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Derivatives: Measuring Growth

The basic question throughout this course is, "What measures growth, and how does that give me a calculational advantage?" The course starts with data based questions about growth, moves on to average growth, and then to derivatives via instantaneous growth rates. This is the course with the now famous Race Track Principle, the mean value theorem in an active voice. There's a heavy introductory dose of differential equations to help internalize the idea that derivatives measure growth.

Here's the list of lessons.

	Growth		Differential Equations
	The Exponential and Log Functions		The Race Track Principle
	Instantaneous Growth		More Differential Equations
	Rules of the Derivative		Parametric Plotting
	Using the Tools

Here are some pages with snapshots of problems from the course. Be careful if you look at these. They are chock full of graphics, and may take very long to download.

• A predator-prey problem from the Basics section.
• A problem on versions of the Race Track Principle from the Give It A Try homework.
• Fitting data with exponential functions.

If you want, you may download pre-evaluated samplers from this course.

If you have a Macintosh computer: Click and hold and save the file to your disk.

If you have a Windows machine: Right mouse click and save.

Here's a sampler from each lesson.

Lesson 1 Sampler Lesson 2 Sampler Lesson 3 Sampler

Lesson 4 Sampler Lesson 5 Sampler Lesson 6 Sampler

Lesson 7 Sampler Lesson 8 Sampler Lesson 9 Sampler

If you are new to the courseware's structure, or to the structure of Mathematica notebooks, take a quick look at what to do once you download a sample lesson.

To view the samples, if you don't have a copy of Mathematica, you'll need to download a copy of MathReader from Wolfram Research, Inc

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