Solution techniques for elementary partial differential equations

Abstract

Ordinary Differential Equations: Brief Revision First-Order Equations Homogeneous Linear Equations with Constant Coefficients Nonhomogeneous Linear Equations with Constant Coefficients Cauchy-Euler Equations Functions and Operators Fourier Series The Full Fourier Series Fourier Sine Series Fourier Cosine Series Convergence and Differentiation Sturm-Liouville Problems Regular Sturm-Liouville Problems Other Problems Bessel Functions Legendre Polynomials Spherical Harmonics Some Fundamental Equations of Mathematical Physics The Heat Equation The Laplace Equation The Wave Equation Other Equations The Method of Separation of Variables The Heat Equation The Wave Equation The Laplace Equation Other Equations Equations with More than Two Variables Linear Nonhomogeneous Problems Equilibrium Solutions Nonhomogeneous Problems The Method of Eigenfunction Expansion The Heat Equation The Wave Equation The Laplace Equation Other Equations The Fourier Transformations The Full Fourier Transformation The Fourier Sine and Cosine Transformations Other Applications The Laplace Transformation Definition and Properties Applications The Method of Green's Functions The Heat Equation The Laplace Equation The Wave Equation General Second-Order Linear Partial Differential Equations with Two Independent Variables The Canonical Form Hyperbolic Equations Parabolic Equations Elliptic Equations The Method of Characteristics First-Order Linear Equations First-Order Quasilinear Equations The One-Dimensional Wave Equation Other Hyperbolic Equations Perturbation and Asymptotic Methods Asymptotic Series Regular Perturbation Problems Singular Perturbation Problems Complex Variable Methods Elliptic Equations Systems of Equations Answers to Odd-Numbered Exercises Appendix Bibliography Index Exercises appear at the end of each chapter.