A2 - NAME Assignment 2 DUE Feb 3 2011(In Class MAP 2302 001...

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Unformatted text preview: NAME Assignment 2 DUE: Feb. 3, 2011 (In Class) MAP 2302 001 Please show all your work. The answers without solutions will not be graded. You may work together in groups of 2 or 3 on this assignment. Each student must explain what they contributed on the assignment. 1. Consider the intial value problem dy dx = x 2 + y and y (- 2) =- 2. (a) Use Existence-Uniqueness Theorem to show that the intial value problem has a unique solution. (b) Verify that y ( x ) =- 2- 2 x- x 2 is a solution to the intial value problem. (c) Let h = 0 . 1. Use Euler’s Method to esitmate y (8). (100 steps.) (d) Let h = 0 . 1. Use Improved Euler’s Method to estimate y (8). (100 steps.) (e) Graph the points from Euler’s Method, Improved Euler’s Method and the explicit solution and compare. 2. We will use Maple to further investigate problem number 1 by visualizing the slope field. (a) First we must load the Maple package DEtools ....
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