# 10.1 - 8/24/2011 1 10.1 Taylor Series Method 8/23/2011...

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Unformatted text preview: 8/24/2011 1 10.1 Taylor Series Method 8/23/2011 Initial Value Problems ODE like + 9 = ? with solution = ? 1 ??3 + ? 2 ???3 Consider the initial value problem for a first order differential equation = ? , ? = ??? ?? It is understood that is a function of : = ?(, ) 8/24/2011 2 Examples Some examples of I.V.P.s ODE I.V. Solution = + 1 = 0 = ? 1 = 6? 1 1 = 6 = 3? 2 ? + 4 = ? + 1 = 0 = ? 2 + 1 1 Not every ODE can be solved analytically Even when we can solve an ODE in closed form, the expression could be too complicated to be evaluated Where do ODEs come from in applications? Newtons second Law of Motion = ?? An ODE in disguise ? = 8/24/2011 3 A Rocket Launch Example We illustrate with a simplified model of a rocket being fired at time...
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## This note was uploaded on 11/27/2011 for the course MAP 4371 taught by Professor Xli during the Fall '11 term at University of Central Florida.

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10.1 - 8/24/2011 1 10.1 Taylor Series Method 8/23/2011...

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