Allan Struthers - Differential Equations: For Scientists and Engineers

Whether designed for mathematics or engineering majors, many universities offer a hybrid course in linear algebra and differential equations, and this text is written for precisely such a class. At other institutions, linear algebra and differential equations are treated in two separate courses; in settings where linear algebra is a prerequisite to the study of differential equations, this text may also be used for the differential equations course, with its first chapter on linear algebra available as a review of previously studied material. More on the ways, the book can be implemented in these courses which follow shortly in the section . An overriding theme of the book is that if a differential equation or system of such equations is linear, then we can usually solve it exactly.

In most other texts that present the subjects of differential equations and linear algebra, the presentation begins with first-order differential equations, followed by second- and higher-order linear differential equations. Following these topics, a modest amount of linear algebra is introduced before beginning to consider systems of linear differential equations. Here, however, we begin on the very first page of the text with an example that shows the natural way that systems of linear differential equations arise and use this example to motivate the need to study linear algebra. We then embark on a one-chapter introduction to linear algebra that aims not only to introduce such important concepts as linear combinations, linear independence, and eigenvalue problem but also to foreshadow the use of such topics in the study of differential equations.

Following Chap.. In that setting, we show how the eigenvalues of an nn matrix A naturally provide the general solution to systems of linear differential equations in the form x = Ax . Moreover, we include examples that show how any single higher-order linear differential equation may be converted to a system of equations, thus providing further motivation for why we choose to study systems first. Through this approach, we again strive to emphasize critical connections between linear algebra and differential equations and to demonstrate the most important ideas that arise in the study of each.

Instructors and students alike will find several consistent features in the presentation.