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Differential Equations

An Introduction with Mathematica®

  • Textbook
  • © 2004

Overview

Authors:
  1. Clay C. Ross

    1. Department of Mathematics, The University of the South, Sewanee, USA

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  • Offers a huge variety of examples and exercises
  • Lots of Mathematica® code, which is well integrated into the main discussion
  • Includes supplementary material: sn.pub/extras
  • Request lecturer material: sn.pub/lecturer-material

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIII
    Download chapter PDF

  2. About Differential Equations

    • Clay C. Ross
    Pages 1-25

  3. Linear Algebra

    • Clay C. Ross
    Pages 26-51

  4. First-Order Differential Equations

    • Clay C. Ross
    Pages 52-89

  5. Applications of First-Order Equations

    • Clay C. Ross
    Pages 90-128

  6. Higher-Order Linear Differential Equations

    • Clay C. Ross
    Pages 129-178

  7. Applications of Second-Order Equations

    • Clay C. Ross
    Pages 179-209

  8. The Laplace Transform

    • Clay C. Ross
    Pages 210-239

  9. Higher-Order Differential Equations with Variable Coefficients

    • Clay C. Ross
    Pages 240-296

  10. Differential Systems: Theory

    • Clay C. Ross
    Pages 297-368

  11. Differential Systems: Applications

    • Clay C. Ross
    Pages 369-422

  12. Back Matter

    Pages 423-433
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Keywords

About this book

Goals and Emphasis of the Book Mathematicians have begun to find productive ways to incorporate computing power into the mathematics curriculum. There is no attempt here to use computing to avoid doing differential equations and linear algebra. The goal is to make some first ex­ plorations in the subject accessible to students who have had one year of calculus. Some of the sciences are now using the symbol-manipulative power of Mathemat­ ica to make more of their subject accessible. This book is one way of doing so for differential equations and linear algebra. I believe that if a student's first exposure to a subject is pleasant and exciting, then that student will seek out ways to continue the study of the subject. The theory of differential equations and of linear algebra permeates the discussion. Every topic is supported by a statement of the theory. But the primary thrust here is obtaining solutions and information about solutions, rather than proving theorems. There are other courses where proving theorems is central. The goals of this text are to establish a solid understanding of the notion of solution, and an appreciation for the confidence that the theory gives during a search for solutions. Later the student can have the same confidence while personally developing the theory.

Reviews

From the reviews of the second edition:

"The introductory differential equations textbook presents a convenient way for professors to integrate … . Each new idea is interactively developed … . After first learning about the fundamentals of differential equations and linear algebra, the student is immediately given an opportunity to examine … . the student is encouraged to think about what the computations reveal, how they are consistent with the mathematics … . The new revised edition updates … and offers a more extensive treatment of linear algebra." (Zentralblatt für Didaktik der Mathematik, January, 2005)

"This text instructs students in solving and using differential equations with both paper-and-pencil techniques and the Mathematica symbolic manipulation program. … This is a good, thorough standard textbook with good explanations." (Steven Dunbar, MathDL, January, 2005)

Authors and Affiliations

  • Department of Mathematics, The University of the South, Sewanee, USA

    Clay C. Ross

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