94165 - Topics in Mathematical Methods and Models in Theoretical Physics

Learning outcomes

The course introduces students to topics and tools of modern theoretical physics. At the end of the course, students will be able to deal with appropriate mathematical methods and apply theoretical models to the description of some among the most significative problems of physics

Course contents

The course contents are the following ones:

1) Convolutions: Young inequality, functions with compact support and regularising sequances

2) Fourier series: basic properties, mean convergence, uniform convergence, applications in physics

3) Fourier transform: basic properties, convolutions and correlations, discrete Fourier transform, applications in physics

4) Ordinary differential equations: solutions, existence theorem for first order ordinary differential equations, Sturm-Liouville problems

5) Systems of ordinary differential equations: basic properties, linear systems of ordinary differential equations, autonomous systems of ordinary differential equations, classification of critical points, applications in physics

6) Partial differential equations: basic properties, the Laplacian operator, the diffusion operator, the wave operator, applications in physics

7) Introduction to group theory

Readings/Bibliography

Lecture notes will be provided at the beginning of the course. Several lectures will be based on parts of the following book:

"Higher Mathematics for Physics and Engineering", Tsuneyoshi Nakayama, Hiroyuki Shima, Springer

Teaching methods

Blackboard lectures

Assessment methods

Oral interview. The duration of the exam is around 30 minutes. The oral interview is divided into 2 parts: (1) solution of 1 or more exercises among those discussed during the lectures; (2) answers to questions related to the theory part of the lectures.

The final mark takes into account the performance of the student in both parts of the oral examination. To get a mark which is greater or equal to 18 it is necessary to have a satisfactory performance in at least one of the two parts of the exam. To get a very high evaluation is it necessary to pass both parts of the oral exam with distinction.

Office hours

See the website of Francisco Manuel Soares Verissimo Gil Pedro

See the website of Gianmassimo Tasinato

See the website of Erica Ivonne Zavala Carrasco