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2010 | OriginalPaper | Buchkapitel
The Derivative
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The derivative of a map is the linear term in its Taylor approximation; it is a map itself. Because linear approximations are simpler than those of higher order, and because linear maps are easier to visualize than nonlinear ones, the derivative is an especially important part of the study of maps. It gives us valuable local information. We study the derivative in this chapter, beginning with the familiar connection to tangents.