Undergraduate Texts in Mathematics

Ordinary Differential Equations

Authors: Adkins, William, Davidson, Mark G.

  • 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 springer.com
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eBook $59.99
price for USA (gross)
  • ISBN 978-1-4614-3618-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-1-4614-3617-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4899-8767-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
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About this Textbook

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.

About the authors

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

Reviews

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)


Table of contents (9 chapters)

  • First Order Differential Equations

    Adkins, William A. (et al.)

    Pages 1-100

  • The Laplace Transform

    Adkins, William A. (et al.)

    Pages 101-202

  • Second Order Constant Coefficient Linear Differential Equations

    Adkins, William A. (et al.)

    Pages 203-273

  • Linear Constant Coefficient Differential Equations

    Adkins, William A. (et al.)

    Pages 275-329

  • Second Order Linear Differential Equations

    Adkins, William A. (et al.)

    Pages 331-381

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4614-3618-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-1-4614-3617-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4899-8767-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Ordinary Differential Equations
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-3618-8
DOI
10.1007/978-1-4614-3618-8
Hardcover ISBN
978-1-4614-3617-1
Softcover ISBN
978-1-4899-8767-9
Series ISSN
0172-6056
Edition Number
1
Number of Pages
XIII, 799
Number of Illustrations and Tables
121 b/w illustrations
Topics