PřF:M4010 Equations of math. physics - Course Information

M4010 Equations of mathematical physics

Extent and Intensity

3/2/0. 4 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
In-person direct teaching

Teacher(s)

prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Zdeněk Pospíšil, Dr.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science

Prerequisites

Single- and multivariable differential and integral calculus, curve and surface integral, ordinary differential equations.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physics (programme PřF, B-FY)

Course objectives

The discipline is a part of the fundamental course of mathematical analysis for students of physics. It is devoted to classical methods to solving partial differential equations.

Learning outcomes

At the end of this course, students should be able to:
classify partial differential equations;
select an appropriate classical analytic method of solution depending on type of equation;
find solution in terms of integral or infinite series for basic equations.

Syllabus

• Boundary value problems for ordinary differential equations.
• Special functions: Gamma function, Bessel functions, Legendre, Laguerre a Hermite polynomials.
• Distributions.
• Methods of characteristics: quasilinear 1st order equation, canonical form of 2nd order equations, initial value problem for wave equations.
• Methods of integral transforms: Fourier, Laplace transforms.
• Methods of separation of variables: wave equation, heat equation, eliptic equation, Schroedinger equation.
• Eliptic equations: harmonic functions, potentials, Green function.

Literature

• Franců Jan. Parciální diferenciální rovnice. VUT Brno, 2000
• EVANS, Gwynne, Jonathan M. BLACKLEDGE and Peter YARDLEY. Analytic methods for partial differential equations. London: Springer-Verlag, 1999, xii, 299. ISBN 3540761241. info
• RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
• BARTÁK, Jaroslav. Parciální diferenciální rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1988, 220 s. URL info
• MÍKA, Stanislav and Alois KUFNER. Parciální diferenciální rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1983, 181 s. info
• MÍKA, Stanislav and Alois KUFNER. Okrajové úlohy pro obyčejné diferenciální rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1981, 88 s. URL info
• TICHONOV, Andrej Nikolajevič and Aleksandr Andrejevič SAMARSKIJ. Rovnice matematické fysiky. Translated by Alois Apfelbeck - Karel Rychlík. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1955, 765 s. info

Teaching methods

Lecture and class exercises with demonstrative and individual solution of tasks. The teaching is carried out by contact form.

Assessment methods

Written examination and subsequent oral one. One half of possible points in the written part is necessary to pass (usually 25 points of 50 total).

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

Teacher's information

The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

• Enrolment Statistics (Spring 2025, recent)
  
• Permalink: https://is.muni.cz/course/sci/spring2025/M4010