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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Selected Mathematical Methods

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Code Completion Credits Range Language
BI-VMM Z,ZK 4 2P+2C Czech
Garant předmětu:
Tomáš Kalvoda
Lecturer:
Tomáš Kalvoda
Tutor:
Tomáš Kalvoda
Supervisor:
Department of Applied Mathematics
Synopsis:

We start reviewing geometric properties of linear spaces with inner product. Next, we introduce and analyze the discrete Fourier transform (DFT) and its fast implementation (FFT).

Further we deal with differential calculus of functions involving multiple variables. We present methods for the localization of extreme values of functions. For this purposes, we study normed linear spaces and quadratic forms. In addition, we introduce the least square method.

The last part of the course is devoted to optimization and duality. The linear programming and the Simplex method is analyzed in more detail.

Requirements:

The fundamental knowledge of mathematical analysis and linear algerbra is required as they are given in BI-ZMA and BI-LIN.

Syllabus of lectures:

1. Complex numbers, complex function of complex variable, exponential function.

2. Fourier series.

3. Hilbert spaces of finite dimension, unitary matrices.

4. Discrete Fourier transformation (DFT) and Fast Fourier transform (FFT).

5. Basic objects from theory of multivariate functions.

6. (Constrained) extrema of multivariate functions.

7. General optimization problem.

8. Weak and strong duality.

9. Linear programming (introduction, formulation).

10. Linear programming (problem in standard form).

11. SIMPLEX algorithm.

12. Examples and applications of Linear programming.

Syllabus of tutorials:

1. Complex numbers, complex function of complex variable, exponential function.

2. Fourier series.

3. Hilbert spaces of finite dimension, unitary matrices.

4. Discrete Fourier transformation (DFT) and Fast Fourier transform (FFT).

5. Basic objects from theory of multivariate functions.

6. (Constrained) extrema of multivariate functions.

7. General optimization problem.

8. Weak and strong duality.

9. Linear programming (introduction, formulation).

10. Linear programming (problem in standard form).

11. SIMPLEX algorithm.

12. Examples and applications of Linear programming.

Study Objective:

The goal of the course is to improve student's mathematical skills and to present classical mathematical methods with applications in IT.

Study materials:

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).

Note:
Further information:
https://courses.fit.cvut.cz/BI-VMM/
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
roomTH:A-s135
Kalvoda T.
16:15–17:45
(lecture parallel1)
Thákurova 7 (budova FSv)
As135
Wed
roomT9:155
Kalvoda T.
14:30–16:00
(lecture parallel1
parallel nr.101)

Dejvice
Posluchárna
Thu
Fri
The course is a part of the following study plans:
Data valid to 2024-03-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet3315206.html