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Mathematics is a grand subject in the way it can be applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. 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.
Table of Contents
Preface to the classics edition
Mechanical Vibrations: Introduction to Mathematical Models in the Physical Sciences
Newton's Law as Applied to a Spring-Mass System
Oscillation of a Spring-Mass System
Dimensions and Units
Qualitative and Quantitative Behavior of a Spring-Mass System
Initial Value Problem
A Two-Mass Oscillator
Oscillations of a Damped System
Overdamped and Critically Damped Oscillations
How Small is Small?
A Dimensionless Time Variable
Nonlinear Frictionless Systems
Linearized Stability Analysis of an Equilibrium Solution