457-0308/02 – Equations of Mathematical Physics (RMFPM)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. RNDr. Marek Lampart, Ph.D.Subject version guarantordoc. RNDr. Marek Lampart, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2003/2004Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA04 Mgr. Bohumil Krajc, Ph.D.
LAM05 doc. RNDr. Marek Lampart, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

The main aim of the subject is to formulate classical partial differential equations motivated by physical phenomena and to use classical methods for their solutions.

Teaching methods

Lectures
Individual consultations
Tutorials

Summary

This course is devoted to the analytical methods of the solution of the partial differentia equations. All the methods will give us fruitful imagination of the qualitative behavior of the mathematical modeling. This information will be very useful tor the future modeling of more complicated problems. During this course there will be given standard set of the classical partial differential equations and their properties. Also stability and uniqueness will be discussed.

Compulsory literature:

P. Drábek, G. Holubová: Parciální diferenciální rovnice (Úvod do klasické teorie). Skripta ZČU Plzeň, 2001. J. Franců: Parciální diferenciální rovnice. Skripta VUT Brno, 2000. S. Míka, A. Kufner: Parciální diferenciální rovnice I. Stacionární rovnice. Edice MVŠT, sešit XX, SNTL Praha, 1983. J. Barták, L. Herrmann, V. Lovicar, O. Vejvoda: Parciální diferenciální rovnice II. Evoluční rovnice. Edice MVŠT, sešit XXI, SNTL Praha, 1988. W. A. Strauss: Partial Differential Equations (An Introduction), John Wiley & Sons, Inc., New York 1992.

Recommended literature:

Textbook for students of the PDE.

Way of continuous check of knowledge in the course of semester

Study control: There will be tests and projects needed for a credit. Conditions for the credit: Student will pass a credit if all projects are submitted on time

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Talks: First order equations, Cauchy problem, characteristic equations. Cauchy problem for equations of higher degrees. Classification equations of the second order. Formulation of the classical equations given by physical phenomenon (formulation boundary and initial conditions) like: heat eq., diffusion eq., wave eq., Laplace and Poisson eq., etc. Solution by method of characteristic. Solution by Fourier method. Solution by integral transformations. Solution by Green function. Maximal principle and uniqueness of solution. Solution by method of potentials. Seminars: Examples of solutions of the classical partial differential equations, compare PDE and ODE. Classification of the equations, reduction to the canonical form. Formulation of the classical type eq and their boundary and initial conditions. Solution of several eq. by characteristic method. Solution of several eq. by Fourier method. Solution of several eq. by Green functions. Application of the Green function. Solution of the uniqueness problem of the eq. Solution of several eq. using potentials. Solution of several eq. by using mathematical software. Projects: Students will solve standard problems based on typical equations and their applications.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Examination Examination 70  0
        Exercises evaluation Credit 30 (30) 10
                1. Písemka Written test 15  0
                2. Písemka Written test 15  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner