Mathematics of classical and quantum physics/ Frederick W. Byron, Robert W. Fuller.

1 Vectors in Classical Physics; Introduction; 1.1 Geometric and Algebraic Definitions of a Vector; 1.2 The Resolution of a Vector into Components; 1.3 The Scalar Product; 1.4 Rotation of the Coordinate System: Orthogonal Transformations; 1.5 The Vector Product; 1.6 A Vector Treatment of Classical Orbit Theory; 1.7 Differential Operations on Scalar and Vector Fields; *1.8 Cartesian-Tensors; 2 Calculus of Variations; Introduction; 2.1 Some Famous Problems; 2.2 The Euler-Lagrange Equation; 2.3 Some Famous Solutions. 2.4 Isoperimetric Problems --
Constraints2.5 Application to Classical Mechanics; 2.6 Extremization of Multiple Integrals; *2.7 Invariance Principles and Noether's Theorem; 3 Vectors and Matrices; Introduction; 3.1 Groups. Fields. and Vector Spaces; 3.2 Linear Independence; 3.3 Bases and Dimensionality; 3.4 Isomorphisms; 3.5 Linear Transformations; 3.6 The Inverse of a Linear Transformation; 3.7 Matrices; 3.8 Determinants; 3.9 Similarity Transformations; 3.10 Eigenvalues and Eigenvectors; *3.11 The Kronecker Product; 4 Vector Spaces in Physics; Introduction; 4.1 The Inner Product. 4.2 Orthogonality and Completeness4.3 Complete Orthonormal Sets; 4.4 Self-Adjoint (Hermitian and Symmetric) Transformations; 4.5 Isometries-Unitary and Orthogonal Transformations; 4.6 The Eigenvalues and Eigenvectors of Self-Adjoint and Isometric Transformations; 4.7 Diagonalization; 4.8 On the Solvability of Linear Equations; 4.9 Minimum Principles; 4.10 Normal Modes; 4.11 Perturbation Theory-Nondegenerate Case; *4.12 Perturbation Theory-Degenerate Case; 5 Hilbert Space-Complete Orthonormal Sets of Functions; Introduction; 5.1 Function Space and Hilbert Space. 5.2 Complete Orthonormal Sets of Functions5.3 The Dirac <U+0065>-Function; 5.4 Weierstrass's Theorem: Approximation by Polynomials; 5.5 Legendre Polynomials; 5.6 Fourier Series; 5.7 Fourier Integrals; 5.8 Spherical Harmonics and Associated Legendre Functions; 5.9 Hermite Polynomials; 5.10 Sturm-Liouville Systems-Orthogonal Polynomials; 5.11 A Mathematical Formulation of Quantum Mechanics; 6 Elements and Applications of the Theory of Analytic Functions; Introduction; 6.1 Analytic Functions-The Cauchy-Riemann Conditions; 6.2 Some Basic Analytic Functions. 6.3 Complex Integration-The Cauchy-Goursat Theorem6.4 Consequences of Cauchy's Theorem; 6.5 Hilbert Transforms and the Cauchy Principal Value; 6.6 An Introduction to Dispersion Relations; 6.7 The Expansion of an Analytic Function in a Power Series; 6.8 Residue Theory-Evaluation of Real Definite Integrals and Summation of Series; 6.9 Applications to Special Functions and Integral Representations; 7 Green's Functions; Introduction; 7.1 A New Way to Solve Differential Equations; 7.2 Green's Functions and Delta Functions; 7.3 Green's Functions in One Dimension.