全微分求偏导法和比较系数方法的同一性

给出了全微分求偏导法的证明,指出了比较系数法和全微分求偏导方法的同一性,并且给出了具体的例子.     

Pattern avoiding ballot paths and finite operator calculus

Counting pattern avoiding ballot paths begins with a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of →$\to$ and ↑$\uparrow$ steps determine the solution of the recursion formula. If the recursion can be solved by a polynomial sequence, we apply the Finite Operator Calculus to find an explicit form of the solution in terms of binomial coefficients.     

Symbolic Itô calculus in AXIOM: An ongoing story

Symbolic Itô calculus refers both to the implementation of Itô calculus in a computer algebra package and to its application. This article reports on progress in the implementation of Itô calculus in the powerful and innovative computer algebra package AXIOM, in the context of a decade of previous implementations and applications. It is shown how the elegant algebraic structure underlying the expressive and effective formalism of Itô calculus can be implemented directly in AXIOM using the package's programmable facilities for strong typing of computational objects. An application is given of the use of the implementation to provide calculations for a new proof, based on stochastic differentials, of the Mardia-Dryden distribution from statistical shape theory.     

用求导法则证明一类组合恒等式

本文利用函数积的 n阶导数的求导法则 ,引入适当的辅助函数 ,证明了两个组合恒等式及其几个推论     

基于问题驱动的"微积分基本公式"教学设计

从实例出发,借助问题驱动,以微积分基本公式讲授为例进行教学设计,意在引导学生发现问题、分析问题、解决问题,从而加深对定理的理解和应用。     

谈谈求极限的方法

本文总结了求极限的几种方法,比如用定义,公式,定理,性质求极限等。     

Symbolic solutions of some linear recurrences

A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a random variable with no reference to any probability space. We give several examples of applications and state an explicit form for the class of linear recurrences involving Sheffer sequences satisfying a special initial condition. The results here presented can be easily implemented in a symbolic software.