Abstract
Calculus is the study of the rate of change and the total accumulation of processes described by functions. In this chapter we review some familiar notions of function and explore functions that are defined by sequences of functions.
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Notes
- 1.
There is a record of an educational conference in the Middle Ages on the topic, “Can one teach long division without flogging?”
- 2.
There once was a function named g,
approximated closely by p.
When we put in x nearly,
we thought we’d pay dearly,
but g(x) was as close as can be. –Anon.
This limerick expresses that \(\ \left \vert g(x) - p(x_{\mathrm{approx}})\right \vert \leq \left \vert g(x) - p(x)\right \vert + \left \vert p(x) - p(x_{\mathrm{approx}})\right \vert\).
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Lax, P.D., Terrell, M.S. (2014). Functions and Continuity. In: Calculus With Applications. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7946-8_2
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DOI: https://doi.org/10.1007/978-1-4614-7946-8_2
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-7945-1
Online ISBN: 978-1-4614-7946-8
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