Ordinary and Partial Differential Equations: With Special Fucntions, Fourier Series, and Boundary Value Problems

 

Preface.- Solvable Differential Equations.- Second Order Differential Equations.- Preliminaries to Series Solutions.- Solution at an Ordinary Point.- Solution at a Singular Point.- Solution at a Singular Point (Continued).- Legendre Polynomials and Functions.- Chebyshev, Hermite and Laguerre Polynomials.- Bessel Functions.- Hypergeometric Functions.- Piecewise Continuous and Periodic Functions.- Orthogonal Functions and Polynomials.- Orthogonal Functions and Polynomials (Continued).- Boundary Value Problems.- Boundary Value Problems (Continued).- Green’s Functions.- Regular Perturbations.- Singular Perturbations.- Sturm-Liouville Problems.- Eigenfunction Expansions.- Eigenfunction Expansions (Continued).- Convergence of the Fourier Series.- Convergence of the Fourier Series (Continued).- Fourier Series Solutions of Ordinary Differential Equations.- Partial Differential Equations.- First-Order Partial Differential Equations.- Solvable Partial Differential Equations.- The Canonical Forms.- The Method of Separation of Variables.- The One-Dimensional Heat Equation.- The One-Dimensional Heat Equation (Continued).- The One-Dimensional Wave Equation.- The One-Dimensional Wave Equation (Continued).- Laplace Equation in Two Dimensions.- Laplace Equation in Polar Coordinates.- Two-Dimensional Heat Equation.- Two-Dimensional Wave Equation.- Laplace Equation in Three Dimensions.- Laplace Equation in Three Dimensions (Continued).- Nonhomogeneous Equations.- Fourier Integral and Transforms.- Fourier Integral and Transforms (Continued).- Fourier Transform Method for PDEs.- Fourier Transform Method for PDEs (Continued).- Laplace Transforms.- Laplace Transforms (Continued).- Laplace Transform Method for ODEs.- Laplace Transform Method for PDEs.- Well-Posed Problems.- Verification of Solutions.- References for Further Reading.- Index.