1 About Differential Equations -- 2 Linear Algebra -- 3 First-Order Differential Equations -- 4 Applications of First-Order Equations -- 5 Higher-Order Linear Differential Equations -- 6 Applications of Second-Order Equations -- 7 The Laplace Transform -- 8 Higher-Order Differential Equations with Variable Coefficients -- 9 Differential Systems: Theory -- 10 Differential Systems: Applications -- References.

This introductory differential equations textbook presents a convenient way for professors to integrate symbolic computing into the study of differential equations and linear algebra. Mathematica provides the necessary computational power and is employed from the very beginning of the text. Each new idea is interactively developed using it. After first learning about the fundamentals of differential equations and linear algebra, the student is immediately given an opportunity to examine each new concept using Mathematica. All ideas are explored utilizing Mathematica, and though the computer eases the computational burden, the student is encouraged to think about what the computations reveal, how they are consistent with the mathematics, what any conclusions mean, and how they may be applied. This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout. Dr. Clay C. Ross taught mathematics at the university level from 1967 through his retirement in May of 2003. He continues to pursue his interests in mathematics, travel and nature photography, still plays in the University orchestra, and serves as organist at his church. Those activities and much reading keep him productively occupied.