470-4122/01 – Integral Transformations (IT)
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 | Compulsory |
Year | 1 | Semester | winter |
| | Study language | Czech |
Year of introduction | 2016/2017 | Year of cancellation | 2020/2021 |
Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
Student would know basics of the mathematical tools for the understanding of Laplace transform and Fouries series after passing this subject. Moreover, the next abilities should be reached: application of Laplace transform for solving ordinary differential equations; to construct Fourier series in real and complex domain, to use Gibbs phenomena a apply to suitable applications.
Teaching methods
Lectures
Tutorials
Project work
Summary
Functions of complex variable are one of the basic tools of effective solution of technical problems. The goal of the subject is to introduce basic notions and techniques of Laplace Transformations and Fourier series. Both topics are endowed by suitable theory and depicted by relevant examples.
Compulsory literature:
G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
Robert T. Seeley, An Introduction to Fourier Seriese and Integrals, Dover Publications, Mineola, New York, 2006.
Recommended literature:
G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
Robert T. Seeley, An Introduction to Fourier Seriese and Integrals, Dover Publications, Mineola, New York, 2006.
Way of continuous check of knowledge in the course of semester
Two tests, one project, final exam.
E-learning
Other requirements
There are no additional requirements on students.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Definition of Laplace transformation (LT)
2. Basic properties of LT
3. Application of LT on solving of ordinary differential equations
4. Fourier series (RF) in real form
5. FR in complex form
6. Convergence of FR
7. Gibbs property
8. Application of FR
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction