A First Course in Differential Equations (Undergraduate Texts in Mathematics)

From the reviews:

"Logan has produced a well-crafted text, densely packed with interesting applications from diverse fields. The chapters cover (ordinary) differential equations, analytical solutions and approximations, second-order differential equations, Laplace transforms, linear and nonlinear systems. The material is well presented and introduces new concepts ... . The text will certainly provide a good mental workout." (Christopher Howls, The Times Higher Education Supplement, November, 2006)

"This is a textbook for those who ... want to learn some methods and techniques to handle mathematical models described by ordinary differential equations. ... the book contains topics which are not included in other similar texts. ... In addition, four appendices are added to complete the presentation ... . The book is written in a pleasant and friendly style. It provides the reader with enough knowledge to engage with more advanced topics of differential equations ... ." (Gheorghe Morosanu, Zentralblatt MATH, Vol. 1088 (14), 2006)

From the reviews of the second edition:

“Designed for standard second-year courses in differential equations, this text covers the basic ideas, models and solution methods in a format intended to be accessible to engineering, economics and mathematics students. Logan emphasises analytical, graphical and numerical techniques, and provides a strong connection to applications with motivations in mechanics and heat transfer, circuits, biology, economics and chemical reactors.” (Times Higher Education, May, 2011)

“The new edition covers essentially the same material as the first, with minor rearrangements, and it is about one-third longer. The coverage of linear systems in the plane is nicely detailed and illustrated. ... Simple numerical methods are illustrated and the use of Maple and MATLAB is encouraged. There are over thirty pages of solutions and hints to selected exercises as well. ... select Dave Logan’s new and improved text for my course.” (Robert E. O’Malley, Jr., SIAM Review, Vol. 53 (2), 2011)

“Aims to provide material for a one-semester course that emphasizes the basic ideas, solution methods, and an introduction to modeling. ... The book that results offers a concise introduction to the subject for students of mathematics, science and engineering who have completed the introductory calculus sequence. ... There are an adequate number of exercises ... . Solutions are provided for ... exercises in an appendix. This book is worth a careful look as a candidate text for the next differential equations course you teach.” (William J. Satzer, The Mathematical Association of America, January, 2011)