Name:
Math 362, Spring 2006, Professor Callahan Final Exam, Tue., May 9
As was usually the case with scientific problems, what seemed clear and simple in an abstract or a summary became more complica
Mathematics 362 Advanced Mathematics for Engineers and Scientists
Professor Tim Callahan Time: T 4:405:55 in PSA 308. Books: Vector Calculus, by P. C. Matthews. A reader will be available later, and w
Name:
Math 362, Spring 2006, Professor Callahan Test #1, ThuFri, Feb. 2324.
1 Note 1: This test is closed book. You may use one 8 2 11 sheet of notes (both sides).
Note 2: Show your work. Clarity c
Math 362, Spring 2006, Professor Callahan Test #2, ThuFri, Apr. 1314.
Subtly, very subtly, Nowhere neglect the Use of Intelligence. -Sun Tzu, "The Art of War" Note 1: This test is open note, open home
MAT 362 Answers to selected exercises, week of Sept. 19
Graded problems
1. Parametrize the surface using polar coordinates: (r, ) = r cos , r sin , 1 1 r2 . 3 (a) Direct calculation. We need the cr
MAT 362 Answers to selected exercises, week of Sept. 28
Graded problems
1. The work done is the dierence in the potential function: W = f (r2 ) f (r1 ), where f (r) = GMm/r. We have G = 6.7 108 cm3
MAT 362 Answers to selected exercises, week of Oct. 3
Graded problems
1. The divergence theorem applies to ux of a smooth vector eld across a surface that encloses a volume. The fallacy in the argumen
MAT 362 Answers to selected exercises, week of Oct. 12
Graded problems
1. We have F = r/ r 3 , which is undened at the origin. The divergence theorem cannot be applied because F is not C 1 on the unit
MAT 362 HOMEWORK 5
. Exercise 27 grad = 1 r 4 grad r = 4r3 r div r = 1 r curl grad = 0 div grad = 2 = 0 div curl = 0 . Exercise 29 x J= (x, y, z) = (r, , )
r y r z r x y z x y