Math 2573H Honors Calculus III Fall Semester 2002

On Thursday December 5 you will have the third mid-term exam during the recitation period. The Thursday before this is Thanksgiving, and so I have decided that the assignment below should be handed in on Tuesday 12/3/2002. There will be no quiz on that date.

The exam on 12/3/2002 will be on Chapter 7 Sections 1, 2, 3, 4, 6, Chapter 8 Sections 1, 4 and Chapter 9 Section 1. You may use a calculator, but no book or notes.

Assignment 12 - Due Tuesday 12/3/2002

Read: Williamson and Trotter, Chapter 9 Section 2, Chapter 9 Section 3, Chapter 9 Section 6A.

The main thing in Chapter 9 Section 6A is a list of formulas for grad, div and curl which I have already mentioned in class (I did not realize at the time that they are presented later in the book).

I find Chapter 9 Section 2 rather complicated to read, and will try to present it more clearly in class. the basic idea is that on a 2-dimensional 'convex' region (with no holes in the middle), it is equivalent to require of a vector field that (a) path integrals only depend on the end points, or (b) the vector field is the gradient of a scalar function, or (c) the curl of the vector field is zero. When the region is not convex things are more subtle, and the subtlety is illustrated by Example 2 on page 356 which is about a vector field defined on a region with a hole in the middle. Apart from this, if a vector field is indeed the gradient of a scalar function there arises the problem of calculating the scalar function, and two methods are available for this. That summarizes Chapter 9 Section 2.

Exercises:
Chap 9 Sec 2 pages 371-373: 3, 3b*, 4, 5, 6*, 7, 7a*, 8*, 11, 13, 14, 15, 17*, 18.
Chap 9 Sec 3 pages 382-386: 3*, 5, 6, 7*, 8, 9b*, 17b*, 25, 26, 27
Chap 9 Sec 6 pages 408-409: 1(identity 4 only)*, 2, 3, 4*