20e-lecture5

20e-lecture5 - Lecture 5 : Wednesday April 8th...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 5 : Wednesday April 8th jacques@ucsd.edu Key concepts : Vector valued function, gradient, differentiability, properties, chain rule 5.1 Derivatives of vector-valued functions We have not until now discussed derivatives of functions f : R n R m . In order to state the rules, we need some notation. A function f : R n R m assigns to each vector x = ( x 1 ,x 2 ,...,x n ) a new vector ( f 1 ( x ) ,f 2 ( x ) ,...,f m ( x )). The derivative of f if it exists can be defined in terms of limits. However, for our purposes, we only need to know that f j ( x ) = ( f 1 j ( x ) ,f 2 j ( x ) ,...,f mj ( x )) . Remember f j ( x ) means the derivative of f with respect to x j . So f 1 j ( x ) is the derivative of f 1 ( x ) with respect to x j . Thus the derivative is found by taking derivatives of each of the components of f ( x ). Example. Let f ( x,y ) = ( x + y,x/y,x- y ). This is a function f : R 2 R 3 . Then f 1 ( x,y ) = (1 , 1 /y, 1) and f 2 ( x,y ) = (1 ,- x/y 2 ,- 1) ....
View Full Document

This note was uploaded on 02/12/2010 for the course MATH 20E taught by Professor Enright during the Spring '07 term at UCSD.

Page1 / 3

20e-lecture5 - Lecture 5 : Wednesday April 8th...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online