Lab1_Section2_4

Lab1_Section2_4 - Math 306 – Lab 1 Euler’s Method...

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Unformatted text preview: Math 306 – Lab 1 Euler’s Method Printed Name: Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit! This lab will investigate Euler’s Method for approximating the solutions to differential equations. As an example, the simple differential equation dy dx = e- x 2 y (0) = 1 . has a unique solution – namely y ( x ) = R x e- u 2 du . Unfortunately, there is no elementary way to perform this integration. Instead, we shall try to approximate the solution. Consider the general IVP dy dx = f ( x,y ) , y ( x 1 ) = y 1 . The idea is • We pick an initial point, say ( x 1 ,y 1 ) • The slope through the point ( x 1 ,y 1 ) is given by f ( x 1 ,y 1 ). We move a small distance along the slope segment through this point to the next point ( x 2 ,y 2 ). • At the point ( x 2 ,y 2 ), we have a new slope given by f ( x 2 ,y 2 ). We now move a small distance along the slope segment through ( x 2 ,y 2 ) to the next point ( x 3 ,y 3 )....
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This note was uploaded on 01/16/2012 for the course MATH 306 taught by Professor Keithemmert during the Fall '11 term at Tarleton.

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Lab1_Section2_4 - Math 306 – Lab 1 Euler’s Method...

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