Course detail
Mathematics for Applications
FSI-9MPAAcad. year: 2024/2025
The exposition will face across the traditional classification of mathematical branches so that it will respect students´ needs and options. It will be directed in an interactive form in order to respond to suggestions of students. A global view of problems enables students to see connections among apparently remote branches of mathematics.
Language of instruction
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Attendance at lectures is recommended. The lessons are planned on the basis of a weekly schedule. It is possible to study individually according to the recommended literature with the use of consultations.
Aims
Students get acquainted with a broad range of mathematical concepts occurring in physical applications.
Study aids
Prerequisites and corequisites
Basic literature
G. B. Arfken, V. J. Walker: Mathematical Methods for Physicists (4th ed.). Academic Press, 1995. (EN)
G. B. Thomas, R. L. Finney: Calculus and Analytic Geometry, Addison Wesley 2003 (EN)
Recommended reading
J. Karásek, L. Skula: Lineární algebra. Teoretická část, Cerm 2005
J. Karásek, L. Skula: Obecná algebra, Cerm 2008
J. Karásek: Matematika II., Cerm 2002
J. Nedoma: Matematika I., Cerm 2001
M. Druckmüller, A. Ženíšek: Funkce komplexní proměnné, PC-Dir 2000
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
The semester program can be modified due to the professional focus of the students
Advanced Linear Algebra
1. Dual vector spaces, tensors.
2. Miknowsky geometry, cone of events
3. Complex vector spaces, quantum mechanics
4. Quaternions and rotation algebra
5. Spin group
Control theory / optimization
1. Non-holonomic mechanics geometrically
2. Hamiltonian vector fields
3. Pontryagin's maximization principle
4. Two-player game theory and the simplex method
5. Cooperative games