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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 complicated the more precise an explanation I required. -S
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 will be used for the rest of the course. You should
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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 counts. If I can't follow your reasoning I can't gi
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 homework, open solutions and open book. Feel free to q
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 cross product of the surface tangent vectors to obta
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 /s2 g, m = 6 1027 g, M = 3.3 105 m, r1 = 1.5 10
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 argument lies in its use of Stokes theorem, which cannot
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 sphere. The ux integral must be evaluated directl
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 z
cos() sin() r sin() sin() r cos() cos()