2018/02/08 by Jingzhong Zhang, Zhang, Jingzhong, Zengxiang Tong +1
Engineering · Mathematics · Social Sciences · #Experimental Learning in Engineering #FOS: Mathematics #General Mathematics (math.GM) #Mathematical and Theoretical Analysis #Mathematics Education and Teaching Techniques
paper · pdf · doi:10.48550/arxiv.1802.03029
openalex publication_date 2018/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.