Mathematics for Applications (FSI-9MPA)

Academic year 2023/2024
Supervisor: doc. Mgr. Jaroslav Hrdina, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech or English
Aims of the course unit:
The aim of the subject is a summarization, extension, and enlargement of knowledge of mathematics from bachelor´s and master´s studies with a view to applications, especially in physical engineering.
Learning outcomes and competences:

Students get acquainted with a broad range of mathematical concepts occurring in physical applications.
Prerequisites:
Linear algebra, differential and integral calculus.
Course contents:
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.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
The course is finished by an oral examination. The examiner verifies the knowledge of definitions, theorems, and algorithms and the ability of their use in concrete applications.
Controlled participation in lessons:
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.
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture

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
Literature - fundamental:
1. G. B. Arfken, V. J. Walker: Mathematical Methods for Physicists (4th ed.). Academic Press, 1995.
2. G. B. Thomas, R. L. Finney: Calculus and Analytic Geometry, Addison Wesley 2003
3. A. A. Howard: Elementary Linear Algebra, Wiley 2002
Literature - recommended:
1. J. Nedoma: Matematika I., Cerm 2001
2. J. Karásek: Matematika II., Cerm 2002
3. J. Karásek, L. Skula: Lineární algebra. Teoretická část, Cerm 2005
4. J. Karásek, L. Skula: Lineární algebra. Cvičení, Cerm 2005
5. J. Karásek, L. Skula: Obecná algebra, Cerm 2008
6. M. Druckmüller, A. Ženíšek: Funkce komplexní proměnné, PC-Dir 2000
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D-FIN-P full-time study --- -- DrEx 0 Recommended course 3 1 S
D-FIN-K combined study --- -- DrEx 0 Recommended course 3 1 S