Ordinary Differential Equations

  • William A. Adkins
  • Mark G. Davidson

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

Introduction

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.

Keywords

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

  • William A. Adkins
    • 1
  • Mark G. Davidson
    • 2
  1. 1.Department of MathematicsLouisiana State University Department of MathematicsBaton RougeUSA
  2. 2.Department of MathematicsLouisiana State University Department of MathematicsBaton RougeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-3618-8
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-3617-1
  • Online ISBN 978-1-4614-3618-8
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • About this book