Partial Differential Equations for Scientists and Engineers

by Farlow, Stanley J.

• ISBN13: 9780486676203
• ISBN10: 048667620X
• Edition: Reprint
• Format: Paperback
• Copyright: 1993-09-01
• Publisher: Dover Publications

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.