Mathematical Methods in Physics

Code:

F4025

Acronym:

F4025

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Master in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:F	19	Official Study Plan	1	-	6	42	162
			2

Teaching language

Suitable for English-speaking students

Objectives

1. Know selected mathematical methods used in physics, in particular complex function of complex variable and theory of discrete and continuous groups.


2. Analyze a set of problems in various areas of physics in the perspective of the application addressed mathematical methods.


3. To model problems in Physics.

Learning outcomes and competences

1. Understanding of mathematical concepts in the areas of complex functions of a complex variable, Fourier and other transforms, special functions and group theory.


2. Application of the methods covered in modeling and solving physical problems, for example, Electromagnetism, Optics, Fluid Mechanics, Condensed Matter Physics and Particle Physics.


3. Development of knowledge and skills that streamline research and development activities, in particular facilitating calculations, the development of new models, and the understanding of specialized literature in this area.

Working method

Presencial

Program

1. Complex functions of a complex variable --- Mapping. Branch lines and Riemann surfaces. The deferential calculus of functions of a complex variable. Complex integration. Series representations of analytic functions. Conformal transformations. Integration by the method of residues. Fourier series.


2. Special functions --- Bessel functions of the first and second kind, modified Bessel functions, spherical Bessel functions. Legendre Polynomials, associated Legendre equation, spherical harmonics. Hermite functions. Laguerre functions.


3. Group theory --- Mathematical background and basic theorems. Representation theory, characters, basis functions. Discrete groups, point symmetry groups. Continuous groups, Lie groups and algebras, Lorentz group.

Mandatory literature

George B. Arfken, Hans J. Weber; Mathematical methods for physicists (7th edition), Academic Press, 2012. ISBN: 9780123846549
Phillips E. G.; Functions of a complex variable with applications

Teaching methods and learning activities

Lectures, problem solving sessions; individual study.

keywords

Physical sciences > Physics > Mathematical physics
Physical sciences > Mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

Attendance is not required to be eligibile to take the final exam.

Calculation formula of final grade

The final score is that of the final exam.

Observations

Juri: Ariel Guerreiro, José Miguel Nunes da Silva, Vitor M. Pereira