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

Czech

Mode of study

Not applicable.

Guarantor

doc. Mgr. Jaroslav Hrdina, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Linear algebra, differential and integral calculus.

Rules for evaluation and completion of the course

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.
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

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.

Students get acquainted with a broad range of mathematical concepts occurring in physical applications.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

A. A. Howard: Elementary Linear Algebra, Wiley 2002 (EN)
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. Cvičení, Cerm 2005
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

  • Programme D-FIN-P Doctoral 1 year of study, summer semester, recommended course
  • Programme D-FIN-K Doctoral 1 year of study, summer semester, recommended course

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

doc. Mgr. Jaroslav Hrdina, Ph.D.

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