Solution techniques for elementary partial differential equations / Christian Constanda.

Includes bibliographical references and index.

-- Contents Foreword Preface to the Second Edition Preface to the First Edition Chapter 1 Ordinary Differential Equations: Brief Review 1.1 First-Order Equations 1.2 Homogeneous Linear Equations with Constant Coefficients 1.3 Nonhomogeneous Linear Equations with Constant Coefficients 1.4 Cauchy-Euler Equations 1.5 Functions and Operators Exercises Chapter 2 Fourier Series 2.1 The Full Fourier Series 2.2 Fourier Sine Series 2.3 Fourier Cosine Series 2.4 Convergence and Differentiation Exercises Chapter 3 Sturm---Liouville Problems 3.1 Regular Sturm---Liouville Problems 3.2 Other Problems 3.3 Bessel Functions 3.4 Legendre Polynomials 3.5 Spherical Harmonics Exercises Chapter 4 Some Fundamental Equations of Mathematical Physics 4.1 The Heat Equation 4.2 The Laplace Equation 4.3 The Wave Equation 4.4 Other Equations Exercises Chapter 5 The Method of Separation of Variables 5.1 The Heat Equation 5.2 The Wave Equation 5.3 The Laplace Equation 5.4 Other Equations 5.5 Equations with More than Two Variables Exercises Chapter 6 Linear Nonhomogeneous Problems 6.1 Equilibrium Solutions 6.2 Nonhomogeneous Problems Exercises Chapter 7 The Method of Eigenfunction Expansion 7.1 The Heat Equation 7.2 The Wave Equation 7.3 The Laplace Equation 7.4 Other Equations Exercises Chapter 8 The Fourier Transformations 8.1 The Full Fourier Transformation 8.2 The Fourier Sine and Cosine Transformations 8.3 Other Applications Exercises Chapter 9 The Laplace Transformation 9.1 Definition and Properties 9.2 Applications Exercises Chapter 10 The Method of Green's Functions 10.1 The Heat Equation 10.2 The Laplace Equation 10.3 The Wave Equation Exercises Chapter 11 General Second-Order Linear Partial Differential Equations with Two Independent Variables 11.1 The Canonical Form 11.2 Hyperbolic Equations 11.3 Parabolic Equations 11.4 Elliptic Equations Exercises Chapter 12 The Method of Characteristics 12.1 First-Order Linear Equations 12.2 First-Order Quasilinear Equations 12.3 The One-Dimensional Wave Equation 12.4 Other Hyperbolic Equations Exercises Chapter 13 Perturbation and Asymptotic Methods 13.1 Asymptotic Series 13.2 Regular Perturbation Problems 13.3 Singular Perturbation Problems Exercises Chapter 14 Complex Variable Methods 14.1 Elliptic Equations 14.2 Systems of Equations Exercises Answers to Odd-Numbered Exercises Appendix Bibliography Index