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Material Type:  Review Sheet 
Professor:  Staff 
Class:  22M 026  Calculus II 
Subject:  Mathematics 
University:  University of Iowa 
Term:   
Keywords:   Particularly
 Any Questions
 Behind (of)
 Initial Condition
 Convergence
 Integrating
 Differentiate
 Partial Sums
 Logistic Growth
 Linear Equation

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CALC II 22M:026:AAA
FINAL EXAM REVIEW
Chapter 9  Differential Equations
. Euler's Method
 Euler's Method approximates the solution to a differential equation. The idea
behind it is that even if we can't solve for y, knowing yprime gives us the slope of the
tangent line to y at any point (xi,yi). The equation used in Euler's method is a
series of steps where we use the slope to approximate a little piece of the curve,
then move to the top of that piece and repeat until we're at the xvalue we want.
 Given yprime = F(x,y) y(x0) = y0 h = stepsize,
we have xn = h + xn?1 yn = yn?1 + hF(xn?1,yn?1)
 Example: Use Euler's Method with stepsize 0.2 to estimate y(1.4),
given yprime = F(x,y) = x?xy and y(1) = 0.
x0 = 1 y0 = 0
x1 = 1.2 y1 = y0 + 0.2F(x0,y0) = 0 + 0.2(1?0) = 0.2
x2 = 1.4 y2 = y1 + 0.2F(x1,y1) = 0.2 + 0.2(1.2?1.2?0.2) = 0.392
So our answer is y(1.4) ? 0.392 since we're at the desired xvalue, x = 1.4.
 Suggested Problems: 9.2  # 21, 22, 23, 28ac
. Separable Equations
 If we have ypr...
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