Fast Track to Differential Equations fits squarely within a long tradition of accessible introductions to applied mathematics, and it sets itself apart through a steady emphasis on why solutions work instead of how to compute them. I found this focus surprisingly refreshing. Many introductory texts rely heavily on symbolic routines, but this volume slows the reader down in a good way and draws attention to the underlying structure of a differential equation and the modeling choices that shape it. The book often feels practical, occasionally understated, but consistently clear.

The early sections revisit familiar calculus ideas such as exponential functions, power series, and the fundamental theorem of calculus. These topics are handled briefly with enough detail to orient the reader toward later applications. I especially appreciated the treatments of direction fields and exponential growth, which are simple topics but easy to mishandle. As the book moves forward, the author presents a wide collection of first order models from physics, chemistry, economics, and environmental science. Some will feel familiar, while examples like elasticity or evaporation models add a welcome sense of variety. The short Mathematica commands and the informal references to Wolfram Alpha give students a very accessible way to experiment with computation.

The later chapters introduce second order equations, coupled systems, and several mechanical models. The exposition remains restrained and avoids unnecessary digressions, though there is enough context to make sense of the ideas. The numerical methods section, which covers Euler, Heun, and Runge Kutta techniques, is supported by examples such as tennis ball trajectories and sky-diving. These are standard choices, but they work well. Near the end, the brief discussions of climate modeling and epidemiology feel timely and give readers a sense of how differential equations continue to shape scientific conversations.

There are moments when the presentation feels a bit terse. I sometimes wished for one more paragraph or even a diagram to round out an explanation. Still, this compact style appears intentional, and the included solutions help soften the effect. In a way, the minimalism gives the reader room to think, which I personally appreciated.

Fast Track to Differential Equations offers a well shaped and genuinely engaging entry to the subject. Instructors who value modeling and conceptual clarity will find much to appreciate, and motivated students will discover a resource that encourages exploration rather than passive reading.

Hyeeun Jang is an Assistant Professor of Mathematics at Abilene Christian University.