Mathematical Methods in Physics 0800-MMF

Lectures and classes
I. Complex analysis
1) Cauchy-Riemann conditions,
2) Cauchy theorem,
3) Infinite complex series
4) residua and its applications,
5) contour integration,
II. Tensor calculus
1) tensor algebra,
2) exterior algebra
3) manifolds and tangent vectors,
4) tensor fields
5) tensor analysis: covariant derivative, parallel transport,
Lie derivative, Killing vectors, differential forms
6) Riemannian manifolds
III. Elements of group theory
1) introduction to discrete and continuous group,
2) basics of representation theory, Schur lemma, orthogonality conditions
3) basics of Lie group and Lie algebra theory.

Term 2025/26Z:

None

Total student workload

Contact hours with teacher: - participation in lectures and classes - 60 hrs Self-study hours: - preparation for lectures - 10 hrs - preparation for classes – 20 hrs - preparation for tests - 10 hrs - preparation for examination- 25 hrs Altogether: 125 hrs ( 5 ECTS)

Learning outcomes - knowledge

Student W1: has knowledge of mathematical models used in theoretical physics, K_W01, W2: is familiar with selected mathematical methods related to tensor calculus, complex analysis and group theory, and their applications in physics K_W03, K_W05, W3: has knowledge concerning the current trends in the development of mathematical and theoretical physics, K_W06

Learning outcomes - skills

Student U1: is able to derive specific physical quantities using some mathematical models and scientific reasoning, K_U01, K_U03 U2: has skills to adapt knowledge and methodology of tensor calculus, complex analysis, group and representation theory to selected topics in physics, K_U07

Learning outcomes - social competencies

Student: K1: knows the limitations of his own knowledge and skills related to mathematical methods and theoretical physics, K_K01 K2: can formulate his own opinions related to some topics of modern physics, K_K05

Teaching methods

Lectures and classes.

Expository teaching methods

- informative (conventional) lecture

Exploratory teaching methods

- practical

Type of course

compulsory course

Prerequisites

Rudiments of linear algebra and analysis presented during the first level of physics studies.

Course coordinators

Dariusz Chruściński
Jacek Jurkowski

Assessment criteria

Assessment methods:
- written examination - W1-W3, U1-U3
- written test - W1-W3, U1-U3

fail- less than 50%
satisfactory- 50-60%
satisfactory plus- 60-70%
good - 70-80%
good plus- 80-90%
very good- more than 90%

Bibliography

1. S. Hassani, Mathematical Physics. A modern introduction to its applications, Springer 2002
2. J.W. Brown and R. V. Churchill, Complex variables and applications, McGraw-Hill Education (2013)
3.. M. Hamermesh, Group theory and its applications to physical problems, Dover Publication, 2012

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 0800-MMF in USOSweb