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Partial Differential Equations for Scientists and Engineers

by
Edition:
Reprint
ISBN13:

9780486676203

ISBN10:
048667620X
Format:
Paperback
Pub. Date:
9/1/1993
Publisher(s):
Dover Publications
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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.

Author Biography

Partial Differential Equations & Beyond
Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers is one of the most widely used textbooks that Dover has ever published. Readers of the many Amazon reviews will easily find out why. Jerry, as Professor Farlow is known to the mathematical community, has written many other fine texts — on calculus, finite mathematics, modeling, and other topics. We followed up the 1993 Dover edition of the partial differential equations title in 2006 with a new edition of his An Introduction to Differential Equations and Their Applications. Readers who wonder if mathematicians have a sense of humor might search the internet for a copy of Jerry's The Girl Who Ate Equations for Breakfast (Aardvark Press, 1998).

Critical Acclaim for Partial Differential Equations for Scientists and Engineers:
"This book is primarily intended for students in areas other than mathematics who are studying partial differential equations at the undergraduate level. The book is unusual in that the material is organized into 47 semi-independent lessonsrather than the more usual chapter-by-chapter approach.

"An appealing feature of the book is the way in which the purpose of each lesson is clearly stated at the outset while the student will find the problems placed at the end of each lesson particularly helpful. The first appendix consists of integral transform tables whereas the second is in the form of a crossword puzzle which the diligent student should be able to complete after a thorough reading of the text.

"Students (and teachers) in this area will find the book useful as the subject matter is clearly explained. The author and publishers are to be complimented for the quality of presentation of the material." — K. Morgan, University College, Swansea

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.


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