470-4109/01 – Functions of Complex Variable and Integral Transformations (FKP IT)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. RNDr. Marek Lampart, Ph.D.Subject version guarantordoc. RNDr. Marek Lampart, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesUSP, FMT, FEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
HOR33 doc. Ing. David Horák, Ph.D.
LAM05 doc. RNDr. Marek Lampart, Ph.D.
ULC0011 Ing. David Ulčák
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.

Teaching methods

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. William L. Briggs, Van Emden Henson: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN 0-89871-342-0. Michael W. Frazier: An introduction to wavelets through Linear Algebra, Springer,1999, ISBN 0-387-98639-1.

Recommended literature:

Howie J.M., Complex Analysis, Springer-Verlag London, 2003, ISBN 978-1-85233-733-9. Needham T., Visual complex analysis, Oxford University Press, 1997, ISBN 0-19-853446-9.

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. Written exam.

E-learning

Další požadavky na studenta

No additional requirements are imposed on the student.

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: 2012/2013 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 40 (40) 20
                Sem. pr. 1 Project 10  0
                Sem. pr. 2 Project 10  0
                Test 1 Written test 10  0
                Test 2 Written test 10  0
        Examination Examination 60  11
Mandatory attendence parzicipation:

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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
V - ECTS - mgr. 2014/2015 Full-time Czech Optional 401 - Study Office stu. block
V - ECTS - mgr. 2013/2014 Full-time Czech Optional 401 - Study Office stu. block
V - ECTS - mgr. 2012/2013 Full-time Czech Optional 401 - Study Office stu. block
V - ECTS - mgr. 2011/2012 Full-time Czech Optional 401 - Study Office stu. block