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
NEWIncludes a variety of new sections
that include discussions on:
Direction fields and Euler's method for first order differential
Row space and column space of a matrix and the rank-nullity theorem.
Non-linear systems of differential equations including phase
Change of variables for differential equations with examples
of first order homogeneous DE's, Bernoulli equations, and Ricatti
NEWSeveral application problems are
introduced in the first section of the text and then used throughout
the following chapters.
Motivates the study of differential equations.
NEWMaterial 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
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.
NEWChapters on vector spaces and linear
transformations have been completely rewritten:
More emphasis is now placed on R^n before introducing abstract
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
NEWWhat 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 subjectWith material that is accessible
to the average student yet challenging to all students.
Organizes material in a way that is highly flexibleFor
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.
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
Appendix 5. Linearly Independent Solutions to:
x2 y" + xp(x) y' + q(x)y = 0.
Answers to Odd Numbered Problems.