Lecturer(s)


Fürst Tomáš, RNDr. Ph.D.

Horák Jiří, doc. RNDr. CSc.

Vodák Rostislav, RNDr. Ph.D.

Course content

1. Equations of mathematical physics. 2. Classification of equations of the second order, canonic form of the equations. 3. Derivation of the basic equations of mathematical physics. 4. Wave and heat equations and their fundamental solutions (d'Alembert method and Fourier transform). 5. Fourier method for the wave, heat and Poisson equations. 6. The maximum principle. 7. Uniqueness of solution. 8. Three potentials theorem. 9. Harmonic functions and their properties (the maximum principle, Harnack theorems).

Learning activities and teaching methods

Lecture, Demonstration
 Attendace
 52 hours per semester
 Preparation for the Exam
 40 hours per semester

Learning outcomes

Understand classical approach to PDE's.
Application Apply differential and intergral calculus of functions of several variables in the classic theory of PDEs.

Prerequisites

Understanding the mathematical tools of differential and integral calculus of functions of several variables.
KMA/ODR1

Assessment methods and criteria

Written exam
Credit: the student has to pass one written test (i.e. to obtain at least half of the possible points). Exam: the student has to understand the subject and be able to prove all theorems.

Recommended literature


A. N. Tichonov, A. A. Samarskij. (1955). Rovnice matematické fyziky. ČSAV, Praha.

L. C. Evans. (1998). Partial Differential Equations. University of Berkeley, 1994 a Amer.Math.Soc. Providence.

M. Renardy, R. C. Rogers. (1993). An Introduction to Partial Differential Equations. SpringerVerlag.

O. John, J. Nečas. (1977). Rovnice matematické fyziky. Skripta MFF UK Praha.

S. G. Michlin. (1977). Linějnyje uravněnija v častnych proizvodnych (v ruštině). Vyššaja škola, Moskva.
