Summary

This course is about the essence of science -- understanding the world in which we live. We use mathematics as a language to help us describe and understand our world. Because the purpose of Mathematical Modeling is to "talk about" our world, the most important parts of this course are the applications -- our mathematical discussions about real world phenomena. In this chapter we have looked at the following applications.

Applications of Modeling

• Two species sharing a habitat. These models were studied in both the second and third modules in this chapter.
• In the fourth module of this chapter we discussed systems with a spring and mass and habitats shared by a predator and a prey.
• In the last three modules we discussed the temperature variation inside a house with adobe walls.
  • Newton's Model of Cooling Revisited. This module also touches on tides and the variation of temperature over the course of a day or year.
  • Heat Flow, I.
  • Heat Flow, II.

These applications along with the other applications we develop in this course are the foundation of our discussion of mathematical modeling. The best way to learn any subject is by using it and the only way to learn mathematical modeling is by building, analyzing, and interpreting models.

Mathematical Techniques

We have looked at the following mathematical ideas and techniques.

• Numerical, Graphical, and Algebraic Techniques for Studying Single Variable Madules.
• Graphical Techniques for Studying Two Variable Models in the second and third modules.
• Numerical and Graphical Techniques for Studying Cyclic Behavior.
• Graphical Techniques for Studying Heat Flow.
• Using Systems of Differential Equations to Study Heat Flow.
• Using Partial Differential Equations to Study Heat Flow.

Physical Experimentation

In this chapter we used the TI-CBL to collect data for the following phenomena.

• Daily Temperature Variation.

Using the World Wide Web and the Internet to Collect Data

In this chapter we used the Internet to collect data for the following phenomena.

• Tides and Daily Temperature Variation.