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Partial Differential Equations for Scientists and Engineers
by Stanley J. FarlowEdition:
Reprint
ISBN13:
9780486676203
ISBN10:
048667620X
Format:
Trade Paper
Pub. Date:
9/1/1993
Publisher(s):
Dover Publications
List Price: $19.15
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Summary
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 | |
| Introduction to Partial Differential Equations | |
| Diffusion-Type Problems | |
| 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 | |
| Duhamel's Principle | |
| The Convection Term u subscript x in Diffusion Problems | |
| Hyperbolic-Type 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) | |
| Dimensionless Problems | |
| 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) | |
| Elliptic-Type Problems | |
| 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 | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
