Title: Applied partial differential equations :
Authors: Jeffrey, Alan.
Date: 2002
Publisher: Academic Press,
Physical description: xiv, 394 pages : illustrations ; 23 cm
Language: English
LC classification: Q
Contents: Introduction to Partial Differential Equations -- What Is a Partial Differential Equation? -- Representative Problems Leading to PDEs, Initial and Boundary Conditions -- What Is a Solution of a PDE? -- The Cauchy Problem -- Well-Posed and Improperly Posed Problems -- Coordinate Systems, Vector Operators, and Integral Theorems -- Linear and Nonlinear First-Order Equations and Shocks -- Linear and Semilinear Equations in Two Independent Variables -- Quasi-Linear Equations in Two Independent Variables -- Propagation of Weak Discontinuities by First-Order Equations -- Discontinuous Solutions, Conservation Laws, and Shocks -- Classification of Equations and Reduction to Standard Form -- Classification of PDEs, and Their Reduction to Standard Form -- Classification of Second-Order PDE in Many Independent Variables -- Well-Posed Problems for Hyperbolic, Parabolic, and Elliptic Partial Differential Equations -- Linear Wave Propagation in One or More Space Dimensions -- Linear Waves and the Wave Equation -- The D'Alembert Solution and the Telegraph Equation -- Mixed Initial and Boundary Value Problems for the Wave Equation -- The Poisson Formula for the Wave Equation, the Method of Descent, and the Difference between Waves in Two and Three Space Dimensions -- Kirchhoff's Solution of the Wave Equation in Three Space Variables and Another Representation of Huygens' Principle -- Uniqueness of Solutions of the Wave Equation -- Fourier Series, Legendre and Bessel Functions -- An Introduction to Fourier Series -- Major Results Involving Fourier Series -- A Summary of the Properties of the Legendre and Bessel Differential Equations -- Background to Separation of Variables with Applications -- A General Approach to Separation of Variables -- Properties of Eigenfunctions and Eigenvalues -- Applications of Separation of Variables -- General Results for Linear Elliptic and Parabolic Equations -- General Results for Elliptic and Parabolic Equations -- Laplace Equation -- The Heat Equation -- Self-Similarity Solutions -- Fundamental Solution of the Heat Equation -- Duhamel's Principle -- Hyperbolic Systems, Riemann Invariants, Simple Waves, and Compound Riemann Problems -- Properly Determined First-Order Systems of Equations -- Hyperbolicity and Characteristic Curves -- Riemann Invariants -- Simple Waves -- Shocks and the Riemann Problem.
Subject headings (LCSH): Conservation laws (Mathematics); Differential equations, Partial.; Separation of variables.