516-0873/01 – Selected Chapters of Mathematical Physics I (VKMFI)
Gurantor department | Institute of Physics | Credits | 5 |
Subject guarantor | RNDr. Eva Janurová, Ph.D. | Subject version guarantor | RNDr. Eva Janurová, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 2 | Semester | winter |
| | Study language | Czech |
Year of introduction | 2003/2004 | Year of cancellation | 2014/2015 |
Intended for the faculties | HGF | Intended for study types | Bachelor |
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
Other requirements
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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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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