Lecturer(s)


Sedlák Michal, Mgr. Ph.D.

Fiurášek Jaromír, doc. Mgr. Ph.D.

Course content

1. Partial differential equations in physics, wave equation, equation heat conduction, the Helmholtz equation, Schrödinger equation 2. Initial and boundary conditions, classification problems for linear partial Differential Equations 2nd Procedure 3. Dirac delta function, generalized functions 4. Generalized functions of slow growth 5. Fourier and Laplace transform of generalized functions 6. Use of generalized functions to solve equations of mathematical physics 7. Fundamental solutions, Green's function 8. Volume potential, the potential of single and double layer 9. Analytical solutions of the equations of mathematical physics in Mathematica 10. Numerical solutions of the equations of mathematical physics in Matlab

Learning activities and teaching methods

Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Preparation for the Exam
 58 hours per semester
 Homework for Teaching
 70 hours per semester
 Attendace
 52 hours per semester

Learning outcomes

Advanced course in equations of mathematical physics. Students will become familiar with the theory of generalized functions and their application in solving partial differential equations.
Knowledge of theory of generalized functions and ability to apply these advanced mathematical tools to finding solutions to partial differential equations. Ability to define main concepts and describe main methods and approaches, ability to apply the theoretical knowledge when solving specific problems.

Prerequisites

Knowledge of mathematical analysis, algebra and theory of integral transforms at the level of bachelor study of mathematics.

Assessment methods and criteria

Oral exam
Attendance of exercises is obligatory, attendance of lectures is voluntary but recommended. Course credit prior to examination is awarded for attendance at the exercises and for solving sets of homework probelems. Oral exam covers the tought topics as specified in the Content.

Recommended literature


Čihák, P. a kol. (2003). Matematická analýza pro fyziky (V). Praha.

Dont, M. (2008). Úvod do parciálních diferenciálních rovnic. Praha.

Franců, J. (2003). Parciální diferenciální rovnice. Brno.

Vladimirov, V.S. (1971). Equations of Mathematical Physics. Marcel Dekker, New York.
