Mathematical Methods in Physics 390-FS2-1MMF
Elements of differential geometry: vectors, kovytectors, covariant derivative, differential operators (laplassian, rotation, divergence) in any coordinate system.
Elements of complex analysis. Holomorphic functions, singular points, residue theorem. Basic information about conformal mappings, Euler's gamma function and elliptic functions.
Ordinary differential equations of the second order with variable coefficients. The Frobenius method (solution by series expansion). Basic information about the Bessel equation, the Fuchs equation and the hypergeometric series.
Classical orthogonal polynomials. Generating functions. Spherical harmonics.
Hilbert space. Integral operators. The operator's spectrum. Distributions. Convolution. Fourier series. Fourier transformation.
The boundary and initial problem for different types of partial differential equations of the second order. Basic information about methods of solving these equations, such as separation of variables, Fourier transform, or Green functions.
Type of course
Course coordinators
Learning outcomes
Student:
1. He learns advanced methods of higher mathematics necessary for in-depth study of physics and related disciplines.
2. Can apply the methods of higher mathematics to the problems of physical and natural sciences.
3. Gains calculation efficiency and the ability to use mathematical tools to set and solve physical problems.
4. Learns the concepts and computational techniques necessary to solve partial differential equations.
5. Can use a computer (Mathematica environment or other software of this type) to find mathematical tools and use them in practice.
6. Uses advanced mathematical language to describe physical reality.
7. Has computational efficiency in solving simple partial differential equations
Additional information
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