J. Zhang, and Z. Tong. (2018)cite arxiv:1802.03029Comment: 14 pages and no figures.
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.
%0 Generic
%1 zhang2018calculus
%A Zhang, Jingzhong
%A Tong, Zengxiang
%D 2018
%K 2018 arxiv calculus physics
%T Calculus without Limit Theory
%U http://arxiv.org/abs/1802.03029
%X 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.
@misc{zhang2018calculus,
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.},
added-at = {2018-03-29T19:33:28.000+0200},
author = {Zhang, Jingzhong and Tong, Zengxiang},
biburl = {https://www.bibsonomy.org/bibtex/2c207ea39cd7206375d35d7420682358a/achakraborty},
description = {[1802.03029] Calculus without Limit Theory},
interhash = {ce4898481bcb3be1ac8d58324dc17259},
intrahash = {c207ea39cd7206375d35d7420682358a},
keywords = {2018 arxiv calculus physics},
note = {cite arxiv:1802.03029Comment: 14 pages and no figures},
timestamp = {2018-03-29T19:33:28.000+0200},
title = {Calculus without Limit Theory},
url = {http://arxiv.org/abs/1802.03029},
year = 2018
}