457-0308/01 – Equations of Mathematical Physics (RMFPM)

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	2	Semester	winter
		Study language	Czech
Year of introduction	2003/2004	Year of cancellation	2009/2010
Intended for the faculties	FEI	Intended for study types	Follow-up Master

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	2+2

Subject aims expressed by acquired skills and competences

The main aim of the subject is to formulate classical partial differential equations motivated by physical phenomena and to use classical methods for their solutions.

Teaching methods

Lectures
Individual consultations
Tutorials

Summary

This course is devoted to the analytical methods of the solution of the partial differentia equations. All the methods will give us fruitful imagination of the qualitative behavior of the mathematical modeling. This information will be very useful tor the future modeling of more complicated problems. During this course there will be given standard set of the classical partial differential equations and their properties. Also stability and uniqueness will be discussed.

Compulsory literature:

P. Drábek, G. Holubová: Parciální diferenciální rovnice (Úvod do klasické teorie). Skripta ZČU Plzeň, 2001. J. Franců: Parciální diferenciální rovnice. Skripta VUT Brno, 2000. S. Míka, A. Kufner: Parciální diferenciální rovnice I. Stacionární rovnice. Edice MVŠT, sešit XX, SNTL Praha, 1983. J. Barták, L. Herrmann, V. Lovicar, O. Vejvoda: Parciální diferenciální rovnice II. Evoluční rovnice. Edice MVŠT, sešit XXI, SNTL Praha, 1988. W. A. Strauss: Partial Differential Equations (An Introduction), John Wiley & Sons, Inc., New York 1992.

Recommended literature:

Textbook for students of the PDE.

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Rovnice 1. řádu, Cauchyova úloha, charakteristika rovnice. Cauchyova úloha pro rovnice vyšších řádů. Klasifikace rovnic 2. řádu, převod na kanonický tvar. Odvození vybraných rovnic matematické fyziky, příklady formulací počátečních a okrajových úloh: rovnice vedení tepla, rovnice difúze, vlnová rovnice, Laplaceova a Poissonova rovnice, rovnice průhybu membrány, rovnice stacionárního vedení tepla popř. elektrického proudu. Metoda charakteristik. Fourierova metoda. Použití integrálních transformací. Metoda Greenovy funkce. Principy maxima a jednoznačnost úloh. Metoda potenciálů.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Exercises evaluation and Examination	Credit and Examination	100 (100)	51	3
Examination	Examination	70	0	3
Exercises evaluation	Credit	30 (30)	10	1
1. Písemka	Written test	15	0	1
2. Písemka	Written test	15	0	1

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
2003/2004	(N2646) Information Technology	(1103T021) Computational Mathematics			P	Czech	Ostrava	2			Compulsory	study plan
2003/2004	(N2646) Information Technology	(1103T021) Computational Mathematics			K	Czech	Ostrava	2			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

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