
Differential Equations and Linear Algebra, 2/e
Stephen W. Goode, California State University, Fullerton Published August, 1999 by Prentice Hall Engineering/Science/Mathematics
 
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—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.
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.
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2. SecondOrder 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 FirstOrder Differential Equations. Appendix 5. Linearly Independent Solutions to: x2 y" + xp(x) y' + q(x)y = 0. Answers to Odd Numbered Problems. Index.
