n次分部积分法研究及其应用  

A Study of N-order Integration by Parts and Its Applications

作　　者：沈澄[1] 

机构地区：[1]浙江工商职业技术学院,浙江宁波315012

出　　处：《佳木斯大学学报（自然科学版）》2017年第3期516-520,共5页Journal of Jiamusi University：Natural Science Edition

摘　　要：分部积分法是基于两种不同类型函数乘积导数运算的可逆性,而推寻得出的积分重要理论之一。因连续多次分部造成的运算繁复、算式冗长以及系数符号的频繁改变,容易导致运算错误。为解决需n次分部积分之困惑,探究分部积分法并拓展到n次分部积分法法则,在实践中简捷证明了Taylor定理、简明分析了泛函极值的必要条件、提炼形成了n次分部积分的速解模型。Integration by parts, derived based on the reversibility of the derivative of the product of differ- ent types of functions, is one of the important theories of integral computation. In advanced mathematics, there are plenty of integral problems that cannot be solved by applying integration by parts once. Applying integration by parts multiple times results in heavy and complicated computations, tediously long equations, as well as fre- quently changing signs of coefficients, which makes computation error - prone. To solve the puzzle, new ways of thinking and methods are explored and exercised. In practice, the expanded n- way integration by parts is able to succinctly prove Taylor~ theorem, concisely analyse the necessary condition of functional extremum, as well as abstract and form a fast solving model for n -way integration by parts.

关 键 词：n次分部积分 n重可积函数 变分算子 速解模型 

分 类 号：O13[理学—数学]