Università di Pavia - Offerta formativa

MATHEMATICAL PHYSICS EQUATIONS

Enrollment year

2018/2019

Academic year

2020/2021

Regulations

DM270

Academic discipline

MAT/07 (MATHEMATICAL PHYSICS)

Department

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

Course

MATHEMATICS

Curriculum

PERCORSO COMUNE

Year of study

3°

Period

2nd semester (01/03/2021 - 11/06/2021)

ECTS

6

Lesson hours

56 lesson hours

Language

Italian

Activity type

ORAL TEST

Teacher

Prerequisites

Differential and integral calculus in multiple dimensions. Elements of classical mechanics.

Learning outcomes

Aim of the course is to provide an introduction to the study of the main equations of mathematical physics, using almost exclusively classical tools of mathematical analysis.

Course contents

Classical vector analysis. Partial differential equations of first and second order.

Extended summary

Reminders on vectorial calculus, gradient, curl and divergence. Divergence theorem. Stokes's theorem. Green's formuals. Orthogonal curvilinear coordinate systems. Transport equations. Partial differential equations of the second order. Classification. Elliptic equations. Laplace equation, the mean value theorem, the maximum principle. Introduction to complex analysis (analytic functions, Cauchy-Riemann formulas). Dirichlet and Neumann problems for the circle. Parabolic equations. Heat diffusion. Exact solutions and the method of similarity. Heat diffusion: resolution of the Cauchy problem using the one-dimensional Fourier method. Initial-boundary value problem for the heat equation: the method of separation of variables. Hyperbolic equations. The wave equation. Vibrations of membranes. Introduction to the mechanics of fluids.

Extended summary

Reminders on vectorial calculus, gradient, curl and divergence. Divergence theorem. Stokes's theorem. Green's formuals. Orthogonal curvilinear coordinate systems. Transport equations. Partial differential equations of the second order. Classification. Elliptic equations. Laplace equation, the mean value theorem, the maximum principle. Introduction to complex analysis (analytic functions, Cauchy-Riemann formulas). Dirichlet and Neumann problems for the circle. Parabolic equations. Heat diffusion. Exact solutions and the method of similarity. Heat diffusion: resolution of the Cauchy problem using the one-dimensional Fourier method. Initial-boundary value problem for the heat equation: the method of separation of variables. Hyperbolic equations. The wave equation. Vibrations of membranes. Introduction to the mechanics of fluids.

Teaching methods

Lectures

Reccomended or required readings

Enrico Persico, INTRODUZIONE ALLA FISICA MATEMATICA, Bologna : Zanichelli, 1971, third ed.

Assessment methods

Examination is only oral and will be based on lessons learned. The student will have to demonstrate that he has achieved full understanding of the themes and has thus achieved the training objectives of the course.

Further information

Sustainable development goals - Agenda 2030