ENG 6 Lecture Notes - Lecture 11: Bracketing, Taylor Series, Matlab

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Numerical calculus: matlab has good built in methods to give numerical solutions, have to make sure answers make sense. Review: anonymous functions: one line function that you can use quickly. Quick numerical derivative estimations: derivative is change in y over change in x, function diff. Caution: dimensions of slope vector will not be the same as x and y vectors, there will be one less. Slope = diff(y). /diff(x): slope is now vector of slopes at all points corresponding to x and y vectors. Find index of array closest to 3. 4 and read out value of slope. Forward difference approx. of first derivative: to approximate derivative at x(i), find point to the right, x(i+1), and find slope between the two points. Backward difference approx of first derivative: look at point behind x(i) this time f"(x(i)) = (f(x(i))-f(x(i-1)))/(x(i)-(x(i-1)) Central difference approx. of first derivative: take points from behind and in front of x(i, der_cent=@(t,delt) (func(t+delt) func (t delt)). /(2.

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