500 Examples and Problems of Applied Differential Equations
Springer International Publishing (Verlag)
978-3-030-26383-6 (ISBN)
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.
Ravi P. Agarwal is a Professor at the Texas A&M University in Kingsville, USA. He is also a Distinguished University Professor of Mathematics at the Florida Institute of Technology, Melbourne, FL, USA. He did his PhD at the Indian Institute of Technology, India. Dr. Agarwal authored, co-authored and co-edited over 60 books, including "An Introduction to Ordinary Differential Equations" (978-0-387-71275-8) and "Ordinary and Partial Differential Equations" (978-0-387-79145-6), both co-authored by Donal O'Regan and published by Springer. 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.
1. First Order Linear Differential Equations.- 2. Some First Order Nonlinear Differential Equations.- 3. Second and Higher Order Differential Equations.- 4. Power Series Solutions.- 5. Systems of First Order Linear Differential Equations.- 6. Runge-Kutta Method.- 7. Stability Theory.- 8. Linear Boundary Value Problems.- 9. Nonlinear Boundary Value Problems.- Index.
"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)
| Erscheinungsdatum | 07.01.2020 |
|---|---|
| Reihe/Serie | Problem Books in Mathematics |
| Zusatzinfo | IX, 388 p. 84 illus., 3 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 757 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | first order differential systems • first order linear differential equations • first order nonlinear differential equations • Fourier method • linear boundary value problems • nonlinear boundary value problems • Numerical Methods • Ordinary differential equations • Partial differential equations • power series solutions • Runge–Kutta method • Runge-Kutta Method • second and higher order differential equations • Stability Theory |
| ISBN-10 | 3-030-26383-5 / 3030263835 |
| ISBN-13 | 978-3-030-26383-6 / 9783030263836 |
| Zustand | Neuware |
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