2nd Edition
Partial Differential Equations and Mathematica
Early training in the elementary techniques of partial differential equations is invaluable to students in engineering and the sciences as well as mathematics. However, to be effective, an undergraduate introduction must be carefully designed to be challenging, yet still reasonable in its demands. Judging from the first edition's popularity, instructors and students agree that despite the subject's complexity, it can be made fairly easy to understand.
Revised and updated to reflect the latest version of Mathematica, Partial Differential Equations and Boundary Value Problems with Mathematica, Second Edition meets the needs of mathematics, science, and engineering students even better. While retaining systematic coverage of theory and applications, the authors have made extensive changes that improve the text's accessibility, thoroughness, and practicality.
New in this edition:
With its emphasis firmly on solution methods, this book is ideal for any mathematics curricula. It succeeds not only in preparing readers to meet the challenge of PDEs, but also in imparting the inherent beauty and applicability of the subject.
Introduction
Conventions
Getting Started
File Manipulation
Differential Equations
To the Instructor
To the Student
MathSource
INTRODUCTION
Notation and Definitions
Initial and Boundary Conditions
Classification of Second Order Equations
Some Known Equations
Superposition Principle
METHOD OF CHARACTERISTICS
First Order Equations
Linear Equations with Constant Coefficients
Linear Equations with Variable Coefficients
First Order Quasi-Linear Equations
First Order Nonlinear Equations
Geometrical Considerations
Some Theorems on Characteristics
Second Order Equations
Linear and Quasi-linear Equations
LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS
Inverse Operators
Homogeneous Equations
Nonhomogeneous Equations
ORTHOGONAL EXPANSIONS
Orthogonality
Orthogonal Polynomials
Series of Orthogonal Functions
Trigonometric Fourier Series
Eigenfunction Expansions
Bessel Functions
SEPARATION OF VARIABLES
Introduction
Hyperbolic Equations
Parabolic Equations
Elliptic Equations
Cylindrical Coordinates
Spherical Coordinates
Nonhomogeneous Problems
INTEGRAL TRANSFORMS
Laplace Transforms
Notation
Basic Laplace Transforms
Inversion Theorem
Fourier Transforms
Fourier Integral Theorems
Properties of Fourier Transforms
Fourier Sine and Cosine Transforms
Finite Fourier Transforms
GREEN'S FUNCTIONS
Generalized Functions
Green's Functions
Elliptic Equations
Parabolic Equations
Hyperbolic Equations
Applications of Green's Functions
Computation of Green's Functions
BOUNDARY VALUE PROBLEMS
Initial and Boundary Conditions
Implicit Conditions
Periodic Conditions
Wave Propagation and Dispersion
Boundary Layer Flows
Miscellaneous Problems
WEIGHTED RESIDUAL METHODS
Line Integrals
Variational Notation
Multiple Integrals
Weak Variational Formulation
Gauss-Jacobi Quadrature
Rayleigh-Ritz Method
Choice of Test Functions
Transient Problems
Other Methods
PERTURBATION METHODS
Perturbation Problem
Taylor Series Expansions
Successive Approximations
Boundary Perturbations
Fluctuating Flows
FINITE DIFFERENCE METHODS
Finite Difference Schemes
First Order Equations
Second Order Equations
Appendix A: Green's Identities
Appendix B: Orthogonal Polynomials
Appendix C: Tables of Transform Pairs
Appendix D: Glossary of Mathematica Functions
Appendix E: Mathematica Packages and Notebooks
Bibliography
Index
Each chapter also contains sections of Mathematica Projects and Exercises
Biography
Kythe, Prem K.; Schäferkotter, Michael R.; Puri, Pratap
