© 2015

A First Course in Differential Equations


Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. J. David Logan
    Pages 1-77
  3. J. David Logan
    Pages 79-136
  4. J. David Logan
    Pages 137-175
  5. J. David Logan
    Pages 177-245
  6. J. David Logan
    Pages 247-316
  7. J. David Logan
    Pages 317-332
  8. Back Matter
    Pages 333-369

About this book


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® supplement that gives basic codes and commands for solving differential equations. MATLAB® is not required; students are encouraged to utilize available software to plot many of their solutions. Solutions to even-numbered problems are available on

From the reviews of the second edition:

“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. …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. …This book is worth a careful look as a candidate text for the next differential equations course you teach.”

—William J. Satzer, MAA Reviews, January, 2011


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Authors and affiliations

  1. 1.Department of MathematicsUniversity of Nebraska--LincolnLincolnUSA

About the authors

J. David Logan is Willa Cather Professor of Mathematics at the University of Nebraska Lincoln. He received his PhD from The Ohio State University and has served on the faculties at the University of Arizona, Kansas State University, and Rensselaer Polytechnic Institute. For many years he served as a visiting scientist at Los Alamos and Lawrence Livermore National Laboratories. He has published widely in differential equations, mathematical physics, fluid and gas dynamics, hydrogeology, and mathematical biology. Dr. Logan has authored 7 books, among them Applied Partial Differential Equations, now in its 3rd edition, published by Springer.

Bibliographic information