Overview
- Highlights an unprecedented number of real-life applications of differential equations and systems
- Includes problems in biomathematics, finance, engineering, physics, and even societal ones like rumors and love
- Includes selected challenges to motivate further research in this field
Part of the book series: Problem Books in Mathematics (PBM)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (10 chapters)
-
Front Matter
-
Back Matter
Keywords
- first order linear differential equations
- second and higher order differential equations
- first order nonlinear differential equations
- power series solutions
- first order differential systems
- numerical methods
- stability theory
- linear boundary value problems
- nonlinear boundary value problems
- Runge–Kutta method
- Fourier method
- ordinary differential equations
- partial differential equations
About this book
This book highlights an unprecedented number of real-life applications of differential equations together with the underlying theory and techniques. The problems and examples presented here touch on key topics in the discipline, including first order (linear and nonlinear) differential equations, second (and higher) order differential equations, first order differential systems, the Runge–Kutta method, and nonlinear boundary value problems. Applications include growth of bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood vessels, price-demand-supply relations, predator-prey relations, and many more.
Upper undergraduate and graduate students in Mathematics, Physics and Engineering will find this volume particularly useful, both for independent study and as supplementary reading. While many problems can be solved at the undergraduate level, a numberof challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.
Reviews
“The book provides an excellent collection of ideas to spice up a lecture on differential equations with an analytical approach and thus to increase the motivation of students.” (Volker H. Schulz, SIAM Review, Vol. 62 (3), 2020)
Authors and Affiliations
About the authors
Simona Hodis is an Assistant Professor at the Texas A&M University in Kingsville, USA. She got her PhD from the University of Western Ontario, Canada. Her research interests include mathematical modeling in medicine and engineering, fluid dynamics, applied mathematics, partial differential equations, and numerical analysis.
Donal O’Regan is a Professor at the National University of Ireland.His research interests are in nonlinear functional analysis. His previous publications with Springer include “Constant-Sign Solutions of Systems of Integral Equations” (978-3-319-01254-4) and “Fixed Point Theory for Lipschitzian-type Mappings with Applications” (978-0-387-75817-6), both as a co-author.
Bibliographic Information
Book Title: 500 Examples and Problems of Applied Differential Equations
Authors: Ravi P. Agarwal, Simona Hodis, Donal O’Regan
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-030-26384-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-26383-6Published: 19 December 2019
Softcover ISBN: 978-3-030-26386-7Published: 21 January 2021
eBook ISBN: 978-3-030-26384-3Published: 24 September 2019
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: IX, 388
Number of Illustrations: 81 b/w illustrations, 3 illustrations in colour
Topics: Ordinary Differential Equations, Difference and Functional Equations, Partial Differential Equations, Sequences, Series, Summability, Numerical Analysis