final07 - problems 1 6 7 12 13 18 19 24 25 30 total scores...

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1 - 6 7 - 12 13 - 18 19 - 24 25 - 30 total scores Final Exam, Dec 13, Calculus III, Fall, 2007, W. Stephen Wilson I agree to complete this exam without unauthorized assistance from any person, materials or device. Name: Date: TA Name and section: NO CALCULATORS, NO PAPERS, SHOW WORK . (30 points total) To use cylindrical coordinates we have RRR f ( x, y, z ) dx dy dz = RRR f ( r cos θ, r sin θ, z ) r dr dθ dz . To use spherical coordinates we have RRR f ( x, y, z ) dx dy dz = RRR f ( ρ cos θ sin φ, ρ sin θ sin φ, ρ cos φ ) ρ 2 sin φ dρ dθ dφ. You can use formulas like R 2 π 0 cos 2 k +1 θ dθ = R 2 π 0 sin 2 k +1 θ dθ = 0 and R 2 π 0 cos 2 θ dθ = R 2 π 0 sin 2 θ dθ = π . To evaluate the average value of a function on a curve, surface or solid, you integrate the function over the object and divide by the length/area/volume of the object. There is no partial credit on this exam. Every problem is worth 1 point. DRAW a BOX around your ANSWER. If the correct answer is in the box you will get 1 point IF you have work on the page in a clear way that justifies the answer. If the work is NOT there but the answer in the box is correct, no point will be awarded. REMEMBER TO PUT A BOX AROUND YOUR ANSWERS. Problems 23-29 use the same vector field but we use both Stoke’s and Gauss’s theorems. It is easy to get confused but I advise against it because only the correct answer counts. This exam if much much too long so it isn’t necessary to do the stuff you don’t know. Do what you know and get the right answer and you’ll be okay. Don’t panic, relax, just get the right answers for what
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This note was uploaded on 10/15/2008 for the course 110 202 taught by Professor Wilson during the Spring '08 term at Johns Hopkins.

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final07 - problems 1 6 7 12 13 18 19 24 25 30 total scores...

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