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

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
HOR33	doc. Ing. David Horák, Ph.D.
KAL0063	prof. RNDr. René Kalus, Ph.D.
LAM05	prof. RNDr. Marek Lampart, Ph.D.
MRO0010	Ing. Martin Mrovec

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	2+2
Part-time	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:

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

Full-time form (validity from: 2016/2017 Winter semester, validity until: 2020/2021 Summer semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
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	3

Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Spec.	Zaměření	Form	Study language	Tut. centre	Year	W	S	Type 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 name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

2017/2018 Winter