• **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 *n*th 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.