Ordinary differential equations (ODEs) and linear algebra are foundational post-calculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system.

The book:

systematically develops the linear algebra needed to solve systems of ODEs;

includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters);

emphasizes mathematical modelling; and

contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modelling of a system, the solution of the model, and the resulting physical description.

It is intended for students who have had one year of calculus and are taking a first class in ODEs.