Calculus without Limit Theory

Jingzhong Zhang; Zengxiang Tong

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arXiv · 1802.03029

Calculus without Limit Theory

Jingzhong Zhang·Zengxiang Tong

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Abstract

This paper establishes calculus upon two physical facts: (1) any average velocity is always between two instantaneous velocities, and (2) the motion of an object is determined once its velocity has been determined. It directly defines derivative and definite integral on an ordered field, proves the fundamental theorem of calculus with no auxiliary conditions, easily reveals the common properties of derivatives, and obtains differentiation formulas for elementary functions. Further discussion shows that the new definitions are in accord with the traditional concepts for continuously differentiable functions. This is a result of the authors' research in the field of educational mathematics, which hopes to provide a more elementary and effective way to teach calculus.

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BibTeX RIS

Jingzhong Zhang, Zengxiang Tong. 2018-02-08. Calculus without Limit Theory. https://arxiv.org/abs/1802.03029

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