Introduction to mathematical physics: William Band, Princeton, N.J., Toronto, London, New York, D. Van Nostrand Co., Inc., 1959, X, 326 pp., ill.

Abstract

1 Infinite Sequences and Series. 1.1 Real and Complex Numbers. 1.2 Convergence of Infinite Series and Products. 1.3 Sequences and Series of Functions. 1.4 Asymptotic Series. 2 Finite-Dimensional Vector Spaces. 2.1 Linear Vector Spaces. 2.2 Linear Operators. 2.3 Eigenvectors and Eigenvalues. 2.4 Functions of Operators. 2.5 Linear Dynamical Systems. 3 Geometry in Physics. 3.1 Manifolds andCoordinates. 3.2 Vectors, Differential Forms, and Tensors. 3.3 Calculuson Manifolds. 3.4 Metric Tensor and Distance. 3.5 Dynamical Systems and Vector Fields. 3.6 Fluid Mechanics. 4 Functions of a Complex Variable. 4.1 Elementary Properties of Analytic Functions. 4.2 Integration in theComplex Plane. 4.3 Analytic Functions. 4.4 Calculus of Residues: Applications. 4.5 Periodic Functions Fourier Series. 5 Differential Equations: Analytical Methods. 5.1 Systems of Differential Equations. 5.2 First-Order Differential Equations. 5.3 Linear Differential Equations. 5.4 Linear Second-Order Equations. 5.5 Legendre's Equation. 5.6 Bessel's Equation. 6 Hilbert Spaces. 6.1 Infinite-Dimensional Vector Spaces. 6.2 Function Spaces Measure Theory. 6.3 Fourier Series. 6.4 Fourier Integral Integral Transforms. 6.5 Orthogonal Polynomials. 6.6 Haar Functions Wavelets. 7 Linear Operators on Hilbert Space. 7.1 Some Hilbert Space Subtleties. 7.2 General Properties of Linear Operators on Hilbert Space. 7.3 Spectrum of Linear Operators on Hilbert Space. 7.4 Linear Differential Operators. 7.5 Linear Integral Operators Green Functions. 8 Partial Differential Equations. 8.1 LinearFirst-OrderEquations. 8.2 The Laplacian and Linear Second-Order Equations. 8.3 Time-Dependent Partial Differential Equations. 8.4 Nonlinear Partial Differential Equations. 9 Finite Groups. 9.1 General Properties of Groups. 9.2 Some Finite Groups. 9.3 The Symmetric Group SN. 9.4 Group Representations. 9.5 Representations of the Symmetric Group SN. 9.6 Discrete Infinite Groups. 10 Lie Groups and Lie Algebras. 10.1 Lie Groups. 10.2 Lie Algebras. 10.3 Representationsof Lie Algebras. Index.