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 x-value 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 x-value, x = 1.4. - Suggested Problems: 9.2 - # 21, 22, 23, 28ac . Separable Equations - If we have ypr...