470-4112/02 – Equations of Mathematical Physics (RMFPM)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorMgr. Bohumil Krajc, Ph.D.Subject version guarantorMgr. Bohumil Krajc, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA04 Mgr. Bohumil Krajc, Ph.D.
VLA04 Ing. Oldřich Vlach, 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 10+10

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:

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

There are not defined other requirements for student.

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

Combined form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan
2019/2020 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics P English Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner