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ECTS Course Overview



Functions of Complex Variable and Integral Transformations

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code470-4109/03
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *Second Cycle
Year of Study *
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
LAM05doc. RNDr. Marek Lampart, Ph.D.
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.
Learning Outcomes of the Course Unit
To give students knowledge of basic concepts of complex functions of complex variable and integral transformations.
Course Contents
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.
Recommended or Required Reading
Required Reading:
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.
Galajda, P., Schrötter, Š.: Funkce komplexní proměnné a operátorový počet, Alfa-Bratislava, 1991.
Škrášek, J., Tichý, Z.: Základy aplikované matematiky II, SNTL, Praha, 1986.
G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
Kozubek, T., Lampart, M.: Integrální transformace, http://mi21.vsb.cz/modul/integralni-transformace
Bouchala, J.: Funkce komplexní proměnné, http://mi21.vsb.cz/modul/funkce-komplexni-promenne
Recommended Reading:
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.
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.
Planned learning activities and teaching methods
Lectures, Tutorials, Project work
Assesment methods and criteria
Tasks are not Defined