MATHEMATICAL PHYSICS

Course objectives

General objectives: To acquire basic knowledge on modeling and solving classical problems of continuum physics. Specific objectives: Knowledge and understanding: At the end of the course the student will know the fundamental equations of mathematical physics (transport, waves, Laplace, heat), their derivation from concrete physical problems and the classical techniques of solution. Applying knowledge and understanding: Students who have passed the exam will be able to solve transport and Liouville's equation, simple initial and boundary value problems for wave and heat equations and boundary value problems for Laplace and Poisson equations, using the classical techniques of mathematical physics, like Green's functions and Fourier method. Making judgments : Students who have passed the exam will be able to recognize a mathematical physics approach to problems, linking the mathematical properties of the models based on partial differential equations to the concrete description of the problems of continuum physics. Communication skills: Students who have passed the exam will have gained the ability to communicate concepts, ideas and methodologies of Mathematical Physics related to continuum physics. Learning skills: The acquired knowledge will allow a study, individual or given in other courses, concerning more advanced methods of Mathematical Physics.

Channel 1
GIADA BASILE Lecturers' profile
Channel 2
ALESSANDRO TETA Lecturers' profile

Program - Frequency - Exams

Course program
Basic notions of the theory of distributions, Dirac delta. Elements of Fourier series. Introduction to Fourier transform. Laplace and Poisson equations, properties of the potential, harmonic functions, maximum principle and uniqueness. Solutions of boundary value problems by Green's function and Fourier method. Other physical problems described by Laplace and Poisson equations. Derivation of the equation of the vibrating string. From Maxwell's equations in vacuum to the wave equation. D'Alembert solution, Duhamel formula. Solution of one dimensional wave equation in bounded domains by Fourier method. Solution of the wave equation in dimension two and three in the whole space. Maxwell equations in vacuum, solution of the Cauchy problem, conservation of energy, radiation fields. Fourier law and heat equation. Solution of the Cauchy problem in the whole space. Maximum principle, uniqueness. Solution of heat equation in bounded domains by Fourier method.
Prerequisites
It is required a good knowledge of the arguments covered in the courses of Analisi Matematica II and Analisi Reale.
Books
P. Butta', Note del corso di Fisica Matematica, available on the personal website of P. Buttá S. Salsa, Equazioni a derivate parziali, Springer, 2010 A.N. Tichonov, A.A. Samarkij, Equazioni della fisica matematica, Mir, 1981 L.C. Evans, Partial Differential Equations, A.M.S., 2004 A.N. Kolmogorov, S.V. Fomin, Elementi di teoria delle funzioni e di analisi funzionale, Mir, 1981 V.I. Smirnov, Corso di matematica superiore II, Ed. Riuniti, 1977 A. Teta, Appunti di Fisica Matematica, available on the personal website of A. Teta
Frequency
Attendance at lessons is essential for a good understanding of the course
Exam mode
During the exam the student is required to solve an exercises of the type solved during the course and to discuss some theoretical topics illustrated in the course. To pass the exam the student need to achieve a grade not less than 18/30. The student must demonstrate that he has acquired a sufficient knowledge of the topics and that he is able to apply the methods learned in the course to the simplest examples treated. To achieve a grade of 30/30 cum laude, the student must demonstrate that he has acquired an excellent knowledge of all the topics covered during the course and that he is able to expose them in a logical and coherent way.
Lesson mode
Lectures (60%), examples and exercises (40%).
  • Lesson code1022388
  • Academic year2025/2026
  • Coursecorso|33592
  • CurriculumGenerale
  • Year3rd year
  • Semester1st semester
  • SSDMAT/07
  • CFU9
  • Subject areaFormazione Modellistico-Applicativa