Chapter 3
Calculus for Vector-Valued Functions
Basic Object: | R^{n} |
Basic Map: | Differentiable functions f : R^{n} → R^{m} |
Basic Goal: | Inverse Function Theorem |
3.1 Vector-Valued Functions
A function f : R^{n} → R^{m} is called vector-valued since for any vector x in R^{n}, the value (or image) of f (x) is a vector in R^{m}. If (x_{1}, ..., x_{n}) is a coordinate system for R^{n}, the function f can be described in terms of m real-valued functions by simply writing:
Such ...
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