Elementary Differential Equations: Applications, Models, and Computing

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CRC Press, Dec 13, 2018 - Mathematics - 554 pages
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Elementary Differential Equations, Second Edition is written with the knowledge that there has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage. This second edition has been created to address these changes and help instructors facilitate new teaching methods and the latest tools, which includes computers.

The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers in teaching elementary or ordinary differential equations. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package.

Features:

  • Focuses on numerical methods and computing to generate solutions
  • Features extensive coverage of nonlinear differential equations and nonlinear systems
  • Includes software programs to solve problems in the text which are located on the author's website
  • Contains a wider variety of non-mathematical models than any competing textbook

This second edition is a valuable, up-to-date tool for instructors teaching courses about differential equations. It serves as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines and other sciences. They also will find that the textbook will aide them greatly in their professional careers because of its instructions on how to use computers to solve equations.

 

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Contents

Chapter 1 Introduction
1
Chapter 2 The Initial Value Problem y f x y yc d
33
Chapter 3 Applications of the Initial Value Problem y f x y yc d
93
Chapter 4 Nth Order Linear Differential Equations
143
Chapter 5 The Laplace Transform Method
199
Chapter 6 Applications of Linear Differential Equations with Constant Coefficients
247
Chapter 7 Systems of FirstOrder Differential Equations
285
Chapter 8 Linear Systems of FirstOrder Differential Equations
305
Chapter 9 Applications of Linear Systems with Constant Coefficients
347
Chapter 10 Applications of Systems of Equations
369
Appendix A Numerical Solution of the Initial Value Problem y f x y yc d
459
Answers to Selected Exercises
489
References
523
Index
527
Copyright

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About the author (2018)

Charles E. Roberts, Jr. is a Professor Emeritus in the Department of Mathematics and Computer Science at Indiana State University. He has written other books and papers about ordinary differential equations.

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