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All the Mathematics You Missed by Lori Pedersen, Thomas A. Garrity

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Chapter 3

Calculus for Vector-Valued Functions

Basic Object:

Rn

Basic Map:

Differentiable functions f : RnRm

Basic Goal:

Inverse Function Theorem

3.1  Vector-Valued Functions

A function f : RnRm is called vector-valued since for any vector x in Rn, the value (or image) of f (x) is a vector in Rm. If (x1, ..., xn) is a coordinate system for Rn, the function f can be described in terms of m real-valued functions by simply writing:

image

Such ...

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