The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students in physics, engineering, the biosciences, economics and mathematics. Instructors are likely to find that the first four or five chapters are suitable for a first course in the subject. This edition contains a healthy increase over earlier editions in the number of worked examples and exercises, particularly those routine in nature. Two appendices include a review with practice problems, and a MATLAB℗ʼ supplement that gives basic codes and commands for solving differential equations. MATLAB℗ʼ is not required; students are encouraged to utilize available software to plot many of their solutions. Solutions to even-numbered problems are available on springer.com. From the reviews of the second edition: ℓ́ℓThe coverage of linear systems in the plane is nicely detailed and illustrated. ℓ́ŒSimple numerical methods are illustrated and the use of Maple and MATLAB is encouraged. ℓ́Œselect Dave Loganℓ́ℓs new and improved text for my course.ℓ́ℓ ℓ́ℓRobert E. Oℓ́ℓMalley, Jr., SIAM Review, Vol. 53 (2), 2011 ℗ℓℓ́ℓAims to provide material for a one-semester course that emphasizes the basic ideas, solution methods, and an introduction to modeling. ℓ́ŒThe book that results offers a concise introduction to the subject for students of mathematics, science and engineering who have completed the introductory calculus sequence. ℓ́ŒThis book is worth a careful look as a candidate text for the next differential equations course you teach.ℓ́ℓ ℓ́ℓWi