Math 2573H Honors Calculus III Fall Semester 2002

Assignment 8 - Due Thursday 10/31/2002

Read: Williamson and Trotter, Chapter 6 Section 5, Chapter 7 Section 1

I am not sure whether you will already know about the various coordinate systems described in Chapter 6 Section 5 from physics. In any case, they are easily described, and you do need to know what they are. The harder thing to understand is what happens to derivatives of functions when they are expressed in these unusual coordinates. There is discussion about this in section 5D, and the question you have to hand in is also about this. The trouble is that derivatives have to do with linear maps, which have to do with matrices, but these only work if we are using Cartesian coordinates. This means that we have to think rather carefully if we want to interpret the matrix of partial derivatives of a function when it is expressed in curvilinear coordinates. The safest thing to do in this situation is revert to Cartesian coordinates.

Chap 6 Sec 5 pages 248-249: 5, 6, 7, 8, 9*
Chap 7 Sec 1 pages 263-264: 2, 6, 8*, 12, 20*, 22*
Chap 7 Sec 2 pages 275-277: 1a*, 4, 6, 7.