MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING

The aim of the course is to provide the students with a solid foundation in some particular advanced mathematics techniques and to describe some of their applications in the field of Physics and Engineering. Despite the strong methodological rigor that characterizes the mathematics courses, the course will therefore have a strong emphasis on problem solving and examples, thus allowing you to easily tackle all the topics of the more advanced courses.

During the course, students will learn to:
1. Be able to identify the main aspects of a complex problem
2. Knowing how to break down a complex problem into easier-to-solve sub-problems
3. Knowing how to complete a complex calculation in complete autonomy
At the end of the course, students are expected to have developed the following skills:
1. Knowing how to identify the most suitable technique for a given problem
2. Knowing how to solve the most common differential equations of Physics
3. Knowing how to use the Fourier and Laplace transforms
4. Knowing how to use complex calculus, including integration in the complex field
5. Knowing how to use tensor calculus

The course is designed to be as self-consistent as possible. A standard Calculus course covering up to partial derivatives, integrals and series of functions is required. Useful, but not necessary, are the knowledge of introductory physics concepts in mechanics and electromagnetism, at the same level of those offered at any first level BS degree.

Theory of functions with complex variables; Fourier and Laplace transforms
Distribution theory and Dirac delta; Vector and tensor algebra; Variational principles and Hamiltonian mechanics, Hilbertian spaces, Classical statistical mechanics; Elements of advanced statistics and stochastic processes

Metodi Matematici per l'Ingegneria Codegone, Lussardi, II edizione Zanichelli (2021)
A course in Complex Analysis, Zakeri Princeton Press
Introduzione ai metodi matematici delle scienze fisiche, Luongo e Mancini, McGraw Hill
Theoretical Mechanics of Particles and Continua, A. Fetter, J.D. Walecka, (Mc. Graw Hill, 1980)
I am checking other textbooks, typically notes and materials given at lecture are enough.

Written examinations during the course or a final written course possibly followed by oral examination

Lectures on smart boards and training in the classroom on the problem solving approach

Italian

written and oral

This subject deals with topics related to the macro-area "Human capital, health, education" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development