470-4112/01 – 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 graduateRequirementChoice-compulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KAL0063 prof. RNDr. René Kalus, Ph.D.
KRA04 Mgr. Bohumil Krajc, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time 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: Assigned home tasks. Conditions for the credit: At least 20 points gained.

E-learning

Other requirements

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Part-time form (validity from: 2010/2011 Winter semester, validity until: 2021/2022 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30 (30) 10
                1. Písemka Written test 15  0
                2. Písemka Written test 15  0
        Examination Examination 70  35 3
Mandatory attendence participation: Presentation of assigned tasks at the seminar.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics MFA K Czech Ostrava 1 Compulsory study plan
2022/2023 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics MFA P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics MFA P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics MFA K Czech Ostrava 1 Compulsory study plan
2020/2021 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics MFA K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics MFA P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics MFA P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics MFA K Czech Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2021/2022 Winter
2019/2020 Winter
2018/2019 Winter
2017/2018 Winter
2015/2016 Winter
2014/2015 Winter
2012/2013 Winter