310-3143/02 – Partial Differential Equations (PDR)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Study languageEnglish
Year of introduction2019/2020Year of cancellation2021/2022
Intended for the facultiesFSIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

The course deals with mathematical modeling based on equations of mathematical physics. Students will acquire advanced knowledge and skills of given parts of mathematics adapted to the needs of practical modeling in engineering practice. The course focuses on classical methods of solving problems expressed by partial differential equations.

Teaching methods

Individual consultations
Project work


Studenti se seznámí s Fourierovými řadami a s klasickými metodami řešení parciálních diferenciálních rovnic. V první kapitole jsou probírány Fourierovy řady v rozsahu potřebném pro další výuku. Ve druhé kapitole se studenti velmi stručně seznámí s parciálními diferenciálními rovnicemi prvního řádu. Teorie parciálních diferenciálních rovnic druhého řádu je zaměřena na Fourierovu metodu separace proměnných a metodu charakteristik. Jádro předmětu je v řešení lineárních parciálních diferenciálních rovnic druhého řádu (Laplaceova rovnice, vlnová rovnice, rovnice vedení tepla).

Compulsory literature:

James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993

Recommended literature:

Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.

Way of continuous check of knowledge in the course of semester

Set of homework examples, credit test, oral exam.



Other requirements

Set of homework examples, credit test, oral exam.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

Syllabus of lecture 1. Fourier series: periodic functions, Fourier coefficients, functions of the period 2, function of the period T, even and odd functions 2. Even and odd functions, half - range cosine and sine series, convergence of Fourier series 3. Solution of 2nd order linear differential equations with constant coefficients by Fourier series 4. Partial differential equations: general discussion 5. Methods of solutions of partial differential equations of the first order 6. Methods of solutions of partial differential equations of the second order 7. Fourier´s method of separation 8. 2nd order partial linear differential equations 9. Canonical form of 2nd order partial linear differential equations 10. Laplace equation: separated solutions, boundary conditions 11. Solution of the one-dimensional wave equation: d’Alembert solution, method of the separation of variables, 12. Solution of a boundary problem 13. Solution of the heat-conduction: one dimensional heat conduction equation, separation method. 14. Reserve

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

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Occurrence in special blocks

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Assessment of instruction

Předmět neobsahuje žádné hodnocení.