457-0048/01 – Integral Transforms (INTR)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | doc. Ing. David Horák, Ph.D. | Subject version guarantor | doc. Ing. David Horák, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | 1 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 1992/1993 | Year of cancellation | 2009/2010 |
| Intended for the faculties | FEI | Intended for study types | Master |
Subject aims expressed by acquired skills and competences
Student should understand to basic tools and rules of integral transforms and get familiar with correct approaches for the solution of concrete problems and discuss the chosen way of their solution.
Teaching methods
Lectures
Tutorials
Project work
Summary
Subject Integral transforms belongs to basic mathematical subjects at technical universities. The students will get knowledge about the theory and usage of Laplace transform and Z transform, Fourier series, Fourier, Window Fourier and Wavelet transforms including their applications for signal processing as time-frequency analysis, compression and denoising.
Compulsory literature:
Častová, N.,Kozubek,T:Integral transforms, www.am.vsb.cz
Galajda P., Schrötter Š.: Function of complex variable and operator calculus, Alfa-Bratislava, 1991.
G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
Recommended literature:
Škrášek J., Tichý Z.: The basics of applied mathematics II, SNTL, Praha, 1986.
Way of continuous check of knowledge in the course of semester
Verification of study:
Test of Fourier series - max. 10 points.
Test of Laplace transform - max. 10 points.
Individual project of Laplace transform - max. 10 points.
Individual project of Fourier series - max. 10 points.
Conditions for credit:
Two tests - max. 20 points.
Two individual projects - max. 20 points.
Maximal number of points from exercises - 40 points.
Minimal number of points from exercises - 20 points.
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
Introduction to Fourier series. Orthogonal systems of functions. Generalized Fourier series. Applications.
Introduction to integral transforms. Convolution.
Laplace transform, fundamental properties. Inverse Laplace Transform. Applications.
Fourier transform, fundamental properties. Inverse Fourier transform. Applications.
Z-transform, fundamental properties. Inverse Z-transform. Applications.
Distribution. Dirac impuls.
Exercises:
Examples of orthogonal systems of functions, Fourier series and applications.
Practising of Laplace transform. Solution of differential equation.
Practising of Fourier transform and examples.
Practising of Z-transform. Solution of difference equation.
Projects:
Two individual works and their presentation on the theme:
Fourier series.
Laplace transform.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction