This is a chatty and easy-to-read brief introductory cookbook of ordinary differential equations. The extent of coverage is roughly what is found in good engineering math books (for example, Kreyszig’s Advanced Engineering Mathematics). The most conspicuous omission is the Laplace transform. There are also no numerical methods, although the reader is encouraged to use his favorite computer algebra system to investigate some examples numerically.
The book puts emphasis on qualitative methods, with an especially lengthy discussion of phase diagrams. There are exercises scattered throughout, with various degrees of difficulty, and a variety of applications are given (with the models assumed rather than developed). The book concludes with five term projects for groups, that require some modeling.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.