1. First-Order Differential Equations
2. Matrices and Systems of Linear Equations
3. Determinants
4. Vector Spaces
5. Linear Transformation
6. Linear Differential Equations of Order n
7. Systems of Differential Equations
8. Series Solutions to Linear Differential Equations
9. The Laplace Transform and Some Elementary Applications
Appendices
A. Review of Complex Numbers
B. Review of Partial Fractions
C. Review of Integration Techniques
D. Linearly Independent Solutions to x2yn + xp(x)y1 + q(x)y = 0
E. Answers to Odd-Numbered Exercises

• A better integration of DE and Linear Algebra than other texts on the market.

• 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.

• Highly flexible organization – Enablesinstructors to tailor the course to meet their needs.

• A greater emphasis on geometry – Helps students better visualize the abstract concepts.

• An ample number of worked examples to illustrate concepts.

• Boxed and/or shaded definitions for greater emphasis.

• Several application problems introduced in the first section of the text – Subsequently uses them throughout the following chapters to help motivate students.

• Enhanced visual appeal – Includes a 2-color design as well as a more natural, attractive, and consistent presentation of mathematics.

• Enlargement of most exercise sets – Now features over 2600 problems.

• Enhanced end-of-section pedagogy:

– Includes a list of key terms, skills students should acquire from the section, a true-false review section, and problems.

– Encourages students to take an active role in mastering each section’s concepts.

• End-of-chapter summary and some additional exercises for chapter:

– Give students a broad perspective on the chapter and encourage them to review topics on a larger scale.

– Some chapters also contain project ideas for students interested in deeper applications of the material.

• New problems in many sections – Provide additional practice and exposure to the ideas, methods, theoretical foundation, and applications presented.

• Reorganized material:

– The material on second-order linear differential equations has been moved into Chapter 6, which covers general nth order differential equations.

– Matrix functions are now introduced in Chapter 2.

– The matrix exponential function is now introduced in Chapter 5, which covers linear transformations.

• New sections added to the Third Edition:

– Sections 2.8 and 4.10 keep track of the many characteristics of the invertibility of an n x n matrix.

– Section 4.7 – Change of Basis – introduces the idea of the change of basis matrix, and how components of vectors relative to different bases are related.

– Section 5.5 – The Matrix of a Linear Transformation – illustrates how an arbitrary linear transformation between finite-dimensional vector spaces can be represented by a matrix, once a basis for each vector space has been specified, and shows how linear transformation concepts can be described in terms of matrix algebra.

– Section 5.11 – Jordan Canonical Forms – gives an elementary introduction to the Jordan canonical form of a n X n matrix.