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Unformatted text preview: P r e l i m i n a r y d r a f t o n l y : p l e a s e c h e c k f o r fi n a l v e r s i o n ARE211, Fall 2007 LECTURE #16: TUE, OCT 23, 2007 PRINT DATE: AUGUST 21, 2007 (CALCULUS1) Contents 4. Univariate and Multivariate Differentiation 1 4.1. The fundamental idea: linear approximations to nonlinear functions 2 4.2. Univariate Calculus 3 4. Univariate and Multivariate Differentiation Assume you all know how to calculate the derivative of a single variable function, i.e., given f , calculate d f ( ) d x , denoted also f prime ( ). Important to know the difference between f prime ( ), which is a function and f prime ( x ), which is a number, the function evaluated at a point. Ill try to be careful to use this notation from now on: g ( ) is a RULE, represents a function. Since f prime ( ) is a function, like any other, it may have a derivative; if it does, call it f primeprime ( ). Do example f ( x ) = x 2 . Lots of standard kinds of functions you have to be able to differentiate in your sleep. Equivalent of being able to spell. Brainless activity....
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This note was uploaded on 08/01/2008 for the course ARE 211 taught by Professor Simon during the Fall '07 term at University of California, Berkeley.
- Fall '07