Engineering Calculus Notes 425

Engineering Calculus Notes 425 - 2.2 to indicate the domain...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
4 Mappings and Transformations: Vector-Valued Functions of Several Variables In this chapter we extend diferential calculus to vector-valued Functions oF a vector variable. We shall reFer to a rule (call it F ) which assigns to every vector (or point) −→ x in its domain an unambiguous vector (or point) −→ y = F ( −→ x ) as a mapping From the domain to the target (the plane or space). This is oF course a restatement oF the de±nition oF a Function, except that the input and output are both vectors instead oF real numbers. 1 We shall use the arrow notation ±rst adopted in
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2.2 to indicate the domain and target oF a mapping: using the notation R 2 For the plane and R 3 For space, we will write F : R n R m to indicate that the mapping F takes inputs From R n ( n 3) and yields values in in R m ( m 3). IF we want to speciFy the domain D R n , we write F : D R m . 1 More generally, the notion of a mapping from any set of objects to any (other) set is deFned analogously, but this will not concern us. 413...
View Full Document

This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online