RES.18-005 | Spring 2010 | Undergraduate

Highlights of Calculus

Derivatives (12 videos)

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)          SEE THE EXAMPLES

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.

Course Info

As Taught In
Spring 2010
Learning Resource Types
Lecture Videos
Lecture Notes