Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow

✍ Scribed by Richard Haberman

• Publisher: Society for Industrial and Applied Mathematics
• Year: 1998
• Tongue: English
• Leaves: 412
• Series: Volume 21 of Classics in Applied Mathematics
• Category: Library

✦ Table of Contents

Title
Table of Contents
Foreword
Preface
Mechanical Vibrations
1. Introduction to Mathematical Models in the Physical Sciences
2. Newton's Law
3. Newton's Law as Applied to a Sping-Mass System
4. Gravity
Exercises
5. Oscillation of a Spring-Mass System
Exercises
6. Dimension and Units
7. Qualitative and Quantitative Behavior of a Spring-Mass System
Exercises
8. Initial Value Problem
Exercises
9. A Two-Mass Oscillator
Exercises
10. Friction
Exercises
11. Oscillations of a Damped System
Exercises
12. Underdamped Oscillations
Exercises
13. Overdamped and Critically Damped Oscillations
Exercises
14. A Pendulum
Exercises
15. How Small is Small?
Exercises
16. A Dimensionless Time Variable
Exercises
17. Nonlinear Frictionless Systems
18. Linearized Stability Analysis of an Equilibrium Solution
Exercises
19. Conservation of Energy
Exercises
20. Energy Curves
21. Phase Plane of a Linear Oscillator
Exrcises
22. Phase Plane of a Nonlinear Pendulum
Exercises
23. Can a Pendulum Stop?
Exercises
24. What Happens If a Pendulum Is Pushed Too Hard?
Exercises
25. Period of a Nonlinear Pendulum
Exercises
26. Nonlinear Oscillations with Damping
Exercises
27. Equilibrium Positions and Linearized Stability
Exercises
28. Nonlinear Pendulum with Damping
Exercises
29. Further Readings in Mechanical Vibrations
Population Dynamics-Mathematical Ecology
Traffic Flow
Index