lect116_14rev_f11

lect116_14rev_f11 - Friday, October 7 Lecture 14 : Newtons...

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Friday, October 7 Lecture 14 : Newton’s iterative procedure. (Refers to section 4.1 in your text) Students who have mastered the content of this lecture know about : Newton’s iterative formula for approximating roots of simple functions. Students who have practiced the techniques presented in this lecture will be able to : Use Newton’s iterative formula for approximating roots of simple functions by estimating a root at first and then construct a sequence of numbers which converges to a root, use a spreadsheet to construct such sequences. 14.1 Newton’s iterative procedure for finding roots Let f : R R be a continuous function. We sketch the curve of y = f ( x ). At first glance we can approximate a zero (root) x * of y = f ( x ) by roughly examining where the curve of y = f ( x ) intersects the x -axis. Say our first approximation of the zero x * is denoted by x 1 and we attempt to improve on this approximation. -
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lect116_14rev_f11 - Friday, October 7 Lecture 14 : Newtons...

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