Dover Publications Inc. Mathematical Methods in Physics and Engineering

PrefaceCHAPTER 1. Linear Algebra1.1 Linear Equations. Summation Convention1.2 Matrices1.3 Determinants1.4 Systems of Linear Algebraic Equations. Rank of a Matrix1.5 Vector Spaces1.6 Scalar Product1.7 Orthonormal Basis. Linear Transformations1.8 Quadratic Forms. Hermitian Forms1.9 Systems of Ordinary Differential Equations. Vibration Problems1.10 Linear ProgrammingCHAPTER 2. Hilbert Spaces2.1 Infinite-dimensional Vector Spaces. Function Spaces2.2 Fourier Series2.3 Separable Hilbert Spaces2.4 The Projection Theorem2.5 Linear Functionals2.6 Weak Convergence2.7 Linear Operators2.8 Completely Continuous OperatorsCHAPTER 3. Calculus of Variations3.1 Maxima and Minima of Functions. Lagrange Multipliers3.2 Maxima and Minima of Functionals. Euler's Equation3.3 Hamilton's Principle. Lagrange's Equations3.4 Theory of Small Vibrations3.5 The Vibrating String3.6 Boundary-value Problems of Mathematical Physics3.7 Eigenvalues and Eigenfunctions3.8 Eigenfunction Expansions3.9 Upper and Lower Bounds for EigenvaluesCHAPTER 4. Boundary-value Problems. Separation of Variables4.1 Orthogonal Coordinate Systems. Separation of Variables4.2 Sturm-Liouville Problems4.3 Series Solutions of Ordinary Differential Equations4.4 Series Solutions of Boundary-value ProblemsCHAPTER 5. Boundary-value Problems. Green's Functions5.1 Nonhomogeneous Boundary-value Problems5.2 One-dimensional Green's Functions5.3 Generalized Functions5.4 Green's Functions in Higher Dimensions5.5 Problems in Unbounded Regions5.6 A Problem in Diffraction TheoryCHAPTER 6. Integral Equations6.1 Integral-equation Formulation of Boundary-value Problems6.2 Hilbert-Schmidt Theory6.3 Fredholm Theory6.4 Integral Equations of the First KindCHAPTER 7. Analytic Function Theory7.1 Introduction7.2 Analytic Functions7.3 Elementary Functions7.4 Complex Integration7.5 Integral Representations7.6 Sequences and Series7.7 Series Representations of Analytic Functions7.8 Contour Integration7.9 Conformal Mapping7.10 Potential TheoryCHAPTER 8. Integral Transform Methods8.1 Fourier Transforms8.2 Applications of Fourier Transforms. Ordinary Differential Equations8.3 Applications of Fourier Transforms. Partial Differential Equations8.4 Applications of Fourier Transforms. Integral Equations8.5 Laplace Transforms. Applications8.6 Other Transform TechniquesIndex