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Full Description
This book, translated from Russian, is a comprehensive guide to mathematical methods in physics, offering theoretical insights and problem-solving techniques. Authored by experienced physicists, it is suitable for self-study and has been effectively used in fields such as theoretical physics, plasma physics, and hydrodynamics. The English edition aims to equip readers with the skills to master modern mathematical methods applicable to different physical problems.
Contents
1 Linear Operators
1.1 Finite Dimensional Space
1.2 Functionals and Generalized Functions
1.3 Hilbert Space and Completeness
1.4 Self-Adjoint Operators
1.5 Ket- and Bra- Vectors
2 Method of Characteristics
2.1 Linear First-Order PDE
2.2 Quasilinear Equation
2.3 System of Equations
3 Second-Order Linear Equations
3.1 Canonical Form
3.2 Curvilinear Coordinates
3.3 Separation of Variables
3.4 Fourier Method
4 Self-Similarity and Nonlinear Equations
4.1 Symmetry of Equations
4.2 Nonlinear Equations
5 Special Functions
5.1 Singular Points
5.2 Hypergeometric Functions
5.3 Orthogonal Polynomials
6 Asymptotic Methods
6.1 Asymptotic Power Series
6.2 A Laplace Integral
6.3 Method of Stationary Phase
6.4 Method of Steepest Descents
6.5 The Averaging Method
7 Green's Functions Method
7.1 Green's Functions
7.2 Continuous Spectrum
7.3 Resolvent
8 Integral Equations
8.1 Fredholm Equations
8.2 Degenerate Kernel
8.3 Symmetric Kernel
8.4 Inverse Problem for Schrödinger Operator
9 Groups and Representations
9.1 Groups
9.2 Representations
10 Continuous Groups
10.1 Lie Groups and Algebras
10.2 Representations of the Rotation Group
11 Group Theory in Physics
11.1 Molecular Oscillations
11.2 Level Splitting
11.3 Selection Rules
11.4 Invariant Tensors
