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Introduction to Partial Differential Equations - NMMA339

Title:	Úvod do parciálních diferenciálních rovnic
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time

Guarantor:	prof. Mgr. Milan Pokorný, Ph.D., DSc.
Teacher(s):	prof. Mgr. Milan Pokorný, Ph.D., DSc.
Class:	M Bc. OM M Bc. OM > Zaměření MA M Bc. OM > Zaměření NUMMOD M Bc. OM > Povinně volitelné
Classification:	Mathematics > Differential Equations, Potential Theory
Incompatibility :	NMMA334
Interchangeability :	NMMA334
Is pre-requisite for:	NMMA351, NMNM351
In complex interchangeability with:	NMMA334
In complex incompatibility with:	NMMA334

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Annotation -

An introductory course in partial differential equations for bachelor's program in General Mathematics. Recommended for specializations Mathematical Analysis and Mathematical Modelling and Numerical Analysis.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (29.05.2019)

Course completion requirements -

Credit for the exercise is granted for elaboration of two homeworks and passing successfully two written tests. The exam will consist of written and oral parts.

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (30.09.2024)

Literature - Czech

Základní studijní literatura a studijní pomůcky

L. C. Evans: Partial Differential Equations, AMS 1999

M. Renardy, R. C. Rogers: An introduction to partial differential equations, Springer 1993

Další studijní literatura a studijní pomůcky

O. John, J. Nečas: Rovnice matematické fyziky, SPN 1972

S. J. Farlow: PDE for Scientists and Engineers, Dover, 1993

F. Sauvigny: Partial Differential Equations 1, Foundations and Integral Representations, Springer, 2006

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (30.09.2024)

Requirements to the exam - Czech

Zkouška se skládá z písemné a ústní části. V písemné části bude testována početní technika v rozsahu probraném na cvičeních. Po úspěšném napsání písemky student postupuje k ústní části zkoušky. Zkoušena bude teorie v rozsahu vyložené látky včetně důkazů.

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (30.09.2024)

Syllabus -

Basic examples of PDE's and their numerical solution by the finite difference method. Cauchy problem for a quasilinear PDE of the first order, transport equation, characteristics.

Heat equation: existence of a solution, its properties, maximum principle

Wave equation: existence of a solution, its properties, finite speed of propagation

Laplace and Poisson equation: existence of a solution, its properties, properties of harmonic functions

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (30.09.2024)

Entry requirements -

Knowledge of mathematical analysis, linear algebra and measure theory on the level of obligatory courses recommended for the first two years of the study branch General Mathematics is expected.

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (30.09.2024)