This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 1 : Monday March 30th jacques@ucsd.edu Key concepts : Open ball, open set, continuous surface Know whether a given set is open 1.1 Functions of several variables Recall that R n denotes the set of all ntuples, or ndimensional vectors , of real numbers. For n = 1 we have the usual real line, and for n = 2 we have the plane. In this course, a function f : R n R m assigns to each vector in R n a vector in R m . This is called a function of n variables , since the domain consists of ndimensional vectors. So, for example, the function f : R 2 R 3 defined by f ( x,y ) = ( x,x + y,x/y ) is a function of two variables. Sometimes we will refer to a function f : R n R m for m > 1 as a vectorvalued function or a vector field , especially later in the course. In certain instances, the domain of a function of several variables is restricted to be a subset of R n . For example, the domain of the function above is { ( x,y ) R 2 : y 6 = 0 } ....
View Full
Document
 Spring '07
 Enright
 Math, Vectors

Click to edit the document details