Calculus from a Statistics Perspective

Samuel S. P. Shen; Dov Zazkis; Kimberly Leung; Chris Rasmussen

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arXiv · 1406.2731

Calculus from a Statistics Perspective

Samuel S. P. Shen·Dov Zazkis·Kimberly Leung·Chris Rasmussen

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Abstract

This paper provides an approach to establishing the calculus method from the concept of mean, i.e., average. This approach is from a statistics perspective and can help calculus learners understand calculus ideas and analyze a function defined by data or sampling values from a given function, rather than an explicit mathematical formula. The basics of this approach are two averages: arithmetic mean and graphic mean. The arithmetic mean is used to define integral. Area is used to interpret the meaning of an integral. Antiderivative is introduced from integral, and derivative-antiderivative pair is introduced as a mathematical operation entity. The graphic mean is an average speed in an interval and is used to interpret the meaning of a derivative.

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BibTeX RIS

Samuel S. P. Shen, Dov Zazkis, Kimberly Leung, Chris Rasmussen. 2014-06-10. Calculus from a Statistics Perspective. https://arxiv.org/abs/1406.2731

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