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Chapter6Functions

Objectives

When you have finished this unit you should be able to...

  1. Describe uses for, and construct equations or graphs of, space curves and parametric surfaces.

  2. Find derivatives of space curves, and use this to find velocity, acceleration, and find equations of tangent lines.

  3. Describe uses for, construct graphs of, and find the domain or range of functions of several variables.

    1. For functions of the form \(z=f(x,y)\text{,}\) this includes both 3D surface plots and 2D level curve plots.

    2. For functions of the form \(w=f(x,y,z)\text{,}\) construct plots of level surfaces.

  4. Describe uses for, and construct graphs of, vector fields and transformations.

  5. Explain how to obtain a function for a vector field, or a parametrization for a curve or surface if you are given a description of the vector field, curve, or surface (instead of a function or parametrization),

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.