Final Exam Review

Be sure to review the material listed in the review pages for the First Exam, Second Exam, Third Exam, as well as the topics presented here. The Final Exam will be a cumulative exam.

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Scheduling Information:	Time: Tuesday, May 9, from 8:30-11:30am. Location: CUC McConomy. Review Session: Sunday, May 7, from 6:00-7:20pm in MM A14.

Reading:	Vector Fields (16.1) Line Integrals (16.2) The Fundamental Theorem for Line Integrals (16.3) Green's Theorem (16.4) Curl and Divergence (16.5) Parametric Surfaces and Their Areas (16.6) Surface Integrals (16.7) Stokes' Theorem (16.8) The Divergence Theorem (16.9)

Review Questions:	What does it mean for a region to be connected? Simply connected? What is meant by an "orientation" of a curve? What is the "positive orientation" of a curve that bounds a region? What is the statement of Green's Theorem? What does Green's theorem allow you to do [replace line integral with double integral or vice versa] Can Green's theorem apply to regions that are not simply connected? What do you need to do in that case? What is the implication of Green's theorem related to conservative vector fields? What is the curl of a vector field? What does the curl of a vector field "measure"? What is the divergence of a vector field? What does the divergence of a vector field "measure"? How does Green's theorem relate to divergence and curl of a vector field? What is a parametric surface? A parametrization of a surface? What are the grid curves of a parametrization? What are the grid curves of a parametrized surface? How can you find two vectors that determine the tangent plane at a point on a parametrized surface? How can you find a vector normal to the tangent plane? An equation for the tangent plant? How do you find the area of a parametric surface? How do you find the integral of a function over a parametric surface? How is this related to computing the area of a parametric surface? How do you integrate over a surface that is piecewise smooth? [Integrate over each smooth piece] What does it mean for a surface to be orientable? Oriented? How can you define an orientation of a parametric surface? What is the surface integral of a vector field? How is it related to the integral of a scalar? [integrate the scalar quantity F n.] How do you compute the surface integral of a vector field using a parametrization? What does Stokes' theorem say? How is it similar to Green's theorem?

Exercises:	Section 16.1 #3, 5, 7, 11, 13, 15, 17, 23, 35. Section 16.2 #3, 7, 11, 17, 21, Section 16.3 #7, 11, 15, 21, 25, 29, 35, Section 16.4 #3, 7, 9, 17, 29. Section 16.5 #13, 19, 21, 25. Section 16.6 #1, 3, 5, 13, 15, 19, 21, 33, 35, 39, 45, 49, 51. Section 16.7 #5, 9, 17, 23, 27, 37, 47. Section 16.8 #3, 5, 7, 9. section 16.9 #1, 7, 9, 25, 29.

Reference Tables:	I'll give you this reference table to use with your exam. Once I finalize it, I will post it here, so you will have it before the exam.