516-0873/01 – Selected Chapters of Mathematical Physics I (VKMFI)

Gurantor departmentInstitute of PhysicsCredits5
Subject guarantorRNDr. Eva Janurová, Ph.D.Subject version guarantorRNDr. Eva Janurová, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2003/2004Year of cancellation2014/2015
Intended for the facultiesHGFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
JAN85 RNDr. Eva Janurová, 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

Define and reproduse the chosen terms of linear algebra, analytic geometry, differential geometry, vector and tensor algebra Apply the acquired knowledges for solving of simple physical applications

Teaching methods

Lectures
Tutorials

Summary

The knowledges of mathematics and physics for bachelors are completed in this subject. The students are got acquainted with advantages of linear algebra, analytic and diferential geometry, vector and tenzor algebra and mathematical statistics for mathematical description of physical phenomena.

Compulsory literature:

1. Kvasnica, J.: Mathematical Physics. Academia, Prague 1989 2. Dettman, JW: Mathematical Methods in Physics and Engineering. Academia, Prague 1970 3. Madelung, E.: Handbook of Mathematics for Physicists. Alfa, Bratislava 1975

Recommended literature:

Rektorys, K.: Overview of applied mathematics. Prometheus, Prague, 1995

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

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Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1st ALGEBRA Complex numbers. Linear dependence and independence of variables. Matrix, equality of matrix, n times the matrix. Transposed, symmetric and antisymmetric, complex conjugate, associated hermitian matrix. The sum, difference, linear combinations, multiplication of matrices. Trace of matrix. Inverse, regular and singular, unitary matrix. Rank of a matrix. Solving systems of linear equations. Matrix of systems, extended matrix of systems. Frobenius´s theorem. Determinants, minor, algebraic complement. 2nd ANALYSIS AND DIFFERENTIAL GEOMETRY Coordinate systems in plane and space, orthogonal curvilinear coordinate systems. Basic curves. Basic areas. The geometry of curves - tangent, principal normal, binormal. 3rd VECTOR AND TENSOR ALGEBRA Transformation of coordinates. Scalars, vectors and tensors. Contraction of tensors and invariants of tensors. Scalar, vector, mixed, and double cross product of vectors. Configuration and phase space. Complex vectors.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

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