Mathematical Methods in Physics

Code:

F4025

Acronym:

F4025

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2016/2017 - 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:AST	3	Plano de Estudos oficial desde_2013/14	1	-	6	42	162
			2
M:F	11	Official Study Plan	1	-	6	42	162
			2

Teaching language

Suitable for English-speaking students

Objectives

1. Know some 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 the physical issues.

Learning outcomes and competences

1. Understanding of concepts, advanced mathematical in the area of complex functions of complex variable, Fourier transforms and the like, special functions and group theory.
2. Application of mathematical methods covered in modeling and solving physical problems, for example, Electromagnetism, Optics, Fluid Mechanics, Condensed Matter Physics and Particle Physics.
3. Development of skills and knowledge that streamline research and development activities in particular to facilitate the development of new models and performing calculations, reading and understanding of the area of literature.

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. Green functions. Applications to fluid mechanics and electromagnetism.


2. Group theory. Mathematical background. Representation theory; basis theorems. Characters. Basis functions. Splitting of atomic orbitals. Molecular vibrations. Space groups in real and reciprocal space. Representations. Electron and phonon dispersion relations. Time reversal symmetry and magnetism.


3. Lie algebras. Basic mathematical properties of Lie groups and algebras. Casimir operator. Killing form. Cartan-Weyl basis. SU(N) groups and Lie algebras in particle physics: tensor representations and Young tableaux; SU(2) spin and isospin; SU(3) and the quark model; introduction to Yang-Mills theories and Higgs mechanism.

Mandatory literature

Phillips E. G.; Functions of a complex variable with applications
Arfken George B.; Mathematical methods for physicists. ISBN: 0-12-059825-6
Lyubarskii G. Ya.; The applications of group theory in physics
Georgi Howard; Lie algebras in particle physics. ISBN: 0-7382-0233-9

Teaching methods and learning activities

Lectures, problem solving classes; individual study.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Participação presencial	10,00
Teste	90,00
Total:	100,00

Calculation formula of final grade

Lectures, problem solving classes; individual study.

Assessement: continuous assessement or final exam. The continuous assessement consists on two tests (one regarding the topic 1, and the second one, the topics 2 and 3 of the syllabus), each one has a weight of 50%

Terms of frequency: Attendance to at least 3/4 of classes.

The student can choice the continuous assessement or final exam. In the case of the continuous assessement, the mark of each test can not be less than 8/20.