Information about Exam III for Math 2443-003

Mathematics 2443-003 - Calculus IV - Fall 2007

Information about Exam III

Exam III will be in the usual classroom on Thursday, November 29, 2007. It will cover sections 17.1-17.7. Note: Section 17.7 is difficult, and for Exam III the questions from 17.7 will be straightforward and computational. Sections 17.7-17.9 will be extensively covered on the Final Exam.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with.

The exam will have around 54 points, so you can regain lost ground if you are well prepared. It will emphasize computation as opposed to the (nonetheless important) geometric interpretations of the concepts. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

Important: These formulas will be given on the test. You do not need to memorize them, but you must understand them and be familiar with their details in order to use them effectively.

The following topics are likely to appear, although the exam is not necessarily limited to these topics:

  1. Vector fields.
  2. Line integrals of all three kinds. Calculation using a parameterization.
  3. Conservative vector fields and the Fundamental Theorem for Line Integrals. Finding an f whose gradient is a vector field F. Path independence.
  4. The standard (also called positive) orientation on a closed loop. Green's Theorem, its statement and its use in computation.
  5. curl and div. The emphasis will be on computation rather than abstract properties.
  6. Parameterized surfaces. Normal vectors and the vectors r_u, r_v, and r_u \times r_v.
  7. Surface integrals of functions.
  8. Surface integrals of vectors fields. Their computation using formulas.

You must know how to calculate curl and div of a vector field, and the statement of Green's Theorem.

The following topics do not appear, at least not explicitly: connected sets, open and closed sets, simply-connected domains, proof of Green's Theorem, Green's Theorem for domains with more than one boundary loop, the Laplacian.

Exams from some of my previous Calculus IV classes can be found on their course pages. Some were 50-minute classes, but most were 75-minute classes. Of course, these were different courses, so the exams may be quite a bit different.

1.	Vector fields.
2.	Line integrals of all three kinds. Calculation using a parameterization.
3.	Conservative vector fields and the Fundamental Theorem for Line Integrals. Finding an f whose gradient is a vector field F. Path independence.
4.	The standard (also called positive) orientation on a closed loop. Green's Theorem, its statement and its use in computation.
5.	curl and div. The emphasis will be on computation rather than abstract properties.
6.	Parameterized surfaces. Normal vectors and the vectors r_u, r_v, and r_u \times r_v.
7.	Surface integrals of functions.
8.	Surface integrals of vectors fields. Their computation using formulas.