Highlights of Calculus
Highlights of Calculus (Res.18-005, MIT OCW). Instructor: Professor Gilbert Strang. Highlights of Calculus is a series of short videos that introduces the basics of calculus - how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The series is divided into three sections: 1) Introduction - Why Professor Gilbert Strang created these videos, 2) Highlights of Calculus - Five videos reviewing the key topics and ideas of calculus, Applications to real-life situations and problems, and 3) Derivatives - Twelve videos focused on differential calculus, More applications to real-life situations and problems. (from ocw.mit.edu)
| Lecture 13 - Linear Approximation/ Newton's Method |
The slope of a function y(x) is the slope of its TANGENT LINE. Close to x=a, the line with slope y'(a) gives a "linear" approximation. y(x) is close to y(a) + (x - a) times y'(a). If you want to solve y(x) = 0, choose x so that y(a) + (x - a) y'(a) = 0. This is a really fast way to get close to the exact solution to y(x) = 0 : "Newton's Method" x = a - y(a)/y'(a).
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