# 457-0301/01 – Functions of Complex Variable and Integral Transformations (FKPIT)

 Gurantor department Department of Applied Mathematics Credits 6 Subject guarantor prof. Ing. Tomáš Kozubek, Ph.D. Subject version guarantor prof. Ing. Tomáš Kozubek, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2003/2004 Year of cancellation 2009/2010 Intended for the faculties FEI Intended for study types Master
Instruction secured by
HOR33 doc. Ing. David Horák, Ph.D.
KOZ75 prof. Ing. Tomáš Kozubek, Ph.D.
LAM05 doc. RNDr. Marek Lampart, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Combined Credit and Examination 10+10

### Subject aims expressed by acquired skills and competences

To give students knowledge of basic concepts of complex functions of complex variable and integral transformations.

Lectures
Tutorials
Project work

### Summary

Functions of complex variable and integral transformations are one of the basic tools of effective solution of technical problems. The students will get knowledge of basic concepts of functions of complex variable and integral transformations.

### Compulsory literature:

G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.

### Recommended literature:

G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.

### Way of continuous check of knowledge in the course of semester

Verification of study: Test of complex variable - 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.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Lectures: Complex functions and mappings. Complex differentiation, contour integration and deforming the contour. Complex series: power series, Taylor and Laurent series. Residue theorem. Applications. 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. Exercises: Practising of complex functions, linear and quadratic mappings. Practising of complex differentiation, conformal mappings, contour integration and deforming the contour. Examples of Taylor and Laurent series and applications. 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

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2008/2009 Winter semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Examination Examination 60  0
Exercises evaluation Credit 40 (40) 10
Písemný test č. 1 Written test 10  0
Semestrální projekt č. 1 Semestral project 10  0
Písemný test č. 2 Written test 10  0
Semestrální projekt č. 2 Semestral project 10  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (N2647) Information and Communication Technology (2601T013) Telecommunication Technology P Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (N2649) Electrical Engineering (2612T015) Electronics P Czech Ostrava 1 Compulsory study plan
2009/2010 (N2649) Electrical Engineering (3907T001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (N2647) Information and Communication Technology (2601T013) Telecommunication Technology K Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering K Czech Ostrava 1 Compulsory study plan
2009/2010 (N2649) Electrical Engineering (2612T015) Electronics K Czech Ostrava 1 Compulsory study plan
2009/2010 (N2649) Electrical Engineering (3907T001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology P Czech Ostrava 2 Compulsory study plan
2008/2009 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2008/2009 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology K Czech Ostrava 2 Compulsory study plan
2008/2009 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2008/2009 (N2647) Information and Communication Technology (2601T013) Telecommunication Technology P Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2647) Information and Communication Technology (2601T013) Telecommunication Technology K Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (N2649) Electrical Engineering (2612T015) Electronics P Czech Ostrava 1 Compulsory study plan
2008/2009 (N2649) Electrical Engineering (2612T015) Electronics K Czech Ostrava 1 Compulsory study plan
2008/2009 (N2649) Electrical Engineering (3907T001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (N2649) Electrical Engineering (3907T001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology P Czech Ostrava 2 Compulsory study plan
2007/2008 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2007/2008 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Compulsory study plan
2007/2008 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology K Czech Ostrava 2 Compulsory study plan
2007/2008 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Compulsory study plan
2007/2008 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2007/2008 (N2647) Information and Communication Technology (2601T013) Telecommunication Technology P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (2601T013) Telecommunication Technology K Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (N2649) Electrical Engineering (2612T015) Electronics P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2649) Electrical Engineering (2612T015) Electronics K Czech Ostrava 1 Compulsory study plan
2007/2008 (N2649) Electrical Engineering (3907T001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2649) Electrical Engineering (3907T001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology P Czech Ostrava 2 Compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology K Czech Ostrava 2 Compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2006/2007 (N2647) Information and Communication Technology (2601T013) Telecommunication Technology P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (2601T013) Telecommunication Technology K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering K Czech Ostrava 1 Compulsory study plan
2006/2007 (N2649) Electrical Engineering (2612T015) Electronics P Czech Ostrava 1 Compulsory study plan
2006/2007 (N2649) Electrical Engineering (2612T015) Electronics K Czech Ostrava 1 Compulsory study plan
2006/2007 (N2649) Electrical Engineering (3907T001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (N2649) Electrical Engineering (3907T001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology K Czech Ostrava 2 Compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology K Czech Ostrava 2 Compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology P Czech Ostrava 2 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T018) Electronics and Communication Technology K Czech Ostrava 2 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

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