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Course: Equations of Mathematical Physics

Department/Abbreviation: OPT/RMFY

Year: 2021

Guarantee: 'prof. Mgr. Jaromír Fiurášek, Ph.D.'

Annotation: Introductory course on equations of mathematical physics. Students shall become familiar with the classification and properties of linear partial differential equations of second order and with the methods how to solve them.

Course review:
1) Derivation of selected equations of mathematical physics 2) Partial differential equations of first order 3) Classification of second-order linear partial differential equations, transformation to canonical form 4) Types of problems according to the initial and boundary conditions 5) Solution of wave equation, d'Alembert formula, Poisson formula, Kirchhoff formula 6) Principle of superposition and its application to construction of solution of PDEs 7) Cauchy problem for heat transport equation, integral transform method 8) Green function method 9) Harmonic functions, the maximum principle 10) Method of potentials, volume potential, surface potentials 11) Numerical solutions of PDEs 12) Finite elements method