available at https://sites.google.com/site/sandroprova/didattica-1/appunti-ed-esercizi
R. Esposito, Appunti dalle lezioni di Meccanica Razionale, ed. Aracne
A. Teta, A Mathematical Primer on Quantum Mechanics, Springer 2018
M. Hirsch and S Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press 1974
A. Fasano and S. Marmi, Analytical Mechanics, Oxford Univ. Press 2006
K. Huang: Statistical Mechanics, Wiley, 1991
A. Chorin, J.E. Marsden: A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, 2000.
P. Buttà, G. Cavallaro, C. Marchioro: Mathematical Models of Viscous Friction, Lecture Notes in Mathematics (Springer), 2015.
Teaching mode
Lectures on the theoretical concepts with classroom exercises
Frequency
Attendance at lessons is essential for a good understanding of the course
Exam mode
The examination consists of an interview on the most relevant topics
presented in the course. To pass the exam, the student must be able to
present arguments and repeat calculations discussed and explained
during the course. The student will be asked to apply the
methods learned during the course to exercises or to examples and
situations similar to those that were discussed in the course.
The evaluation takes into account:
- correctness and completeness of the concepts discussed by the
student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).
Bibliography
V.I. Arnold, Mathematical Methods in Classical Mechanics, second ed., Springer-Verlag
C. Marchioro, M. Pulvirenti: Mathematical Theory of Incompressible Nonviscous Fluids, Springer-Verlag, 1994.
Lesson mode
Lectures (70%) on the theoretical concepts with classroom exercises (30%)
GUIDO CAVALLARO
Lecturers' profile
Program - Frequency - Exams
Course program
Dynamical systems: basic elements on ordinary differential equations, Liouville transport theorem, equilibrium and stability, Lyapunov theorem.
Hamiltonian systems: basic elements on Hamilton's equations, action-angle variables, first order canonical perturbation theory.
Many-body systems: Liouville equation; BBGKY hierarchy; Vlasov equation; Boltzmann equation; kinetic models of viscous friction.
Continuous systems: Euler equation; Navier-Stokes equation; examples and applications.
Prerequisites
Good knowledge of the mathematical concepts discussed in the courses:
Analisi, Geometria, Analisi Vettoriale, Modelli e Metodi Matematici della Fisica.
Good knowledge of the basic notions of Mechanics discussed in the course:
Meccanica Analitica e Relativistica.
Books
- Lecture notes available at https://sites.google.com/view/alessandro-teta/didattica-1
- R. Esposito, Appunti dalle lezioni di Meccanica Razionale, ed. Aracne.
- Teta, A Mathematical Primer on Quantum Mechanics, Springer 2018
- M. Hirsch and S Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press 1974
- A. Fasano and S. Marmi, Analytical Mechanics, Oxford Univ. Press 2006
- K. Huang: Statistical Mechanics, Wiley, 1991
- A. Chorin, J.E. Marsden: A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, 2000.
- P. Buttà, G. Cavallaro, C. Marchioro: Mathematical Models of Viscous Friction, Lecture Notes in Mathematics (Springer), 2015.
Frequency
Attendance at lessons is essential for a good understanding of the course
Exam mode
The examination consists of an interview on the most relevant topics
presented in the course. To pass the exam, the student must be able to
present arguments and repeat calculations discussed and explained
during the course. The student will be asked to apply the
methods learned during the course to exercises or to examples and
situations similar to those that were discussed in the course.
The evaluation takes into account:
- correctness and completeness of the concepts discussed by the student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).
Bibliography
V.I. Arnold, Mathematical Methods in Classical Mechanics, second ed., Springer-Verlag
C. Marchioro, M. Pulvirenti: Mathematical Theory of Incompressible Nonviscous Fluids, Springer-Verlag, 1994.
Lesson mode
Lectures (70%) on the theoretical concepts with classroom exercises (30%)
GUIDO CAVALLARO
Lecturers' profile
Program - Frequency - Exams
Course program
Dynamical systems: basic elements on ordinary differential equations, Liouville transport theorem, equilibrium and stability, Lyapunov theorem.
Hamiltonian systems: basic elements on Hamilton's equations, action-angle variables, first order canonical perturbation theory.
Many-body systems: Liouville equation; BBGKY hierarchy; Vlasov equation; Boltzmann equation; kinetic models of viscous friction.
Continuous systems: Euler equation; Navier-Stokes equation; examples and applications.
Prerequisites
Good knowledge of the mathematical concepts discussed in the courses:
Analisi, Geometria, Analisi Vettoriale, Modelli e Metodi Matematici della Fisica.
Good knowledge of the basic notions of Mechanics discussed in the course:
Meccanica Analitica e Relativistica.
Books
- Lecture notes available at https://sites.google.com/view/alessandro-teta/didattica-1
- R. Esposito, Appunti dalle lezioni di Meccanica Razionale, ed. Aracne.
- Teta, A Mathematical Primer on Quantum Mechanics, Springer 2018
- M. Hirsch and S Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press 1974
- A. Fasano and S. Marmi, Analytical Mechanics, Oxford Univ. Press 2006
- K. Huang: Statistical Mechanics, Wiley, 1991
- A. Chorin, J.E. Marsden: A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, 2000.
- P. Buttà, G. Cavallaro, C. Marchioro: Mathematical Models of Viscous Friction, Lecture Notes in Mathematics (Springer), 2015.
Frequency
Attendance at lessons is essential for a good understanding of the course
Exam mode
The examination consists of an interview on the most relevant topics
presented in the course. To pass the exam, the student must be able to
present arguments and repeat calculations discussed and explained
during the course. The student will be asked to apply the
methods learned during the course to exercises or to examples and
situations similar to those that were discussed in the course.
The evaluation takes into account:
- correctness and completeness of the concepts discussed by the student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).
Bibliography
V.I. Arnold, Mathematical Methods in Classical Mechanics, second ed., Springer-Verlag
C. Marchioro, M. Pulvirenti: Mathematical Theory of Incompressible Nonviscous Fluids, Springer-Verlag, 1994.
Lesson mode
Lectures (70%) on the theoretical concepts with classroom exercises (30%)
- Lesson code1055348
- Academic year2025/2026
- CoursePhysics
- CurriculumPhysics of Biological Systems
- Year1st year
- Semester2nd semester
- SSDMAT/07
- CFU6