## Differential Equations and Linear Algebra, 2/e

Stephen W. Goode, California State University, Fullerton

Published August, 1999 by Prentice Hall Engineering/Science/Mathematics

Cloth
ISBN 0-13-263757-X

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Differential Equations and Linear Algebra-Mathematics

For a thorough introduction to the basics of differential equations and linear algebra with a carefully balanced and sound integration of the two topics. Flexible in format, it explains concepts clearly and logically without sacrificing level or rigor and supports material with a vast array of problems of varying levels from which students/instructors can choose.

NEW—Includes a variety of new sections that include discussions on:
—Direction fields and Euler's method for first order differential equations.
—Row space and column space of a matrix and the rank-nullity theorem.
—Non-linear systems of differential equations including phase plane analysis.
—Change of variables for differential equations with examples of first order homogeneous DE's, Bernoulli equations, and Ricatti equations.
NEW—Several application problems are introduced in the first section of the text and then used throughout the following chapters.

• Motivates the study of differential equations.
NEW—Material on second order linear differential equations that was previously in Chapter 9 is now in Chapter 2 and is not dependent on the vector space.
—The longer time spent on DE at the beginning of the course gives students a firmer grasp of the differential equation concept early on and also on the solution techniques for this important class of differential equations.
—Introduces and reinforces the idea of linearity which can then be used to better motivate and illustrate the vector space ideas.
—Placement in Chapter 2 adds flexibility to the text. Since many students have already seem much of this (and the Chapter 1) material in a previous calculus course, some instructors may choose to use this chapter as a review or even omit it altogether.
NEW—Chapters on vector spaces and linear transformations have been completely rewritten:
—More emphasis is now placed on R^n before introducing abstract vector spaces.
—Two sections discussing the row space and column space of a matrix and the rank nullity theorem have been added.
—Material on eigenvalues and eigenvectors (old Chapter 8) now appears in Chapter 7 after the discussion of linear transformations of R^n.
NEW—What were previously Chapters 12 and 13 (Laplace Transforms and Series Solutions of Linear Differential Equations respectively) are now Chapters 3 and 4.
Provides a better integration of DE and Linear Algebra than other texts in the market.
Gives students a complete, fundamental introduction to both linear algebra and differential equations.
• Promotes in-depth understanding (vs. rote memorization)—enabling students to fully comprehend abstract concepts and leave the course with a solid foundation in linear algebra.
Continues to offer one of the most lucid and clearly written narratives on the subject—With material that is accessible to the average student yet challenging to all students.
Organizes material in a way that is highly flexible—For instructors to tailor the course to meet their needs.
Presents a greater emphasis on geometry.
• Help students better visualize the abstract concepts.
Illustrates all concepts with an ample number of worked examples.
Definitions are highlighted via boxes and/or shading.

1. First-Order Differential Equations.
2. Second-Order Linear Differential Equations.
3. Matrices and Systems of Linear Algebraic Equations.
4. Determinants.
5. Vector Spaces.
6. Linear Transformations and the Eigenvalue/Eigenvector Problem.
7. Linear Differential Equations of Order n.
8. Systems of Differential Equations.
9. The Laplace Transform and Some Elementary Applications.
10. Series Solutions to Differential Equations.
Appendix 1. A Review of Complex Numbers.
Appendix 2. A Review of Partial Fractions.
Appendix 3. A Review of Integration Techniques.
Appendix 4. An Existence and Uniqueness Theorem for First-Order Differential Equations.
Appendix 5. Linearly Independent Solutions to:
x2 y" + xp(x) y' + q(x)y = 0.