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Chapter13Triple Integrals

Objectives

This chapter covers the following ideas.

  1. Explain how to setup and compute triple integrals, as well as how to interchange the bounds of integration. Use these ideas to find area and volume.

    You can also use triple integrals to find physical quantities such as center of mass, radii of gyration, etc. for solid regions.

  2. Explain how to change coordinate systems in integration, with an emphasis on cylindrical, and spherical coordinates. Explain what the Jacobian of a transformation is, and how to use it.

  3. Explain how to use the Divergence theorem to compute the flux of a vector fields out of a closed surface.

Wrap Up

You've finished the chapter! Look at the objectives at the beginning of the chapter. Can you now do all the things you were promised?

Review Guide Creation

Your assignment: organize what you've learned into a small collection of examples that illustrates the key concepts. I'll call this your chapter review guide. I'll provide you with a template which includes the chapter's key concepts from the objectives at the beginning. Once you finish your review guide, scan it into a PDF document (use any scanner on campus or photo software) and upload it to Gradescope.

As you create this review guide, consider the following:

  • Before each Celebration of Knowledge we will devote a class period to review. With well created lesson plans, you will have 4-8 pages(for 2-4 Chapters) to review for each, instead of 50-100 problems.

  • Think ahead 2-5 years. If you make these lesson plans correctly, you'll be able to look back at your lesson plans for this semester. In about 20-25 pages, you can have the entire course summarized and easy for you to recall.