© 2012

Ordinary Differential Equations


  • Contains numerous helpful examples and exercises that provide motivation for the reader

  • Presents the Laplace transform early in the text and uses it to motivate and develop solution methods for differential equations

  • Takes a streamlined approach to linear systems of differential equations

  • Protected instructor solution manual is available on


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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. William A. Adkins, Mark G. Davidson
    Pages 1-100
  3. William A. Adkins, Mark G. Davidson
    Pages 101-202
  4. William A. Adkins, Mark G. Davidson
    Pages 203-273
  5. William A. Adkins, Mark G. Davidson
    Pages 275-329
  6. William A. Adkins, Mark G. Davidson
    Pages 331-381
  7. William A. Adkins, Mark G. Davidson
    Pages 383-486
  8. William A. Adkins, Mark G. Davidson
    Pages 487-555
  9. William A. Adkins, Mark G. Davidson
    Pages 557-628
  10. William A. Adkins, Mark G. Davidson
    Pages 629-721
  11. Back Matter
    Pages 723-799

About this book


Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations.

Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.


Laplace transform discontinuous functions existence theorem first order differential equations general linear differential equations impulse functions matrix operations ordinary differential equations phase plane analysis power series methods second order differential equations systems modeling systems of linear differential equations uniqueness theorem

Authors and affiliations

  1. 1.Department of MathematicsLouisiana State University Department of MathematicsBaton RougeUSA
  2. 2.Department of MathematicsLouisiana State University Department of MathematicsBaton RougeUSA

About the authors

William A. Adkins and Mark G. Davidson are currently professors of mathematics at Louisiana State University.

Bibliographic information

  • Book Title Ordinary Differential Equations
  • Authors William A. Adkins
    Mark G. Davidson
  • Series Title Undergraduate Texts in Mathematics
  • Series Abbreviated Title Undergraduate Texts Mathematics
  • DOI
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4614-3617-1
  • Softcover ISBN 978-1-4899-8767-9
  • eBook ISBN 978-1-4614-3618-8
  • Series ISSN 0172-6056
  • Series E-ISSN 2197-5604
  • Edition Number 1
  • Number of Pages XIII, 799
  • Number of Illustrations 121 b/w illustrations, 0 illustrations in colour
  • Topics Ordinary Differential Equations
  • Buy this book on publisher's site


From the reviews:

“The book is meant for an introductory course for second-year undergraduates whose interest in the theory of differential equations is greater than that of the group of students normally taking the class. … Adkins and Davidson … explain the theory in more detail, and they discuss both the geometric and algebraic meaning of theorems. … The volume includes two optional subjects, power series and matrices, in separate chapters. Summing Up: Recommended. Lower-division undergraduates.” (M. Bona, Choice, Vol. 50 (5), January, 2013)

“This volume is ideally suited to any standard undergraduate course in ordinary differential equations at all levels for mathematics and engineering students. … This book is clearly written, contains many illustrations and is very useful for students and teachers. This text is a welcome addition to the differential equations literature, and is strongly recommended as a textbook for classroom use or for individual study.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1259, 2013)