浅谈作反函数代换求不定积分

在求不定积分时,当被积函数中含有某已知函数的反函数时,若令反函数为积分变量,作换元积分法,往往使不定积分更容易求得.下面举例说明.     

关于反函数的不定积分的一种简便求法

反函数的不定积分比较困难，尤其当被积函数的次数较高时。计算很麻烦．利用分部积分法和换元积分法可以推导出关于反函数的不定积分的一种简便求法，使得被积函数的次数降低，运算简化．实例说明这种方法是可行的．     

函数式的恒等变形在不定积分中的应用

函数式的恒等变形在不定积分中的应用樊庐生（合肥市物价学校，合肥２３００５１）高等数学中的不定积分的解法通常有：利用不定积分的性质及基本公式；利用换无法；利用分部积分法，等。对于有理函数、三角函数的有理式、简单无理函数等不定积分也都有确定的模式。但对于...     

不定积分的一个注记

本文对2018年全国硕士研究生入学统一考试中一道不定积分问题进行了研究,给出了5种解法,提出了一种新的计算不定积分的方法——待定函数法.     

两类特殊积分的简便算法

摘要针对被积函数为多项式与指数函数乘积或多项式与三角函数（正弦函数、余弦函数）乘积情形,给出了相应不定积分的简便计算方法．     

三角函数有理式不定积分注记

针对求解三角函数有理式不定积分的问题,借助实例说明传统方法存在不足之处,并给出此类不定积分的完整解．     

巧用换元积分法一题九解

运用换元积分法对一道不定积分习题给出了9种不同解法,探讨总结换元积分法使用中的一些常用技巧．     

一类微分方程特解的逆矩阵求法

根据函数求导运算与函数的不定积分互为逆运算的思想,以及有限维函数向量空间在求导运算下不变的条件,利用逆矩阵方法得到向量空间中基函数的不定积分,从而给出一定条件下用逆矩阵法求一类常系数非齐次线性微分方程特解的新方法.     

分段函数不定积分求法探讨

分段函数在分界点处不连续时所得的不定积分在分界点处的连续性问题，可根据分段函数在分界点的连续性或间断类型来判定，并由此解决分段函数求不定积分时各段所带常数之间的关系问题．     

不定积分中的“积不出”问题

利用刘维尔(J.Liouville)定理讨论了几类不定积分是否初等函数的问题,并给出了相应的判定法则.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.