Abstract
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.
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© 2010 Springer New York
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Callahan, J.J. (2010). The Derivative. In: Advanced Calculus. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7332-0_4
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DOI: https://doi.org/10.1007/978-1-4419-7332-0_4
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7331-3
Online ISBN: 978-1-4419-7332-0
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