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Ordinary Differential Equations

Ordinary Differential Equations
From Calculus to Dynamical Systems


Part of Mathematical Association of America Textbooks

  • Date Published: August 2015
  • availability: Temporarily unavailable - available from TBC
  • format: Hardback
  • isbn: 9781939512048

£ 36.99

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About the Authors
  • Techniques for studying ordinary differential equations (ODEs) have become part of the required toolkit for students in the applied sciences. This book presents a modern treatment of the material found in a first undergraduate course in ODEs. Standard analytical methods for first- and second-order equations are covered first, followed by numerical and graphical methods, and bifurcation theory. Higher dimensional theory follows next via a study of linear systems of first-order equations, including background material in matrix algebra. A phase plane analysis of two-dimensional nonlinear systems is a highlight, while an introduction to dynamical systems and an extension of bifurcation theory to cover systems of equations will be of particular interest to biologists. With an emphasis on real-world problems, this book is an ideal basis for an undergraduate course in engineering and applied sciences such as biology, or as a refresher for beginning graduate students in these areas.

    • Essential reading for students in engineering and other applied sciences
    • The text presents important results in dynamical systems and applications to population biology
    • Numerical and graphical methods are considered alongside analytical methods
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    Product details

    • Date Published: August 2015
    • format: Hardback
    • isbn: 9781939512048
    • length: 326 pages
    • dimensions: 260 x 182 x 22 mm
    • weight: 0.73kg
    • availability: Temporarily unavailable - available from TBC
  • Table of Contents

    Sample course outline
    1. Introduction to differential equations
    2. First-order differential equations
    3. Second-order differential equations
    4. Linear systems of first-order differential equations
    5. Geometry of autonomous systems
    6. Laplace transforms
    Appendix A. Answers to odd-numbered exercises
    Appendix B. Derivative and integral formulas
    Appendix C. Cofactor method for determinants
    Appendix D. Cramer's rule for solving systems of linear equations
    Appendix E. The Wronskian
    Appendix F. Table of Laplace transforms
    About the author.

  • Author

    Virginia W. Noonburg, University of Hartford, Connecticut
    Virginia W. Noonburg gained a BA in Mathematics from Cornell University, before spending four years as a computer programmer at the knolls Atomic Power Lab near Schenectady, New York. After returning to Cornell and earning a PhD in Mathematics, she taught first at Vanderbilt University in Nashville, Tennessee and then at the University of Hartford in West Hartford, Connecticut (from which she has recently retired as professor emerita). During the late 1980s she twice taught as a visiting professor at Cornell, and also earned a Cornell MS Eng degree in Computer Science.

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