Course detail
Equations of Mathematical Physics I
FSI-9RF1Acad. year: 2024/2025
Partial differential equations - preliminaries. First order equations.
Classification and canonical form of the second order equations Derivation of selected equations of mathematical physics, formulation of initial and boundary value problems.
Classical methods: method of characteristics, Fourier series method, integral transform method, Green function method. Maximum principles.
Properties of the solutions to elliptic, parabolic and hyperbolic equations.
Language of instruction
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
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.
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
Evans, L. C.: Partial differential equations, American Math. Society Providence 1998. (EN)
Sobolev, S. L.: Partial differential equations of mathematical physics Pergamon Press, Oxford 1964 (EN)
T. A. Bick: Elementary boundary value problems. Marcel Dekker, New York 1993 (EN)
Williams, W. E.: Partial Differential Equations, Clarendon Press, Oxford 1980. (EN)
Recommended reading
J. Franců: Parciální diferenciální rovnice. Akad. nakl. CERM, Brno 2011 (CS)
Renardy, M., Rogers, R., C.: An introduction to partial differential equations, Springer, New York 2004. (EN)
V. J. Arsenin: Matematická fyzika, Alfa, Bratislava 1977 (SK)
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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.