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Integrals: Measuring Accumulated Growth

Following the lead of Emil Artin in his mid-fifties honors course at Princeton, we say that the integral measures area. Our job, then, is to find out how to calculate those areas. The theme remains the same throughout the course. Many of your favorite results about integrals come directly from that definition. To do the calculations, the Fundamental Theorem of Calculus is presented as the Fundamental Formula. Virtually all applications of the integral can then be done with this one elementary, albeit elusive, formula. You'll find a bit more about differential equations here, and a bit of a surprise in the lesson on the Gauss-Green Formula.

Here's the list of lessons.

	Measuring Area		Integrals and the Gauss-Green Formula
	The Fundamental Formula		More Tools and Measurements
	Measurements		Traditional Pat Procedures
	Transforming Integrals

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.

• Area as integral from the Basics section.
• An introduction to the Fundamental Formula as a problem from the Tutorials.
• Two dimensional integrals and the Gauss-Green Formula.

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

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