# MATHEMATICAL PHYSICS

# MATHEMATICAL PHYSICS

Mathematical Analysis

The course aims at completing the students' basic knowledge on Ordinary Differential Equations - dealing in particular with those of higher order - and at providing an elementary presentation of the Partial Differential Equations of Mathematical Physics, by means of the classical methods of separation of variables and Fourier series. For a reasonable discussion of the latter argument, also some basic results on Hilbert spaces and series expansion in othonormal vectors will be treated.

The course aims at completing the students' basic knowledge on Ordinary Differential Equations - dealing in particular with those of higher order - and at providing an elementary presentation of the Partial Differential Equations of Mathematical Physics, by means of the classical methods of separation of variables and Fourier series. For a reasonable discussion of the latter argument, also some basic results on Hilbert spaces and series expansion in othonormal vectors will be treated.

Notes from the lectures.

Refrences (in increasing order of complexity and completeness: in particular, the PDE are treated in D) and F)):

A) M. Bertsch, R. Dal Passo, L. Giacomelli: Analisi Matematica (Mc Graw-Hill, 2011): Ch. 17, 20.

B) A. Bacciotti - F. Ricci, Lezioni di Analisi Matematica 2 (Levrotto e Bella, 1991): Ch. 6, 7, 9, 10, 11.

C) E. Giusti, Analisi Matematica 2 (Boringhieri, 1983): Ch. 1, 2, 3.

D) C.D. Pagani - S. Salsa, Analisi Matematica 2 (Zanichelli, 2016): Ch. 3, 4, 7.

E) W. Walter, Ordinary Differential Equations (Springer-Verlag, 1998) Ch. 1,2,3,4,6.

F) H.F. Weinberger, A first course in Partial Differential Equations (Blaisdell, 1965): Ch. 2, 3, 4.

Classroom lectures

Final examination

The complete information on the Course (Content, Bibliographical References etc.) and the whole teaching material (Lecture Notes and Recording of the Lectures) are available on the web pages of the Course of Mathematical Physics on the site for the e-learning of UNISI: