714-0521/01 – Mathematical Methods in Physics (MMF)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | doc. RNDr. Jaroslav Vlček, CSc. | Subject version guarantor | doc. RNDr. Jaroslav Vlček, CSc. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | 3 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 1999/2000 | Year of cancellation | 2010/2011 |
| Intended for the faculties | HGF | Intended for study types | Follow-up Master |
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
Other requirements
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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