470-4109/04 – Functions of Complex Variable and Integral Transformations (FKP IT)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | prof. RNDr. Marek Lampart, Ph.D. | Subject version guarantor | prof. RNDr. Marek Lampart, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2015/2016 | Year of cancellation | |
| Intended for the faculties | USP, FEI, FS | Intended for study types | Follow-up Master |
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:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Verification of study:
Test of a complex variable no.1 - max. 10 points.
Test of a complex variable no.2 - max. 10 points.
Individual project on Fourier series - max. 10 points.
Conditions for credit:
Two tests - max. 20 points.
One individual project - max. 10 points.
The maximum number of points from exercises is 30 points.
The minimum number of points from exercises is 15 points.
Final exam (written form).
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.
Project:
One individual project on the topic on Fourier series.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction