310-4001/01 – Classical Methods of Solution of Partial Differential Equations (PDR)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFS, FBI, FEI, FMT, HGF, USP, FASTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
KUC14 prof. RNDr. Radek Kučera, Ph.D.
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:

Strauss, W.A.: Partial differential equations: an introduction. New York: Wiley, 1992. ISBN 0-471-54868-5

Way of continuous check of knowledge in the course of semester

Each student has to create a project on a given topic. Exam Writen part consits of solving three examples (Fourier series, first-order PDE, second-order PDE) The theoretical part consists of defending the program.

E-learning

hhttp://www1.maths.leeds.ac.uk/~kersale/Teach/M3414/Notes/m3414_1.pdftp://mathworld.wolfram.com/PartialDifferentialEquation.html https://arxiv.org/pdf/1901.03022.pdf

Další požadavky na studenta

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

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 PI, 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

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

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2019/2020 (P2346) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

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