Czech

prof. RNDr. Jan Franců, CSc.

Institute of Mathematics

Solution of algebraic equations and system of linear equations, differential and integral calculus of functions of one and more variables, ordinary differential equations.

The examination consists of a practical and a theoretical part.
Practical part: solving examples of P.D.E.:
1) solution of the 1st order equation,
2) classification and transformation of the 2nd order equation to its canonical form,
3) formulation of an initial boundary value problem related to the physical setting
and finding its solution by means of the Fourier series method.
Theoretical part: 3 questions from the theory of P.D.E.
Absence has to be made up by self-study using lecture notes.

The aim of the subject is to provide students with the basic knowledge
of the partial differential equations, particularly equations of
mathematical physics, their basic properties, methods of solving them
and their application in mathematical modelling. Another goal is to teach
the students to formulate and solve the basic problems of mathematical physics.
Elements of the theory of P.D.E. and survey of their application in mathematical modelling. Ability to formulate mathematical model of the selected problems of mathematical physics and to compute the solution in some simple cases.

Programme D-FIN-P: Physical Engineering and Nanotechnology, Doctoral, recommended course

Programme D-FIN-K: Physical Engineering and Nanotechnology, Doctoral, recommended course

20 hours, optionally

prof. RNDr. Jan Franců, CSc.

1 Introduction, 1st order equations.
2 Classification of 2nd order equations.
3-4 Derivation of selected equations of mathematical physics and formulation of initial and boundary value problems.
5 Method of characteristics.
6 Fourier series method.
7 Integral transform method.
8 Green function method.
9 Maximum principles and harmonic functions.
10 Survey of properties of the solutions to hyperbolic, parabolic and elliptic equations.