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Differential Equations and Linear Algebra, 3/E
C. Henry Edwards
David E. Penney, University of Georgia, Athens

ISBN-10: 0136054250
ISBN-13:  9780136054252

Publisher:  Pearson
Copyright:  2010
Format:  Cloth; 792 pp
Published:  10/10/2008
Status: Instock


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Description

For courses in Differential Equations and Linear Algebra.

Acclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this text discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. In the Third Edition, new graphics and narrative have been added as needed—yet the proven chapter and section structure remains unchanged, so that class notes and syllabi will not require revision for the new edition.


Features

• NEW! Key sections have been extensively rewritten with a fresh qualitative approach, particularly in Chapters 1, 5, 7, 8, 10.

• NEW! Chapter 5 (Higher-Order Linear Differential Equations) is significantly enhanced, including:
—New explanation of signs and directions of internal forces in mass-spring systems (page 288);
—New introduction of differential operators and clarification of the algebra of polynomial operators (page 317);
—New introduction and illustration of polar exponential forms of complex numbers (page 322).

• NEW! An expanded discussion of Laplace-transform existence theorem and its extension includes the jump discontinuities that play an important role in many practical applications (page 597–598)


COMPUTING
• Almost 600 computer-generated figures show students vivid pictures of direction fields, solution curves, and phase plane portraits that bring symbolic solutions of differential equations to life.

• About 3 dozen application modules follow key sections throughout. Most outline "technology neutral" investigations illustrating the use of technical computing systems and seek to actively engage students in the application of new technology.

• A fresh numerical emphasis is afforded by the early introduction of numerical solution techniques in Chapter 2 (on mathematical models and numerical methods). Includes numerical algorithms presented in parallel fashion for systems ranging from graphing calculators to MATLAB.

• A conceptual perspective shaped by the availability of computational aids permits a leaner and more streamlined coverage of certain traditional symbolic methods (like exact equations and variation of parameters) in Chapters 1 and 5.


PEDAGOGY
• Offering the best problems sets in any Differential Equations and Linear Algebra textbook, Edwards/Penney includes 300 new or updated problems for this revision.
—Computer-generated graphics throughout the text and answers section show students vivid pictures of slope fields, solution curves, and phase plane portraits that portray the qualitative features of symbolic solutions of differential equations.

• Application modules following key sections throughout the text encourage conceptual development and further use of computer algebra systems like Maple, Mathematica, and MATLAB (at the choice of students and instructors) to actively engage students in the application of new technology.

• The accompanying Applications Manual expands and enhances the text's applications material through technology, and provides detailed coverage of Maple, Mathematica, and MATLAB techniques.

• The text's Companion Web Site presents the projects in the form of interactive Maple, Mathematica, and MATLAB notebooks and worksheets, and also provides generic direction field and phase plane software for student use.

• The accompanying Instructor’s Solutions Manual augments the problem material in the text; student version also available.


New To This Edition

• Key sections have been extensively rewritten with a fresh qualitative approach, particularly in Chapters 1, 5, 7, 8, 10.

• Revised material throughout includes enhanced exposition in every chapter, and in many individual sections of the text for improved student understanding of key concepts.
—The solid class-tested chapter and section structure of the book is unchanged, so class notes and syllabi will not require revision for the new edition.

• Chapter 5 (Higher-Order Linear Differential Equations) is significantly enhanced, including:
—New explanation of signs and directions of internal forces in mass-spring systems (page 288);
—New introduction of differential operators and clarification of the algebra of polynomial operators (page 317);
—New introduction and illustration of polar exponential forms of complex numbers (page 322).

• An expanded discussion of Laplace-transform existence theorem and its extension includes the jump discontinuities that play an important role in many practical applications (page 597–598)


Table of Contents

CHAPTER 1. First-Order Differential Equations
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substitution Methods and Exact Equations

CHAPTER 2. Mathematical Models and Numerical Methods
2.1 Population Models
2.2 Equilibrium Solutions and Stability
2.3 Acceleration–Velocity Models
2.4 Numerical Approximation: Euler's Method
2.5 A Closer Look at the Euler Method
2.6 The Runge–Kutta Method

CHAPTER 3. Linear Systems and Matrices
3.1 Introduction to Linear Systems
3.2 Matrices and Gaussian Elimination
3.3 Reduced Row-Echelon Matrices
3.4 Matrix Operations
3.5 Inverses of Matrices
3.6 Determinants
3.7 Linear Equations and Curve Fitting

CHAPTER 4. Vector Spaces
4.1 The Vector Space R3
4.2 The Vector Space Rn and Subspaces
4.3 Linear Combinations and Independence of Vectors
4.4 Bases and Dimension for Vector Spaces
4.5 Row and Column Spaces
4.6 Orthogonal Vectors in Rn
4.7 General Vector Spaces

CHAPTER 5. Higher-Order Linear Differential Equations
5.1 Introduction: Second-Order Linear Equations
5.2 General Solutions of Linear Equations
5.3 Homogeneous Equations with Constant Coefficients
5.4 Mechanical Vibrations
5.5 Nonhomogeneous Equations and Undetermined Coefficients
5.6 Forced Oscillations and Resonance

CHAPTER 6. Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues
6.2 Diagonalization of Matrices
6.3 Applications Involving Powers of Matrices

CHAPTER 7. Linear Systems of Differential Equations
7.1 First-Order Systems and Applications
7.2 Matrices and Linear Systems
7.3 The Eigenvalue Method for Linear Systems
7.4 Second-Order Systems and Mechanical Applications
7.5 Multiple Eigenvalue Solutions
7.6 Numerical Methods for Systems

CHAPTER 8. Matrix Exponential Methods
8.1 Matrix Exponentials and Linear Systems
8.2 Nonhomogeneous Linear Systems
8.3 Spectral Decomposition Methods

CHAPTER 9. Nonlinear Systems and Phenomena
9.1 Stability and the Phase Plane
9.2 Linear and Almost Linear Systems
9.3 Ecological Models: Predators and Competitors
9.4 Nonlinear Mechanical Systems

CHAPTER 10. Laplace Transform Methods
10.1 Laplace Transforms and Inverse Transforms
10.2 Transformation of Initial Value Problems
10.3 Translation and Partial Fractions
10.4 Derivatives, Integrals, and Products of Transforms
10.5 Periodic and Piecewise Continuous Input Functions

CHAPTER 11. Power Series Methods
11.1 Introduction and Review of Power Series
11.2 Power Series Solutions
11.3 Frobenius Series Solutions
11.4 Bessel Functions

References for Further Study
Appendix A: Existence and Uniqueness of Solutions
Appendix B: Theory of Determinants
Answers to Selected Problems
Index

APPLICATION MODULES
The modules listed here follow the indicated sections in the text. Most provide computing projects that illustrate the corresponding text sections. Maple, Mathematica, and MATLAB versions of these investigations are included in the Applications Manual that accompanies this textbook.

1.3 Computer-Generated Slope Fields and Solution Curves
1.4 The Logistic Equation
1.5 Indoor Temperature Oscillations
1.6 Computer Algebra Solutions
2.1 Logistic Modeling of Population Data
2.3 Rocket Propulsion
2.4 Implementing Euler's Method
2.5 Improved Euler Implementation
2.6 Runge-Kutta Implementation
3.2 Automated Row Operations
3.3 Automated Row Reduction
3.5 Automated Solution of Linear Systems
5.1 Plotting Second-Order Solution Families
5.2 Plotting Third-Order Solution Families
5.3 Approximate Solutions of Linear Equations
5.5 Automated Variation of Parameters
5.6 Forced Vibrations and Resonance
7.1 Gravitation and Kepler's Laws of Planetary Motion
7.3 Automatic Calculation of Eigenvalues and Eigenvectors
7.4 Earthquake-Induced Vibrations of Multistory Buildings
7.5 Defective Eigenvalues and Generalized Eigenvectors
7.6 Comets and Spacecraft
8.1 Automated Matrix Exponential Solutions
8.2 Automated Variation of Parameters
9.1 Phase Portraits and First-Order Equations
9.2 Phase Portraits of Almost Linear Systems
9.3 Your Own Wildlife Conservation Preserve
9.4 The Rayleigh and van der Pol Equations



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Instructor's Solutions Manual for Differential Equations and Linear Algebra, 3/E
Edwards & Penney
©2010  |  Pearson  |  Paper; 602 pp  |  Instock
ISBN-10: 0136054269  |  ISBN-13: 9780136054269

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Applications Manual for Differential Equations and Linear Algebra, 3/E
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©2010  |  Pearson  |  Paper; 250 pp  |  Instock
ISBN-10: 0321615255  |  ISBN-13: 9780321615251
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Student Solutions Manual for Differential Equations and Linear Algebra, 3/E
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