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Edition: 4TH 04

Copyright: 2004

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

Copyright: 2004

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

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Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics.

Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations.

Features

- NEW--Pattern formation for reaction-diffusion equations and the Turing instability--Includes interesting applications such as lift and drag past circular cylinder, reflection and refraction of electromagnetic (light) and acoustic (sound) waves, scattering, dispersive waves, wave guides, fiber optics, and pattern formation.
- NEW--Well-done treatment of numerical methods for PDE--Includes Finite difference methods, Fourier-von Newmann stability analysis, heat equation, wave equation, Laplace's equation, and Finite element method (Introduction).
- NEW--Presentation of derivation of the diffusion of a pollutant--With new exercises deriving PDEs from conservation laws.
- Provides instructors with the option early in the text, of a more concise derivation of the one dimensional heat equation.

- NEW--Improved discussion on time dependent heat equations.
- Shows students how the time dependent heat equation evolves in time to the steady state temperature distribution.

- NEW--Similarity solution for ht heat equation added.
- Provides students with a concise discussion of similarity solution.

- NEW--Green's Functions for Wave and Heat Equations chapter updated.
- Provides students with a presentation of elegant derivations of infinite space Green's functions for heat and wave equations.

- NEW--Traffic flow model presentation updated--i.e. Expansion wave problem and traffic show wave problem added.
- Provides students with the somewhat longer description of the traffic flow model.

- NEW--Shock waves chapter expanded--i.e. Additional derivation of the shock velocity presented; diffusive conservation laws introduced; presentations improved on the initiation of a shock and the formation of caustics for the characteristic.
- Provides students with improved material on shock waves.

- NEW--Curved and rainbow caustics discussion updated.
- NEW--Stability of systems of ordinary differential equation--Including eigenvalues of the Jacobian matrix and bifurcations to motivate stability of PDE.
- Provides students with an expanded presentation on system stability.

- NEW--Wave envelope equations--e.g. Two-dimensional effects and the modulational instability.
- Provides students with new material and a brief derivation of the partial differential equation corresponding to a long wave instability.

- Leads readers step-by-step from simple exercises to increasingly powerful mathematical techniques for solving more complicated and realistic physical problems.
- Eases students into the material so that they can build on their knowledge base.
- Heat flow and vibrating strings and membranes.
- Enables students to understand the relationships between mathematics and the physical problems.
- Emphasizes examples and problem solving.
- Provides students with a thorough and reasoned approach to problem solving, stressing understanding.
- Physical and mathematical derivations addressed carefully.
- Ensures students are aware of assumptions being made.
- Clear and lively writing style.
- Engages students and clearly explains details and ideas with patience and sustained enthusiasm.
- 1000 carefully prepared exercises with varying levels of difficulty and answers to selected exercises in the back of the book.
- Allows instructors flexibility in the selection of material.
- Provides students with background necessary to move on to harder exercises.
- Important pedagogical features--More than 200 figures; equations and statements are frequently boxed; Paragraphs titled in bold; Important formulas are made into tables; and inside covers include important tabulated information.
- Provides students with many well-organized and useful study aids.

**Haberman, Richard : Southern Methodist University**

**1. Heat Equation. 2. Method of Separation of Variables. 3. Fourier Series. 4. Vibrating Strings and Membranes. 5. Sturm-Liouville Eigenvalue Problems. 6. Finite Difference Numerical Methods for Partial Differential Equations. 7. Partial Differential Equations with at Least Three Independent Variables. 8. Nonhomogeneous Problems. 9. Green's Functions for Time-Independent Problems. 10. Infinite Domain Problems--Fourier Transform Solutions of Partial Differential Equations. 11. Green's Functions for Wave and Heat Equations. 12. The Method of Characteristics for Linear and Quasi-Linear Wave Equations. 13. A Brief Introduction to Laplace Transform Solution of Partial Differential Equations. 14. Topics: Dispersive Waves, Stability, Nonlinearity, and Perturbation Methods. **

Bibliography.

Selected Answers to Starred Exercises.

Index.

Summary

Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics.

Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations.

Features

- NEW--Pattern formation for reaction-diffusion equations and the Turing instability--Includes interesting applications such as lift and drag past circular cylinder, reflection and refraction of electromagnetic (light) and acoustic (sound) waves, scattering, dispersive waves, wave guides, fiber optics, and pattern formation.
- NEW--Well-done treatment of numerical methods for PDE--Includes Finite difference methods, Fourier-von Newmann stability analysis, heat equation, wave equation, Laplace's equation, and Finite element method (Introduction).
- NEW--Presentation of derivation of the diffusion of a pollutant--With new exercises deriving PDEs from conservation laws.
- Provides instructors with the option early in the text, of a more concise derivation of the one dimensional heat equation.

- NEW--Improved discussion on time dependent heat equations.
- Shows students how the time dependent heat equation evolves in time to the steady state temperature distribution.

- NEW--Similarity solution for ht heat equation added.
- Provides students with a concise discussion of similarity solution.

- NEW--Green's Functions for Wave and Heat Equations chapter updated.
- Provides students with a presentation of elegant derivations of infinite space Green's functions for heat and wave equations.

- NEW--Traffic flow model presentation updated--i.e. Expansion wave problem and traffic show wave problem added.
- Provides students with the somewhat longer description of the traffic flow model.

- NEW--Shock waves chapter expanded--i.e. Additional derivation of the shock velocity presented; diffusive conservation laws introduced; presentations improved on the initiation of a shock and the formation of caustics for the characteristic.
- Provides students with improved material on shock waves.

- NEW--Curved and rainbow caustics discussion updated.
- NEW--Stability of systems of ordinary differential equation--Including eigenvalues of the Jacobian matrix and bifurcations to motivate stability of PDE.
- Provides students with an expanded presentation on system stability.

- NEW--Wave envelope equations--e.g. Two-dimensional effects and the modulational instability.
- Provides students with new material and a brief derivation of the partial differential equation corresponding to a long wave instability.

- Leads readers step-by-step from simple exercises to increasingly powerful mathematical techniques for solving more complicated and realistic physical problems.
- Eases students into the material so that they can build on their knowledge base.
- Heat flow and vibrating strings and membranes.
- Enables students to understand the relationships between mathematics and the physical problems.
- Emphasizes examples and problem solving.
- Provides students with a thorough and reasoned approach to problem solving, stressing understanding.
- Physical and mathematical derivations addressed carefully.
- Ensures students are aware of assumptions being made.
- Clear and lively writing style.
- Engages students and clearly explains details and ideas with patience and sustained enthusiasm.
- 1000 carefully prepared exercises with varying levels of difficulty and answers to selected exercises in the back of the book.
- Allows instructors flexibility in the selection of material.
- Provides students with background necessary to move on to harder exercises.
- Important pedagogical features--More than 200 figures; equations and statements are frequently boxed; Paragraphs titled in bold; Important formulas are made into tables; and inside covers include important tabulated information.
- Provides students with many well-organized and useful study aids.

Author Bio

**Haberman, Richard : Southern Methodist University**

Table of Contents

**1. Heat Equation. 2. Method of Separation of Variables. 3. Fourier Series. 4. Vibrating Strings and Membranes. 5. Sturm-Liouville Eigenvalue Problems. 6. Finite Difference Numerical Methods for Partial Differential Equations. 7. Partial Differential Equations with at Least Three Independent Variables. 8. Nonhomogeneous Problems. 9. Green's Functions for Time-Independent Problems. 10. Infinite Domain Problems--Fourier Transform Solutions of Partial Differential Equations. 11. Green's Functions for Wave and Heat Equations. 12. The Method of Characteristics for Linear and Quasi-Linear Wave Equations. 13. A Brief Introduction to Laplace Transform Solution of Partial Differential Equations. 14. Topics: Dispersive Waves, Stability, Nonlinearity, and Perturbation Methods. **

Bibliography.

Selected Answers to Starred Exercises.

Index.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

Published: 2004

International: No

Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics.

Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations.

Features

- NEW--Pattern formation for reaction-diffusion equations and the Turing instability--Includes interesting applications such as lift and drag past circular cylinder, reflection and refraction of electromagnetic (light) and acoustic (sound) waves, scattering, dispersive waves, wave guides, fiber optics, and pattern formation.
- NEW--Well-done treatment of numerical methods for PDE--Includes Finite difference methods, Fourier-von Newmann stability analysis, heat equation, wave equation, Laplace's equation, and Finite element method (Introduction).
- NEW--Presentation of derivation of the diffusion of a pollutant--With new exercises deriving PDEs from conservation laws.
- Provides instructors with the option early in the text, of a more concise derivation of the one dimensional heat equation.

- NEW--Improved discussion on time dependent heat equations.
- Shows students how the time dependent heat equation evolves in time to the steady state temperature distribution.

- NEW--Similarity solution for ht heat equation added.
- Provides students with a concise discussion of similarity solution.

- NEW--Green's Functions for Wave and Heat Equations chapter updated.
- Provides students with a presentation of elegant derivations of infinite space Green's functions for heat and wave equations.

- NEW--Traffic flow model presentation updated--i.e. Expansion wave problem and traffic show wave problem added.
- Provides students with the somewhat longer description of the traffic flow model.

- NEW--Shock waves chapter expanded--i.e. Additional derivation of the shock velocity presented; diffusive conservation laws introduced; presentations improved on the initiation of a shock and the formation of caustics for the characteristic.
- Provides students with improved material on shock waves.

- NEW--Curved and rainbow caustics discussion updated.
- NEW--Stability of systems of ordinary differential equation--Including eigenvalues of the Jacobian matrix and bifurcations to motivate stability of PDE.
- Provides students with an expanded presentation on system stability.

- NEW--Wave envelope equations--e.g. Two-dimensional effects and the modulational instability.
- Provides students with new material and a brief derivation of the partial differential equation corresponding to a long wave instability.

- Leads readers step-by-step from simple exercises to increasingly powerful mathematical techniques for solving more complicated and realistic physical problems.
- Eases students into the material so that they can build on their knowledge base.
- Heat flow and vibrating strings and membranes.
- Enables students to understand the relationships between mathematics and the physical problems.
- Emphasizes examples and problem solving.
- Provides students with a thorough and reasoned approach to problem solving, stressing understanding.
- Physical and mathematical derivations addressed carefully.
- Ensures students are aware of assumptions being made.
- Clear and lively writing style.
- Engages students and clearly explains details and ideas with patience and sustained enthusiasm.
- 1000 carefully prepared exercises with varying levels of difficulty and answers to selected exercises in the back of the book.
- Allows instructors flexibility in the selection of material.
- Provides students with background necessary to move on to harder exercises.
- Important pedagogical features--More than 200 figures; equations and statements are frequently boxed; Paragraphs titled in bold; Important formulas are made into tables; and inside covers include important tabulated information.
- Provides students with many well-organized and useful study aids.

**Haberman, Richard : Southern Methodist University**

**1. Heat Equation. 2. Method of Separation of Variables. 3. Fourier Series. 4. Vibrating Strings and Membranes. 5. Sturm-Liouville Eigenvalue Problems. 6. Finite Difference Numerical Methods for Partial Differential Equations. 7. Partial Differential Equations with at Least Three Independent Variables. 8. Nonhomogeneous Problems. 9. Green's Functions for Time-Independent Problems. 10. Infinite Domain Problems--Fourier Transform Solutions of Partial Differential Equations. 11. Green's Functions for Wave and Heat Equations. 12. The Method of Characteristics for Linear and Quasi-Linear Wave Equations. 13. A Brief Introduction to Laplace Transform Solution of Partial Differential Equations. 14. Topics: Dispersive Waves, Stability, Nonlinearity, and Perturbation Methods. **

Bibliography.

Selected Answers to Starred Exercises.

Index.