A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.
BI-VMM Selected Mathematical Methods Extent of teaching: 2P+2C Instructor: Forough M. Completion: Z,ZK Department: 18105 Credits: 4 Semester: L Annotation:
The lecture begins with an introduction to the analysis of complex functions of a complex variable. Next, we present the Lebesgue integral. We then address Fourier series and their properties. Further, we introduce and study the properties of the Discrete Fourier Transform (DFT) and its fast implementation (FFT). We discuss the wavelet transform. We examine the linear programming problem in more detail and its solution using the Simplex algorithm. Each topic is demonstrated with interesting examples.
Lecture syllabus:
1. Complex numbers, complex functions of a complex variable, exponential function. 2. Properties of holomorphic functions. 3. The Lebesgue integral. 4. Fourier series. 5. Finite-dimensional Hilbert spaces, unitary matrices. 6. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT). 7. Wavelet transform. 8. Linear programming (introduction, formulation). 9. Linear programming (standard problem). 10. The SIMPLEX algorithm. 11. Examples and applications of linear programming. 12. Reserve Seminar syllabus:
1. Complex numbers, complex functions of a complex variable, exponential function. 2. Properties of holomorphic functions. 3. The Lebesgue integral. 4. Fourier series. 5. Finite-dimensional Hilbert spaces, unitary matrices. 6. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT). 7. Wavelet transform. 8. Linear programming (introduction, formulation). 9. Linear programming (standard problem). 10. The SIMPLEX algorithm. 11. Examples and applications of linear programming. 12. Reserve Literature:
Howard Karloff: Linear Programming.
O. Julius Smith: Mathematics of the Discrete Fourier Transform with Audio Applications. J. Kopáček: Matematika nejen pro fyziky II (lecture notes in czech). Requirements:
The fundamental knowledge of mathematical analysis and linear algerbra is required as they are given in BI-MA1/2, BI-DML and BI-LA1/2.
Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/BI-VMM/ The course is also part of the following Study plans:
Page updated 6. 7. 2025, semester: L/2022-3, Z/2023-4, Z/2022-3, L/2023-4, Z,L/2024-5, Z,L/2021-2, Z/2025-6, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška