MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING

The aim of the course is to provide the student with a solid foundation in some particular mathematical aspects of Physics and to describe some of their applications in the field of Physics and Engineering. 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. Aim of the course is the learning of the mathematical structures in which Quantum Mechanics is framed and the other advanced courses of Physics that will follow.

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
6. Knowing Lagrangian and Hamiltonian Mechanics
7. To be able to understand Quantum Mechanics

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; Hilbert spaces; Variational principles Lagrangian and Hamiltonian mechanics; Classical statistical mechanics; Elements of advanced statistics and stochastic processes.

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

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

written and oral

Written tests with possible oral exam. Mark in thirtieths.

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