516-0874/01 – Selected Chapters of Mathematical Physics II (VKMFII)

Gurantor departmentInstitute of PhysicsCredits5
Subject guarantordoc. RNDr. Richard Dvorský, Ph.D.Subject version guarantordoc. RNDr. Richard Dvorský, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semestersummer
Study languageCzech
Year of introduction2003/2004Year of cancellation2014/2015
Intended for the facultiesHGFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
DVO54 doc. RNDr. Richard Dvorský, 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 12+0

Subject aims expressed by acquired skills and competences

Deepen their understanding of mathematical methods in describing complex physical probléme Define and characterize the basic mathematical concepts in the field of vector analysis and tenzor analysis Solve the fundamental problems with the applications of differential equations of mathematical physics

Teaching methods

Individual consultations
Tutorials

Summary

The aim of reciting problemes, in sequence on the subject CHOSOSED CHAPTERS FROM MATHEMATIC FYSICS I, is to introduce listeners with basics of vectorial and tensor analysis, with problems of using diferenciál equations in fysics and problems of thé function and operators in Gilberts space. Structure of thé subject is specialized on ephesizing fysical motivation, leading to use particular mathematic applience.

Compulsory literature:

[1] Kvasnica J.: Matematický aparát fyziky. Academia 1997 (in Czech) [2] Rektorys K. a spol.: Základy užité matematiky. SNTL 1968 (in Czech)

Recommended literature:

[3] Arsenin V.A.: Matematická fyzika. Alfa 1977 (in Czech)

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Systematic off-class preparation.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1 Vector and tensor ANALYSIS 1.1 Cartesian coordinates in space E3, their transformations and invariants, Einstein summation convention (opak.) 1.2 General curvilinear coordinates, covariant and contravariant coordinates vectors (opak.) 1.3 Tensors in E3, their algebra, reduction of order tensor contractions tensor invariants 1.4 Physical field as a scalar, vector or tensor function argument vector in E3 1.5 Derivation of three-dimensional tensor fields, increase and decrease tensor order derivatives 6.1 Differential operator "nabla" as gradient "grad" field 1.7 Differential divergence operator as a "wonder" field 8.1 Differential rotation operator as "rot" vector field 1.9 Laplace differential operator of second order "Delta" 1.10 Gauss divergence theorem the vector field 1.11 Stokes theorem on the rotation of the vector field 1.12 Directional and substancionální derivation, a generalized balance equation (Continuity) 2. Differential Equations in Physics 2.1 Description of physical phenomena, methods of infinitesimal calculus, compilation differential equations based on analysis of physical phenomena 2.2 Newton's equation of motion - movement in the field scalar potential 3.2 Newton's equation of motion - an oscillator, damped and forced oscillations 4.2 Diffusion equation 2.5 Heat equation 6.2 Euler's equation 2.7 Stokes equations 8.2 Laplace equation 2.9 Wave equation 2.10 Schödingerova wave equations - harmonic oscillator 3. FUNCTIONS as vectors in a Hilbert space 3.1 The development function in an infinite number of known elementary functions, Cauch and d'Alembertovo convergence criterion 3.2 Taylor expansion of functions 3.3 Fourier development functions, Fourier integral and Fourier transform 3.4 Geometric interpretation of the development - based on vector elementary functions Hilbert space, symbolism Dirackova 3.5 Operators in Hilbert space commutation relations, the matrix elements 3.6 Eigenvalues ​​and operator functions

Conditions for subject completion

Full-time form (validity from: 2012/2013 Winter semester, validity until: 2014/2015 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
        Exercises evaluation Credit 33 (33) 17
                Project Project 33  17
        Examination Examination 67 (67) 34
                Written examination Written examination 30  15
                Oral Oral examination 37  19
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2014/2015 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner