Teaching Design of the First Kind of Curve Integral

DOI: https://doi.org/10.62517/jnse.202417106

Author(s)

Bing Hao*, Yali Yang, Huan Luo

Affiliation(s)

Oxbridge College, Kunming University of Science and Technology, Kunming 650106, Yunnan, China * Corresponding Author.

Abstract

This paper designs the teaching of the first kind of curve integral. Firstly, based on the physical background of the first kind of curve integral, using "the methods of elementary mathematics +the thinking method of limit" and combining the historical background of the differential calculus symbols, the definition of the first kind of curve integral is strengthened in the intuitive thinking; secondly, based on the definition form of the first kind of curve integral, three small problems in the calculation are analyzed from a symbolic perspective, and the basic calculation method of the first kind of curve integral is illustrated with examples; finally, the definition form of the first kind of curve integral is used to generalize and solve the surface area problem of a class of rotating surfaces, deepening the understanding of the application of the first kind of curve integral. This paper aims to provide new inspiration to advanced mathematics enthusiasts and to provide better mathematical logical thinking abilities.

Keywords

Physics Background; Intuitive Thinking; The First Kind of Curve Integral; Calculation Understanding; Area

References

[1] Hua Luogen. Introduction to Higher Mathematics. (Volume II). Higher Education Press, 2009. [2] Deng Fengru, Bi Yajun. Reflections on Curve Integral Teaching. Journal of North China Institute of Areospace Engineering, 2010, 20(2):48-50. [3] Gong Wanzhong. A Research on Teaching the Relationship between Two Type of Line Integrals. Studies In College Mathematics, 2017, 2, 24-27. [4] Yang Chao, Fang Hao, Jiang Xiaoqian. Postgraduate Mathematics 24 Classes. Beijing Institute of Technology Press, 2017. [5] Yang Mei, Wang Zejun, Yang Limin, Gao Jie. Discussion on the Polar Coordinate Formula for Calculating the Arc Length of Plane Curve by Definite Integral. Mathematics Learning and Research, 2022, 6:5-7. [6] Wu Zhenkui, Liang Bangzhu. Complete Guide to Solving Higher Mathematics. (Volume I). Harbin Institute of Technology Press, 2013. [7] Zhou Lansuo, Luan Jinfeng, Yin Xiaojun, Liu Juhong, Zhang Jun. Methods of Transforming Curviliner Integral to Definite Integral. Studies Incollege Mathematics, 2021, 24(2):31-34. [8] Wang Wenlong, Tan Chang, Qu Zhilin. Notes on the Calculation about the Area of Rotation Surface Using First Type Curvilinear Integral. College Mathematics, 2022, 38(6):79-83. [9] Qiao Xu-an. Teaching Methods of Two Kinds of Curve Integral. Journal of AnHui Vocational College of Electronics & Information Technology, 2015, 14(5):56-57. [10] Wan Xichang, Zhang Shuxin. Preliminary Study on the Calculation Method of Two Kinds of Curve Integrals. Journal of Jilin Agricultural Science and Technology University, 2015, 24(4).107-109.