Modeling Oscillating Systems: Mathematics Component|
In a world where computational science is increasingly being used to model complex situations, the need to teach both mathematics and science from a modeling perspective has correspondingly increased.
The mathematics component of this unit allows the students to take data from a symbolic model, created by physics students, and create a mathematical model. Because this unit deals with systems demonstrating oscillatory motion, a trigonometric function is an appropriate mathematical model. Traditionally, pre-calculus or advanced algebra students learn how to draw a graph given a trigonometric function. Now, through computational science and various modeling tools, students can learn to create a graph from periodic data and determine the appropriate trigonometric function that serves as a mathematical model for the data. In other words, instead of creating a graph from the trig function, students are developing the trig function (model) from the graph.
This is more realistic situation. Students will get a much better sense of what a scientist or mathematician actually does, and learn about trigonometric functions and how to use various modeling tools in the process.