714-0521/01 – Mathematical Methods in Physics (MMF)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantordoc. RNDr. Jaroslav Vlček, CSc.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year3Semestersummer
Study languageCzech
Year of introduction1999/2000Year of cancellation2010/2011
Intended for the facultiesHGFIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2

Subject aims expressed by acquired skills and competences

Students learn structural approach to mathematical formulation and solving of problems in mathematical physics, namely to analyze given problem and formulate mathematical task, to choose and correctly use appropriate mathematical method. Mathematical tools of vector analysis and partial differential equations are emphasized.

Teaching methods

Lectures
Individual consultations
Tutorials
Project work

Summary

Mathematical modelling of physical and engineering problems. Classical methods of the solution are based on Fourier series and integral transforms. Main topics: - principles of mathematical modelling, - first order partial differential equations (PDE), method of the characteristics, - boundary problems of second order PDE.

Compulsory literature:

KEENER, J.P.: Principles of Applied Mathematics. Adison-Wesley Publ., 1988

Recommended literature:

JAMES, G.: Advanced Modern Engineering Mathematics. Adison-Wesley Publ., 1995 (2.díl) MATHEMATICAL MODELLING (Ed. M.S. Klamkin). SIAM, 1989 FRIEDMAN, A. - LITTMAN, W.: Industrial Mathematics. SIAM, 1994

Way of continuous check of knowledge in the course of semester

Course-credit: -participation on tutorials is obligatory, 20% of absence can be apologized, -pass the written test (30 points), Point classification: 0-30 points. Exam Semestral thesis classified by 25 – 50 points. Theoretical part of the exam is classified by 0 - 20 points.

E-learning

www.mdg.vsb.cz

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Mathematical modeling of engineering problems: general principles, classification and mathematical formulation. 2. 1st order PDE: Cauchy problem, method of characteristics. 3. 2nd order PDE: Cauchy problem, boundary problems and theit typology. 4. Elliptic equations Laplace and Poisson eq., Fourier separation,conformal mapping and complex potential. 5. Parabolic equations: transport and relaxation problems, applications of integral tansforms. 6. Hyperbolic equations: harmonic oscilations, wave equation, eigenvalue spectrum. 7. Existence and uniqueness of solution.

Conditions for subject completion

Full-time form (validity from: 1996/1997 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 60 (60) 0
                Obhajoba projektu Semestral project 50  25
                Teorie Oral examination 10  0
        Exercises evaluation Credit 40 (40) 0
                Písemný test Written test 40  26
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2004/2005 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 3 Choice-compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 3 Choice-compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 3 Choice-compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 3 Choice-compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 3 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner