Partial Differential Equations for Scientists and Engineers
ISBN: 9780486676203 | 048667620X
Edition: ReprintFormat: Trade Paper
Publisher: Dover Publications
Pub. Date: 9/1/1993
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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.
Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type pro... MORE
Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type pro... MORE
| 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 Se... MORE | |
| 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. |
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