微分

This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering.

本书试图提供外微分形式、微分几何、代数拓扑、微分拓扑、李群、向量丛、Chern公式等前沿知识，它们对于深入理解经典物理、现代物理以及工程都是必需的。

Based on traditional Fourier differentiation matrix and some modifications of the original differentiation operator, this paper refers to a new kind of method——staggered-grid Fourier pseudospectral differentiation operator.

本文在传统傅里叶微分矩阵的基础上，对原始微分算子进行改进，引入了错格微分算子的傅里叶伪谱方法。

Applying Doss\'s method, we can get explicit solutions of the multivalued stochastic differential equations in one dimensional.

即通过解一个常微分方程和一个多值常微分方程得到这类多值随机微分方程的解。

We discuss the initial value value problems and boundary value problem for second-order integro-differential equation of mixed type in Banach space as follow:And give some results of maximal and minimal solutions of them.

我们讨论了如下带有一阶微分项的的二阶非线性积分-微分方程的最小最大解的存在性问题：{·犷"'，一刃，，，，T\x，"双，，、L工LU=工0，x LU=工L上t〔J 在够。3及笋。4中，'我们利用笋。1及笋。2的思路，讨论了相应的一阶、二阶脉冲积分一微分方程。

In exterior differentiation, one studies tensors, exterior algebra, tangent bundle, tangent vector fields, one-parameter groups action on a manifold, Frobenius's theorem, tensors fields, exterior differential form, integration on manifolds, Stokes's theorem etc.

外微分部分主要涉及外代数、切丛，光滑切向量场，单参数变换群，光滑张量场，外微分形式，Frobenius定理，外微分形式的积分，Stokes定理及其应用等。

Differential equations of tile first order in the finite discrete function are established, the solutions of which have very simpler structure.

引入了有限离散函数的微分与积分新概念，它具有与连续函数微分和积分相类似的性质，由它建立的一阶微分方程的解有较简单的代数结构。

The main contents of this course include: the elementary solution of first order differential equations, the theory of existence, uniqueness and continuity dependency of initial value problem of first order differential equations, the structure theory of higher order linear differential equation and the solution of constant coefficient equations, the structure theory of system of linear equations, basic solution matrix and the solution of system of constant coefficient equations.

本课程内容有：一阶微分方程初等解法，一阶微分方程初值问题的存在性、唯一性、连续依赖性理论，高阶线性微分方程解的结构理论和常系数方程解法，线性方程组的结构理论、基解矩阵和常系数方程组的解法。

The results are generalized to first-order neutral functional differential equation.

第四章讨论了一阶泛函微分方程解的零点分布，改进了一阶滞后型泛函微分方程在解的零点间距离的上界估计的结果，并将此结果推广到一阶中立型泛函微分方程。

The linearized partial differential equation of motion is derived based on Euler-Bernoulli beam theory, and reduced to a set of coupled Hill's equations by using Galerkin's method.

首先根据欧拉梁理论建立偏微分运动方程，利用迦辽金法转化偏微分方程为周期变系数常微分方程。

Based on the fundamental theory of impulsive differential systems, employing Green formula, Gauss divergence theorem, Jensen inequality and Gronwall-Bellman inequality with impulse, we discuss the oscillation of impulsive partial differential systems by adopting reduction to absurdity and the stability in via of comparison theorem, respectively. Especially, we take an in-depth study on the oscillation of neutral impulsive parabolic systems and the stability of a class of nonlinear impulsive partial differential equations and obtain some useful conclusions.

本学位论文以脉冲微分系统基本理论为基础，利用反证法的分析方法和比较定理，结合Green公式、Gauss散度定理、Jensen不等式、含脉冲的Gronwall-Bellman不等式以及相关数学工具研究了脉冲偏微分系统的振动理论和稳定性理论，特别对中立型脉冲时滞抛物系统的振动性和一类非线性脉冲偏微分系统的稳定性作了较为深入的研究，给出了一些有用的结论。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。