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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
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. |