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Differential Equations and Linear Algebra, 2/E
C. Henry Edwards
David E. Penney, University of Georgia, Athens

ISBN-10: 0131481460
ISBN-13: 9780131481466

Publisher: Prentice Hall
Copyright: 2005
Format: Cloth; 784 pp
Published: 03/23/2004
Status: Out of Print

Suggested retail price: $133.33

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For courses in Differential Equations and Linear Algebra.

Known for its real-world applications and its blend of algebraic and geometric approaches, this text offers a full treatment of differential equations together with the linear algebra topics that students need. It emphasizes the conceptual development and geometric visualization of reform courses, but retains the solid foundation of symbolic techniques that remain important to science and engineering students. The authors frame the text by discussing mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. Scientific computing environments like Maple, Mathematica, and MATLAB are available in a separate manual (FREE if shrink-wrapped with text).

NEW - Extensive rewriting of key sections with a fresh qualitative approach—Particularly in Chapters 1, 2, 7, 9.

NEW - New sections on rank and orthogonality in Chapter 4.

NEW - A smoother interface between the applied linear algebra and the differential equations chapters.

NEW - Approximately 350 new or revised problems, many with a qualitative emphasis.

NEW - Approximately 10% of text and examples new for this revision.

NEW - Numerical and graphical computer methods distributed throughout the text.

NEW - Treatment of ecological systems and dynamical systems in Chapter 9.

NEW - Revised text material throughout—Includes material emphasizing applications, mathematical modeling, slope fields, phase plane portraits, and qualitative phenomena.

COMPUTING

Almost 600 computer-generated figures, over half of them new and most constructed using Mathematica or MATLAB—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 following 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—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

Computer-generated graphics throughout the text and answers section—Shows 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.

Accompanying Applications Manual—Expands and enhances the text's applications material, and provides detailed coverage of Maple, Mathematica, and MATLAB techniques.

Differential Equations 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 best problems sets in any introductory DE textbook—Includes 300 new or updated a problems for this revision.

Accompanying Instructors Solutions Manual —Augments the problem material in the text; student version also available.

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: Undetermined Coefficients and Variation of Parameters. 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.

Differential Equations and Linear Algebra (Mathematics)

Differential Equations and Linear Algebra, 3/E
Edwards & Penney
©2010 | Prentice Hall | Cloth; 792 pp | Instock
ISBN-10: 0136054250 | ISBN-13: 9780136054252
Brief Description | Buy from myPearsonStore

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.

Companion Website - Edwards, 2/E
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©2005 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0131481509 | ISBN-13: 9780131481503
URL: http://www.prenhall.com/edwards

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Companion Website - Edwards, 2/E
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©2005 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0131481509 | ISBN-13: 9780131481503
URL: http://www.prenhall.com/edwards

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