714-0925/04 – Classical Methods of Solution of Partial Differential Equations (PDR)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantordoc. RNDr. Jarmila Doležalová, CSc.Subject version guarantordoc. RNDr. Jarmila Doležalová, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Web linkhttp://mdg.vsb.czStudy languageCzech
Year of introduction2013/2014Year of cancellation
Intended for the facultiesFEI, FS, HGF, USP, FMMI, FBI, FASTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 20+0
Combined Examination 20+0

Subject aims expressed by acquired skills and competences

Main study goals: (i) to be acquainted with actual progress in this mathematical discipline, (ii) to extend needed theoretical knowledge with emphasized orientation to its applicability, (iii) to increase communication ability of specialists in different branches. With regard to professional orientation of students learning themes modification is offered to fulfill presented aims.

Teaching methods

Lectures
Individual consultations
Tutorials
Project work

Summary

Fourier series: orthogonal functions, Fourier coefficients, even and odd functions, convergence of the Fourier series, complex form, solution of second order linear differential equations. Partial differential equations: general discussion, first-order and second- order partial differential equations (initial and boundary conditions, methods of solution), second-order linear partial differential equations (method of the characteristics, method of separation of variables), the wave equation, the heat-conduction equation, the Laplace equation, Maxwell's equations.

Compulsory literature:

James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

Recommended literature:

James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 Strauss, W.A.: Partial differential equations : an introduction. New York : Wiley, 1992 - ix. ISBN 0-471-54868-5

Way of continuous check of knowledge in the course of semester

Každý student musí vypracovat program na dohodnuté téma. Zkouška Písemná část spočívá ve vyřešení 3 příkladů (Fourierova řada, PDR I. řádu, PDR II. řádu) Teoretická část spočívá v obhajobě programu.

E-learning

Další požadavky na studenta

Each student must discharge: a) examples, b) project.

Minimální znalostní požadavky

Prerequisities

Subject has no prerequisities.

Co-requisities

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

Prezenční form (validity from: 2013/2014 zimní semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Zkouška Zkouška  
Rozsah povinné účasti:

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