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

Fundamental tools of Mathematics and Physics, calculus, linear algebra, probability distributions, entropy

Theory of functions with complex variables; Fourier and Laplace transforms
Distribution theory and Dirac delta; Vector and tensor algebra; Variational principles Lagrangian 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 lectures 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