470-8543/01 – Integral Transforms (ITHGF)
Gurantor department | Department of Applied Mathematics | Credits | 3 |
Subject guarantor | doc. Ing. David Horák, Ph.D. | Subject version guarantor | doc. Ing. David Horák, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | summer |
| | Study language | Czech |
Year of introduction | 2010/2011 | Year of cancellation | 2013/2014 |
Intended for the faculties | HGF | Intended for study types | Follow-up Master, 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
E-learning
Other requirements
There are not defined other requirements for student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
Differential and integral calculus of functions of complex variables: the derivative,
conformal mappings. Complex integral, Cauchy integral theorem.
Taylor and Laurent series, convergence, residua classification of singular
points.
Direct and inverse Laplace transform, properties. Usage for the solution
of differential equations.
Orthogonal systems of functions. Fourier series, the foundations of harmonic analysis.
Direct and inverse Fourier transform, properties and uses.
exercise:
Solving problems on the topic: derivative, conformal mappings, complex integral.
Use of the integral Cauchy's formulas.
Solving problems on the topic: Taylor series, Laurent series, residua.
Solving problems on the topic: direct and inverse Laplace transformation. Usage for the solution
of differential equations.
Solving problems on the topic: orthogonal systems of functions and Fourier series.
projects:
Two individual jobs on the topic:
Fourier series.
Laplace transformation.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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