研究积分学在物理无穷小微元上的体现  

Research on Manifestation of Integral Calculus on Physical Infinitesimal Differential Elements

作　　者：宋亚勋 SONG Yaxun(Basic Course Department,Wuhan Donghu University,Wuhan,Hubei Province,430212 China)

机构地区：[1]武汉东湖学院基础课部,湖北武汉430212

出　　处：《科技资讯》2025年第6期231-235,共5页Science & Technology Information

摘　　要：积分学是微积分的一个重要组成部分。从物理无穷小微元出发,结合之前对微分学的讨论,给出了积分学中相关内容在物理无穷小微元上的体现,包括连续物理函数的不定积分表现为离散函数的不定求和、连续物理函数的定积分表现为离散函数的代数和、连续物理函数的原函数存在定理表现为离散函数的不定求和可以通过部分和表示、连续物理函数的牛顿-莱布尼茨公式表现为离散函数之间的代数关系。这些讨论内容将有助于加深高校教师和学生对“大学物理”知识的理解。Integral calculus is an important component of calculus.Starting from the concept of infinitesimal elements in physics,this research,in conjunction with previous discussions on differential calculus,explores how integral calculus concepts manifest through infinitesimal elements.It includes the notion that the indefinite integral of a continuous physical function is represented by the indefinite sum of discrete functions on the physical infinitesimal element.The definite integral of continuous physical functions is expressed as the algebraic sum of discrete functions on the physical infinitesimal element.The existence theorem of primitive functions of continuous physical functions is manifested as the indefinite sum of discrete functions on the physical infinitesimal element,which can be expressed by partial sums.The Newton-Leibniz formula of continuous physical functions is represented by the algebraic relationship between discrete functions on the physical infinitesimal element These discussions will help deepen the understanding of college physics knowledge among university teachers and students.

关 键 词：积分学 物理无穷小微元 不定积分 定积分 

分 类 号：O411[理学—理论物理]