This is a fun little book on using mathematics to model some simple physical systems. In individual chapters the book introduces several applied mathematical "topics" (linear programming, population growth, optimization, population genetics, and particle collisions) and then proceeds to extend the basic models into more complex situations explaining how the models and analysis change as the complexity increases. Its a great book to get a basic introduction of these topics and to see how these models are use to derive understanding.
The book presents exercises at the end of each section and to test my knowledge I worked them and this document is the result. Hopefully other students of this material will find them helpful.