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Partial Differential Equations and Boundary Value Problems with Maple

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ISBN-10: 0123747325

ISBN-13: 9780123747327

Edition: 2nd 2009

Authors: George A. Articolo, George A. Articolo

List price: $72.95
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Book details

List price: $72.95
Edition: 2nd
Copyright year: 2009
Publisher: Elsevier Science & Technology
Publication date: 7/22/2009
Binding: Paperback
Pages: 744
Size: 7.75" wide x 9.50" long x 1.25" tall
Weight: 2.486
Language: English

Dr. George A. Articolo has 35 years of teaching experience in physics and applied mathematics at Rutgers University, and has been a consultant for several government research laboratories and aerospace corporations. He has a Ph.D. in mathematical physics with degrees from Temple University and Rensselaer Polytechnic Institute.

Preface
Basic Review
Preparation for Maple Worksheets
Preparation for Linear Algebra
Preparation for Ordinary Differential Equations
Preparation for Partial Differential Equations
Ordinary Linear Differential Equations
Introduction
First-Order Linear Differential Equations
First-Order Initial-Value Problem
Second-Order Linear Differential Equations with Constant Coefficients
Second-Order Linear Differential Equations with Variable Coefficients
Finding a Second Basis Vector by the Method of Reduction of Order
The Method of Variation of Parameters-Second-Order Green's Function
Initial-Value Problem for Second-Order Differential Equations
Frobenius Method of Series Solutions to Ordinary Differential Equations
Series Sine and Cosine Solutions to the Euler Differential Equation
Frobenius Series Solution to the Bessel Differential Equation
Chapter Summary
Exercises
Sturm-Liouville Eigenvalue Problems and Generalized Fourier Series
Introduction
The Regular Sturm-Liouville Eigenvalue Problem
Green's Formula and the Statement of Orthonormality
The Generalized Fourier Series Expansion
Examples of Regular Sturm-Liouville Eigenvalue Problems
Nonregular or Singular Sturm-Liouville Eigenvalue Problems
Chapter Summary
Exercises
The Diffusion or Heat Partial Differential Equation
Introduction
One-Dimensional Diffusion Operator in Rectangular Coordinates
Method of Separation of Variables for the Diffusion Equation
Sturm-Liouville Problem for the Diffusion Equation
Initial Conditions for the Diffusion Equation in Rectangular Coordinates
Example Diffusion Problems in Rectangular Coordinates
Verification of Solutions-Three-Step Verification Procedure
Diffusion Equation in the Cylindrical Coordinate System
Initial Conditions for the Diffusion Equation in Cylindrical Coordinates
Example Diffusion Problems in Cylindrical Coordinates
Chapter Summary
Exercises
The Wave Partial Differential Equation
Introduction
One-Dimensional Wave Operator in Rectangular Coordinates
Method of Separation of Variables for the Wave Equation
Sturm-Liouville Problem for the Wave Equation
Initial Conditions for the Wave Equation in Rectangular Coordinates
Example Wave Equation Problems in Rectangular Coordinates
Wave Equation in the Cylindrical Coordinate System
Initial Conditions for the Wave Equation in Cylindrical Coordinates
Example Wave Equation Problems in Cylindrical Coordinates
Chapter Summary
Exercises
The Laplace Partial Differential Equation
Introduction
Laplace Equation in the Rectangular Coordinate System
Sturm-Liouville Problem for the Laplace Equation in Rectangular Coordinates
Example Laplace Problems in the Rectangular Coordinate System
Laplace Equation in Cylindrical Coordinates
Sturm-Liouville Problem for the Laplace Equation in Cylindrical Coordinates
Example Laplace Problems in the Cylindrical Coordinate System
Chapter Summary
Exercises
The Diffusion Equation in Two Spatial Dimensions
Introduction
Two-Dimensional Diffusion Operator in Rectangular Coordinates
Method of Separation of Variables for the Diffusion Equation in Two Dimensions
Sturm-Liouville Problem for the Diffusion Equation in Two Dimensions
Initial Conditions for the Diffusion Equation in Rectangular Coordinates
Example Diffusion Problems in Rectangular Coordinates
Diffusion Equation in the Cylindrical Coordinate System
Initial Conditions for the Diffusion Equation in Cylindrical Coordinates
Example Diffusion Problems in Cylindrical Coordinates
Chapter Summary
Exercises
The Wave Equation in Two Spatial Dimensions
Introduction
Two-Dimensional Wave Operator in Rectangular Coordinates
Method of Separation of Variables for the Wave Equation
Sturm-Liouville Problem for the Wave Equation in Two Dimensions
Initial Conditions for the Wave Equation in Rectangular Coordinates
Example Wave Equation Problems in Rectangular Coordinates
Wave Equation in the Cylindrical Coordinate System
Initial Conditions for the Wave Equation in Cylindrical Coordinates
Example Wave Equation Problems in Cylindrical Coordinates
Chapter Summary
Exercises
Nonhomogeneous Partial Differential Equations
Introduction
Nonhomogeneous Diffusion or Heat Equation
Initial Condition Considerations for the Nonhomogeneous Heat Equation
Example Nonhomogeneous Problems for the Diffusion Equation
Nonhomogeneous Wave Equation
Initial Condition Considerations for the Nonhomogeneous Wave Equation
Example Nonhomogeneous Problems for the Wave Equation
Chapter Summary
Exercises
Infinite and Semi-infinite Spatial Domains
Introduction
Fourier Integral
Fourier Sine and Cosine Integrals
Nonhomogeneous Diffusion Equation over Infinite Domains
Convolution Integral Solution for the Diffusion Equation
Nonhomogeneous Diffusion Equation over Semi-infinite Domains
Example Diffusion Problems over Infinite and Semi-infinite Domains
Nonhomogeneous Wave Equation over Infinite Domains
Wave Equation over Semi-infinite Domains
Example Wave Equation Problems over Infinite and Semi-infinite Domains
Laplace Equation over Infinite and Semi-infinite Domains
Example Laplace Equation over Infinite and Semi-infinite Domains
Chapter Summary
Exercises
Laplace Transform Methods for Partial Differential Equations
Introduction
Laplace Transform Operator
Inverse Transform and Convolution Integral
Laplace Transform Procedures on the Diffusion Equation
Example Laplace Transform Problems for the Diffusion Equation
Laplace Transform Procedures on the Wave Equation
Example Laplace Transform Problems for the Wave Equation
Chapter Summary
Exercises
References
Index