Publisher Description

This book provides a comprehensive collection of problems together with their detailed solutions in the field of Theoretical and Mathematical Physics. All modern fields in Theoretical and Mathematical Physics are covered. It is the only book which covers all the new techniques and methods in theoretical and mathematical edition updated with: Exercises in: Hilbert space theory, Lie groups, Matrix-valued differential forms, Bose-Fermi operators and string theory. All other chapters have been updated with new problems and materials. Most chapters contain an introduction to the subject discussed in the text.

Table of Contents

Volume I: Complex Numbers and Functions; Sums and Product; Discrete Fourier Transform; Algebraic and Transcendental Equations; Vector and Matrix Calculations; Matrices and Groups; Matrices and Eigenvalue Problems; Functions of Matrices; Transformations; L'Hospital's Rule; Lagrange Multiplier Method; Linear Difference Equations; Linear Differential Equations; Integration; Continuous Fourier Transform; Complex Analysis; Special Functions; Inequalities; Functional Analysis; Combinatorics; Convex Sets and Functions; Optimization; Volume II: Groups; Kronecker and Tensor Products; Nambu Mechanics; Gateaux and Frechet Derivatives; Stability and Bifurcations; Nonlinear Ordinary Difference Equations; Nonlinear Ordinary Differential Equations; Lax Representations in Classical Mechanics; Hilbert Spaces; Generalized Functions; Linear Partial Differential Equations; Nonlinear Partial Differential Equations; Symmetries and Group Theoretical Reductions; Soliton Equations; Backlund Transformations; Lax Pairs for Partial Differential Equations; Hirota Technique; Painleve Test; Lie Algebras; Lie Groups; Differential Forms; Matrix-Valued Differential Forms; Lie Derivative; Metric Tensor Fields; Killing Vector Fields; Inequalities; Ising Model and Heisenberg Model; Number Theory; Combinatorial Problems; Fermi Operators; Bose Operators; Bose-Fermi Systems; Lax Representations and Bethe Ansatz; Gauge Transformations; Chaos, Fractals and Complexity.

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