Ordinary Differential Equations

From Calculus to Dynamical Systems
Erscheinungsjahr 2015
ISBN: 978-1-939512-04-8
Verlag: Mathematical Association of America (MAA)

Buch, Englisch, 326 Seiten, Format (B × H): 182 mm x 261 mm, Gewicht: 735 g

Reihe: Mathematical Association of America Textbooks

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.

Autoren/Hrsg.

Noonburg, Virginia W

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Preface; 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; Index; About the author.

Über Autor(innen)

Noonburg, Virginia W
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.