4038T4Su2010_Solutions

4038T4Su2010_Solutions - Final Examination Math 4038 July...

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Unformatted text preview: Final Examination Math 4038 July 2010 (8 points) Print Your Name Here: Show all work in the space provided. We can give credit only for what you write! Indicate clearly if you continue on the back side , and write your name at the top of the scratch sheet if you will turn it in for grading. No books or notes are allowed . A scientific calculator is allowedbut it is not needed. If you use a calculator, you must still write out the operations performed on the calculator to show that you know how to solve the problem and did not just guess or remember the answer. Please do not replace precise answers with decimal approximations. There are six (6) problems worth 32 points each. Writing your name legibly in the box above is worth 8 points. Maximum total score = 200. Beessels Equation: x 2 y 00 + xy + ( x 2 2 ) y = 0 1. (32) Use Greens theorem to find I C F d r if F ( x, y ) = e x + y i + e x y j and C is the triangle with vertices (0 , 0) , (1 , 1) , (1 , 3). 1 Final Examination Math 4038 July 2010 2. (32) Let F ( x, y, z ) = y i + z j + x k and let S be the surface z = 4 x 2 y 2 , z 0, with an upward unit normal n . Evaluate ZZ S ( F ) n dA . Choose your favorite method from the following correct ways: direct evaluation of the surface integral, or use Stokes theorem to convert this to a line integral, which you could then evaluate either directly o r by Greens theorem, or use a clever combination of the Divergence theorem with Stokes theoremwhichever you prefer! 2 Final Examination Math 4038 July 2010 3. (32) Apply the method of Frobenius to the following equation with a regular singular point at x = 0: x 2 y 00 + 2 xy + ( x 2 2 ) y = 0...
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This note was uploaded on 01/06/2012 for the course MATH 4038 taught by Professor Staff during the Summer '08 term at LSU.

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4038T4Su2010_Solutions - Final Examination Math 4038 July...

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