Math 4347: Test 2 - Solutions to Wave, Laplace's, and Heat Equations - Prof. Evans Harrell, Exams of Differential Equations

Download Math 4347: Test 2 - Solutions to Wave, Laplace's, and Heat Equations - Prof. Evans Harrell and more Exams Differential Equations in PDF only on Docsity! Mathematics 4347 Test 2 25 October 2010 NAME: Instructions: Work absolutely on your own, without reference to notes or text. Answers should be as specific as possible and it should be evident how they were obtained. Write the answers where indicated. Each problem has the same point value. However, the one with the lowest score will count half. (This means that it is better to get two completely right than three only mostly correct.) This test will end promptly at 2:55. Sign below and await the signal to begin the test. I am familiar with the Georgia Tech Honor Code and will abide by it. Any stored information about MATH 4347 has been erased from my calculator (or similar storage device) Mathematics 4347 Test 1 25 October 2010 NAME: 1. Solve the wave equation utt = uxx a) with initial conditions u(x, 0) = 0, ut(x, 0) = x2, for −∞ < x <∞. ANSWER: b) with initial and boundary conditions u(x, 0) = 0, ut(x, 0) = x2, for 0 < x <∞; and u(0, t) = 0 for 0 < t. ANSWER: Optional, for possible partial credit: Below here clearly write some key formulae, ideas, or strategies to solve this problem.