Course detail
Mathematics for Applications
FSI-9MPA Acad. year: 2024/2025 Summer semester
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
Supervisor
Department
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.
The study programmes with the given course
Programme D-FIN-K: Physical Engineering and Nanotechnology, Doctoral, recommended course
Programme D-FIN-P: Physical Engineering and Nanotechnology, Doctoral, recommended course
Type of course unit
Lecture
20 hours, optionally
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