Periodo di erogazione dell'insegnamento
Modalità di verifica del profitto e valutazione
Orario di ricevimento
The aim of the course is to provide the basic tools of Mathematical Analysis useful in the study of the differential
equations of Classical Physics and Quantum Mechanics
Complex analysis. Fourier series. Convolution. Fourier transform. Distributions and Dirac delta. Elements of Calculus of Variations.
Holomorphic functions and harmonic functions. Cauchy's theorem. Laurent series. Residue theorem. Jordan Lemma. Calculation of integrals by means of residue theorem.
Reminder on series expansion. Complete orthonormal systems. Parseval formula and inversion formula. Fourier series in real and complex form.
Fourier transform and applications.
Parseval formula and inversion formula. Convolution of functions. Applications to the resolution of the heat, wave and Schroedinger equation. Calculation of Fourier transforms with the residue theorem. Gaussian function. Lorentzian function. Voigt function.
Definition and simple properties. Approximation of the Dirac delta distribution.
Elements of Calculus of Variations.
Functional derivative. Euler-Lagrange equation. Estimation of eigenvalues.
Basic mathematical analysis: differential calculus for functions of one or several variables, ordinary and partial differential equations, integral calculus.
Lectures and exercises.
Textbook and teaching resource
K. F. Riley, M. P. Hobson and S. J. Bence. Mathematical Methods for Physics and Engineering, Cambridge
Further material will be suggested or distributed during the course.
First Semester 2019-20
Written exam: exercises and problems with open questions.
Oral exam: discussion of the written exam; solution of further exercises can be required; questions on definitions, statements and (selected) proofs of theorems.
It is possible to take the oral exam even if the result of the written exam is not sufficient.
By appointment, sending an e-mail to firstname.lastname@example.org