Course detail

Partial Differential Equations

FSI-SPDAcad. year: 2025/2026

Partial differential equations - basic concepts and mathematical models.
Linear first-order equations - methods of characteristics and characteristic coordinates. Linear second-order equations - classification and transformation to canonical form. Derivation of selected equations in mathematical physics (heat conduction, string vibration), formulation of initial and boundary value problems. Laplace and Poisson equations - solving boundary value problems. Methods of integral transformations, Green's function method, and maximum principles.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Mgr. Zdeněk Opluštil, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

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

Rules for evaluation and completion of the course

To obtain course credit, one must pass one written test successfully. The exam grade consists of a written and an oral part.

Aims

The course aims are to introduce students to partial differential equations, their fundamental properties, and their applications in mathematical modeling. Students will learn to formulate initial and boundary value problems that model selected specific physical situations. Another objective is to familiarize students with classical solution methods and teach them how to solve simple problems related to equations of mathematical physics.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

G. F. Carrier, C.E. Pearson: Partial differential equations,
L. C. Evans: Partial Differential Equations, AMS, Providence 1998
V. J. Arsenin: Matematická fyzika, Alfa, Bratislava 1977
W. E. Williams: Partial differential equations,

Recommended reading

J. Franců: Parciální diferenciální rovnice, skripta FSI VUT, CERM 2011 (CS)
J. Škrášek, Z. Tichý: Základy aplikované matematiky II, SNTL, Praha 1986 (CS)
K. Rektorys: Přehled užité matematiky II., Prometheus 1995 (CS)
V. J. Arsenin: Matematická fyzika, Alfa, Bratislava 1977. (SK)

Classification of course in study plans

  • Programme B-MAI-P Bachelor's 3 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Zdeněk Opluštil, Ph.D.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Zdeněk Opluštil, Ph.D.

Syllabus

There will be no distinction between exercises and lectures. According to the topic being covered, examples will be solved in real time.