As an undergraduate text, this textbook offers a very accessible introduction to ODEs through modeling, using a real-world applied motivation for introducing each major topic in this subject. This becomes a natural and easy way to understand the basics of differential equations through growth and decay scenarios, easily comprehensible oscillations, and more.
In no way does this approach cause the author to cut corners. Instead, greater pains are taken to make sure key ideas can be understood from a direct modeling approach. In between these episodes of modeling explanation, required techniques and theory are covered.
The book extends the expected overview, examples and exercises approach with section-embedded “instant exercises”. These are answered exercises with the answers later in the section instead of the back of the book. Occasional but detailed real world case studies, including an interesting one tracking an art forgery, further help to illuminate concepts. Starting from an introduction to ODEs, the text continues on to include chapters on nonhomogenous linear equations, autonomous equations, systems of differential equations, Laplace transforms, and PDEs.