470-4122/01 – Integral Transformations (IT)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. RNDr. Marek Lampart, Ph.D.Subject version guarantordoc. RNDr. Marek Lampart, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2016/2017Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
HOR33 doc. Ing. David Horák, Ph.D.
KAL0063 doc. RNDr. René Kalus, Ph.D.
LAM05 doc. RNDr. Marek Lampart, Ph.D.
MRO0010 Ing. Martin Mrovec
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

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

Další požadavky na studenta

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

Full-time form (validity from: 2016/2017 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30 (30) 10
                Test no. 1 Written test 10  0
                Test no. 2 Written test 10  0
                Project Project 10  0
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2017/2018 (N2661) Designing of Electrical Systems and Technologies P Czech Ostrava 1 Compulsory study plan
2017/2018 (N2661) Designing of Electrical Systems and Technologies K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner