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\(\newcommand{\trace}{\operatorname{tr}} \newcommand{\real}{\operatorname{Re}} \newcommand{\imaginary}{\operatorname{Im}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)


This text is intended for a one-semester undergraduate course in ordinary differential equations.

There are additional exercises or computer projects at the ends of many of the chapters. The computer projects often require a basic knowledge of programming. All of these exercises and projects are more substantial in nature and allow the exploration of new results and theory.

Sage ( is a free, open source, software system for advanced mathematics, which is ideal for assisting with a study of ordinary differential equations. Sage can be used either on your own computer, a local server, or on SageMathCloud ( The Sage code has been tested for accuracy with the most recent version available at this time: Sage Version 7.3 (released 2016–08–5).

Thomas W. Judson
Stephen F. Austin State University
Nacogdoches, Texas 2016