Mathematical models : mechanical vibrations, population dynamics, and traffic flow : an introduction to applied mathematics
The author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models. Haberman develops the method of characteristics to analyze the nonlinear partial differential equations that describe traffic flow. Fan-shaped characteristics describe the traffic situation that occurs when a traffic light turns green and shock waves describe the effects of a red light or traffic accident. Although it was written over 20 years ago, this book is still relevant. It is intended as an introduction to applied mathematics, but can be used for undergraduate courses in mathematical modeling or nonlinear dynamical systems or to supplement courses in ordinary or partial differential equations
eBook, English, ©1998
Society for Industrial and Applied Mathematics, Philadelphia, ©1998
1 online resource (xvii, 402 pages) : illustrations.
9780898714081, 9781611971156, 0898714087, 1611971152
990455863
Foreword
Preface to the Classics edition
Preface
Part 1. Mechanical vibrations. introduction to mathematical models in the physical sciences
Part 2. Population dynamics
mathematical ecology
Part 3. Traffic flow
Index
"This SIAM edition is an unabridged republication of the work first published by Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1977"--Title page verso
English