470-8727/01 – Functions of a Complex Variable (FKP AVAT)
| Gurantor department | Department of Applied Mathematics | Credits | 4 |
| Subject guarantor | prof. RNDr. Marek Lampart, Ph.D. | Subject version guarantor | prof. RNDr. Marek Lampart, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory type A |
| Year | 3 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2015/2016 | Year of cancellation | |
| Intended for the faculties | USP, FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
To give students knowledge of basic concepts of complex functions of complex variable, Laplace transforms and Fourier series.
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, the theory of power series, Taylor and Laurent series, theory of residua, and Laplace transforms and Fouries series..
Compulsory literature:
Recommended literature:
Galajda, P., Schrötter, Š.: Funkce komplexní proměnné a operátorový počet, Alfa-Bratislava, 1991.
Škrášek, J., Tichý, Z.: Základy aplikované matematiky II, SNTL, Praha, 1986.
Way of continuous check of knowledge in the course of semester
Verification of study:
Test of functions of complex variable I. - max. 10 points.
Test of functions of complex variable II. - 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.
E-learning
Other requirements
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.
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.
Projects:
Two individual works and their presentation on the theme:
Fourier series.
Laplace transform.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.