Program Overview

MATHEMATICAL METHODS IN PHYSICS

Course Overview

This course aims to provide adequate knowledge of the most advanced mathematical tools necessary to tackle the study of the physics courses of the third year of the three-year degree. Central themes of the course are the techniques of complex analysis and Fourier and Laplace transforms which will be useful both for subsequent theoretical courses and for courses in experimental physics.

Aims and Content

Learning Outcomes

The aim of the course is to provide students with the advanced mathematical tools used in modern physics: complex variable functions, Fourier and Laplace transforms, Hilbert spaces and classical partial differential equations of mathematical physics.

Aims and Learning Outcomes

The course has as its main objective the acquisition of basic knowledge and skills related to advanced mathematical tools that have general application in Physics. Particular attention is given to the understanding of the arguments, to the rigor in the presentation of concepts and reasonings, to the applicative aspects of the theoretical tools developed.

Prerequisites

Contents of Analysis, algebra, and geometry carried out in the first two years.

Teaching Methods

Both the lessons and the exercises are carried out on the blackboard. Students are always invited to actively participate by asking questions, proposing solutions to the proposed problems.

Syllabus/Content

• Theory of analytic functions. Algebra and geometry of complex numbers. Analytical and geometric characterization of analytic functions. Cauchy-Riemann conditions. Sequences and series of complex numbers and of functions of complex variables.
• Fourier analysis and applications. Generalities on distributions: space of test functions. Definition and properties of the Dirac delta. Integral and derivative of the Dirac delta.
• Vector spaces in infinite dimension. Complete orthonormal systems in infinite dimensional Euclidean spaces. Fourier coefficients. Bessel inequality and Parseval equality.

Recommended Reading/Bibliography

1. Notes provided by the teacher
2. Neeham, Visual complex analysis
3. K顤ner, Fourier Analysis

Teachers and Exam Board

• PIERANTONIO ZANGHI' (President)
• NICOLA PINAMONTI
• PAOLO SOLINAS (President Substitute)

Lessons

The class schedule is published on the Manifesto degli Studi.

Exams

Exam Description

The exam consists of a written test and an interview. The written test consists of some problems that cover a large part of the course contents.

Assessment Methods

The written test is aimed at verifying the ability to solve specific problems similar to those discussed in the course, but original.

Exam Schedule

• 13/01/2026: 10:00, GENOVA, Scritto
• 13/02/2026: 10:00, GENOVA, Scritto
• 10/06/2026: 10:00, GENOVA, Scritto
• 08/07/2026: 10:00, GENOVA, Scritto
• 07/09/2026: 10:00, GENOVA, Scritto

Further Information

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework, and exams, should speak with the instructor.