Mathematical Methods of Physics: Problems with Solutions

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.

Table of 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

About the Author :
Igor V. Kolokolov is a Russian physicist known for his work on magnetism, soft matter physics and statistical hydrodynamics. He is professor at the Physical Department at Higher School of Economics, Moscow, and Director of Landau Institute of Theoretical Physics, Chernogolovka, Russia. Evgeny A. Kuznetsov is a Russian physicist known for his work on nonlinear physics, soliton stability theory, and Hamiltonian formalism for nonlinear waves. He is a member of the Russian Academy of Sciences (RAS), professor at the Moscow Institute of Physics and Technology, and a principal researcher at the Tamm Theoretical Physics Department of the Lebedev Physics Institute of the RAS. Alexander I. Milstein is a Russian physicist, specialist in theoretical elementary particle physics, nuclear and atomic physics, head of the Theoretical Department at Budker Institute of Nuclear Physics, and professor at Novosibirsk State University (NSU). Evgeny V. Podivilov is a Russian physicist known for his work on nonlinear optics and nonlinear interactions of waves in fibers. He is a professor at NSU and a principal researcher at the Institute of Automation and Electrometry of the RAS. Alexander I. Chernykh holds a PhD in physics and mathematics and is engaged in numerical modeling. He has taught various subjects, including methods of mathematical physics, analytical mechanics, statistical physics, and general theory of relativity. David A. Shapiro is a Russian physicist. He is professor at NSU and heads the Photonics Laboratory at the Institute of Automation and Electrometry of the RAS. His current research interests include fiber optics, nanophotonics, and plasma physics. Elena G. Shapiro holds a PhD in physics and mathematics. In 1985, she became a member of the Institute of Automation and Electrometry of the RAS. She had been teaching undergraduate students at the Physics Department of NSU since 1988.

Review :
“An excellent collection of problems and their solutions with elements of theory to accompany the university course on mathematical methods of physics. It covers a broad variety of topics ranging from linear operators, differential and integral equations, special functions, and Green functions to group theory and their applications in physics. The book is recommended to students, PhD students, researchers, and teachers.” Prof. Boris Konopelchenko University of Salento, Italy