Partial Differential Equations and Mathematica

Kythe, Prem K.; Puri, Pratap; Schaferkotter, Michael R.

ISBN 10: 0849378532 / ISBN 13: 9780849378539

Editore: CRC Press, USA, 1997

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Titolo: Partial Differential Equations and ...

Casa editrice: CRC Press, USA

Data di pubblicazione: 1997

Legatura: paperback

Condizione: New

Edizione: First Edition.

Tipologia articolo: Used

Descrizione articolo

Riassunto:

This new book on partial differential equations provides a more accessible treatment of this demanding subject. There is a need to introduce technology into math courses; therefore, the authors integrate the use of Mathematica throughout the book, rather than just providing a few sample problems at the ends of chapters. Although the text is rich in theory and develops the underlying mathematical analysis, it emphasizes the development of methods. Numerous examples in every chapter present the techniques that are representative of virtually every concept in the book. And unlike other textbooks, the answers, hints, and solutions to all exercises are provided on the spot. Partial Differential Equations and Mathematica provides both the basic concepts and the methods for beginners, while also providing training and encouragement for those who plan to continue their studies in the subject itself or in applied areas. This is a textbook that is challenging and instructive, but at the same time, reasonable in its demands.

Contenuti:

Chapter 1: Introduction
Notation and Definitions
Initial and Boundary Conditions
Classification of Second Order Equations
Some Known Equations
Superposition Principle
Exercises
Chapter 2: 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 Theorem on Characteristics
Second Order Equations
Linear and Quasi-linear Equations
Exercises
Chapter 3: Linear Equations with Constant Coefficients
Inverse Operators
Homogeneous Equations
Nonhomogeneous Equations
Exercises
Chapter 4: Orthogonal Expansions
Orthogonality
Orthogonal Polynomials
Series of Orthogonal Functions
Trigonometric Fourier Series
Eigenfunction Expansions
Bessel Functions
Exercises
Chapter 5: Separation of Variables
Introduction
Hyperbolic Equation
Parabolic Equation
Elliptic Equation
Cylindrical Coordinates
Spherical Coordinates
Nonhomogeneous Problems
Exercises
Chapter 6: Integral Transforms
Laplace Transforms
Notation
Basic Laplace Transforms
Inversion Theorem
Exercises
Fourier Transforms
Fourier Integral Theorems
Properties of Fourier Transforms
Fourier Sine and Cosine Transforms
Finite Fourier Transforms
Exercises
Chapter 7: Green's Functions
Definitions
Parabolic Equations
Elliptic Equations
Hyperbolic Equations
Applications
Exercises
Chapter 8: Weighted Residual Methods
Line Integrals
Variational Notation
Multiple Integrals
Weak Variational Formulation
Galerkin Method
Rayleigh-Ritz Method
Choice of Test Functions
Transient Problems
Other Methods
Exercises
Chapter 9: Perturbation Methods
Taylor Series Expansions
Successive Approximations
Boundary Perturbations
Exercises
Chapter 10: Finite Differences
Finite Difference Schemes
First Order Equations
Second Order Equations
Exercises
Appendix A: Green's Identities
Green's Identities
Exercises
Appendix B: Tables of Transform Pairs
Appendix C: Glossary of Mathematica Functions
Appendix D: Mathematica Packages and Notebooks
Bibliography
Index