Course detail
Mathematics - Selected Topics I
FSI-T1K Acad. year: 2021/2022 Summer semester
The course includes selected topics of functional analysis which are necessary for application in physics. It focuses on functional spaces, orthogonal systems and orthogonal transformations.
Language of instruction
Czech
Number of ECTS credits
3
Supervisor
Department
Learning outcomes of the course unit
Basic knowledge of functional analysis, metric, vector, unitary spaces, Hilbert space, orthogonal systems of functions, orthogonal transforms, Fourier transform and spectral analysis, application of the mentioned subjects in physics.
Prerequisites
Real and complex analysis
Planned learning activities and teaching methods
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes
Course-unit credit – based on a written test
Exam has a written and an oral part.
Aims
The aim of the course is to extend students´ knowledge acquired in the basic mathematical course by the topics necessary for study of physical engineering.
Specification of controlled education, way of implementation and compensation for absences
Missed lessons can be compensated for via a written test.
The study programmes with the given course
Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Introduction
2. Metric space
3. Contraction, fix point Banach's theorem
4. Vector space, base, dimension, Vector spaces of functions
5. Unitary space orthogonal a orthonormal spaces
6. Hilbert space, L2 and l2 space
7. Orthogonal bases, Fourier series
8. Orthogonal transforms, Fourier transform
9. Usage of Fourier transform, convolution theorem
10.2D Fourier transform
11.Filtration in space and frequency domain, applications in physics
12. Operators and functionals
13. Variation methods
Exercise
13 hours, compulsory
Teacher / Lecturer
Syllabus
1. Introduction
2. Metric space
3. Fix point Banach's theorem applications
4. Vector space, base, dimension, Vector spaces of functions
5. Unitary space orthogonal a orthonormal spaces
6. Hilbert space, L2 and l2 space
7. Orthogonal bases, Fourier series
8. Orthogonal transforms, Fourier transform
9. Usage of Fourier transform, convolution theorem
10. 2D Fourier transform
11. Filtration in space and frequency domain, applications in physics
12. Operators and functionals
13. Variation methods