What is included with this book?
Foreword | |
Preface to the classics edition | |
Preface | |
Mechanical Vibrations: Introduction to Mathematical Models in the Physical Sciences | |
Newton's Law | |
Newton's Law as Applied to a Spring-Mass System | |
Gravity | |
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 | |
Friction | |
Oscillations of a Damped System | |
Underdamped Oscillations | |
Overdamped and Critically Damped Oscillations | |
A Pendulum | |
How Small is Small? | |
A Dimensionless Time Variable | |
Nonlinear Frictionless Systems | |
Linearized Stability Analysis of an Equilibrium Solution | |
Conservation of Energy | |
Energy Curves | |
Phase Plane of a Linear Oscillator | |
Phase Plane of a Nonlinear Pendulum | |
Can a Pendulum Stop? | |
What Happens if a Pendulum is Pushed Too Hard? | |
Period of a Nonlinear Pendulum | |
Nonlinear Oscillations with Damping | |
Equilibrium Positions and Linearized Stability | |
Nonlinear Pendulum with Damping | |
Further Readings in Mechanical Vibrations | |
Population Dynamics-Mathematical Ecology | |
Introduction to Mathematical Models in Biology | |
Population Models | |
A Discrete One-Species Model | |
Constant Coefficient First-Order Difference Equations | |
Exponential Growth | |
Discrete Once-Species Models with an Age Distribution | |
Stochastic Birth Processes | |
Density-Dependent Growth | |
Phase Plane Solution of the Logistic Equation | |
Explicit Solution of the Logistic Equation | |
Growth Models with Time Delays | |
Linear Constant Coefficient Difference Equations | |
Destabilizing Influence of Delays | |
Introduction to Two-Species Models | |
Phase Plane, Equilibrium, and linearization | |
System of Two Constant Coefficient First-Order Differential Equations, Stability of Two-Species Equilibrium Populations | |
Phase Plane of Linear Systems | |
Predator-Prey Models | |
Derivation of the Lotka-Volterra Equations | |
Qualitative Solution of the Lotka- Volterra Equations | |
Average Populations of Predators and Preys | |
Man's Influence on Predator-Prey Ecosystems | |
Limitations of the Lotka-Volterra Equation | |
Two Competing Species | |
Further Reading in Mathematical Ecology | |
Traffic Flow | |
Introduction to Traffic Flow | |
Automobile Velocities and a Velocity Field | |
Traffic Flow and Traffic Density | |
Flow Equals Density Times Velocity | |
Conservation of the Number of Cars | |
A Velocity-Density Relationship | |
Experimental Observations | |
Traffic Flow | |
Steady-State Car-Following Models | |
Partial Differential Equations | |
Linearization | |
A Linear Partial Differential Equation | |
Traffic Density Waves | |
An Interpretation of Traffic Waves | |
A Nearly Uniform Traffic Flow Example | |
Nonuniform Traffic - The Method of Characteristics | |
After a Traffic Light Turns Green | |
A Linear Velocity-Density Relationship | |
An Example | |
Wave Propagation of Automobile Brake Lights | |
Congestion Ahead | |
Discontinuous Traffic | |
Uniform Traffic Stopped by a Red Light | |
A Stationary Shock Wave | |
The Earliest Shock | |
Validity of Linearization | |
Effect of a Red Light or an Accident | |
Exits and Entrances | |
Constantly Entering Cars | |
A Highway Entrance | |
Further reading in traffic flow | |
Index | |
Table of Contents provided by Publisher. All Rights Reserved. |