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This highly useful text for students and professionals working in the applied sciences shows how to formulate and solve partial differential equations. Realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems and numerical and approximate methods. Suggestions for further reading. Solution guide available upon request. 1982 edition.
Table of Contents
|Introduction to Partial Differential Equations|
|Diffusion-Type Problems (Parabolic Equations)|
|Boundary Conditions for Diffusion-Type Problems|
|Derivation of the Heat Equation|
|Separation of Variables|
|Transforming Nonhomogeneous BCs into Homogeneous Ones|
|Solving More Complicated Problems by Separation of Variables|
|Transforming Hard Equations into Easier Ones|
|Solving Nonhomogeneous PDEs (Eigenfunction Expansions)|
|Integral Transforms (Sine and Cosine Transforms)|
|The Fourier Series and Transform|
|The Fourier Transform and its Application to PDEs|
|The Laplace Transform|
|The Convection Term u subscript x in Diffusion Problems|
|The One Dimensional Wave Equation (Hyperbolic Equations)|
|The D'Alembert Solution of the Wave Equation|
|More on the D'Alembert Solution|
|Boundary Conditions Associated with the Wave Equation|
|The Finite Vibrating String (Standing Waves)|
|The Vibrating Beam (Fourth-Order PDE)|
|Classification of PDEs (Canonical Form of the Hyperbolic Equation)|
|The Wave Equation in Two and Three Dimensions (Free Space)|
|The Finite Fourier Transforms (Sine and Cosine Transforms)|
|Superposition (The Backbone of Linear Systems)|
|First-Order Equations (Method of Characteristics)|
|Nonlinear First-Order Equations (Conservation Equations)|
|Systems of PDEs|
|The Vibrating Drumhead (Wave Equation in Polar Coordinates)|
|The Laplacian (an intuitive description)|
|General Nature of Boundary-Value Problems|
|Interior Dirichlet Problem for a Circle|
|The Dirichlet Problem in an Annulus|
|Laplace's Equation in Spherical Coordinates (Spherical Harmonics)|
|A Nonhomogeneous Dirichlet Problem (Green's Functions)|
|Numerical and Approximate Methods|
|Numerical Solutions (Elliptic Problems)|
|An Explicit Finite-Difference Method|
|An Implicit Finite-Difference Method (Crank-Nicolson Method)|
|Analytic versus Numerical Solutions|
|Classification of PDEs (Parabolic and Elliptic Equations)|
|Monte Carlo Methods (An Introduction)|
|Monte Carlo Solutions of Partial Differential Equations)|
|Calculus of Variations (Euler-Lagrange Equations)|
|Variational Methods for Solving PDEs (Method of Ritz)|
|Perturbation method for Solving PDEs|
|Conformal-Mapping Solution of PDEs|
|Answers to Selected Problems|
|Integral Transform Tables|
|PDE Crossword Puzzle|
|Laplacian in Different Coordinate Systems|
|Types of Partial Differential Equations|
|Table of Contents provided by Publisher. All Rights Reserved.|