470-8543/01 – Integral Transforms (ITHGF)

Gurantor departmentDepartment of Applied MathematicsCredits3
Subject guarantordoc. Ing. David Horák, Ph.D.Subject version guarantordoc. Ing. David Horák, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2010/2011Year of cancellation2013/2014
Intended for the facultiesHGFIntended for study typesFollow-up Master, Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
HOR33 doc. Ing. David Horák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+1

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

Další požadavky na studenta

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

Full-time form (validity from: 2010/2011 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30  10
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2012/2013 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2011/2012 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2010/2011 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner