应用函数

This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

理解和掌握《数学分析》的概念、理论和方法，对于学生加深理解数学的基本思想和方法，培养抽象思维能力和逻辑思维能力，提高数学素养具有重要的意义。主要内容包括：实数集和函数，数列极限，函数极限，连续性，导数和微分，微分中值定理及其应用，实数完备性，积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

The digital algorithms of integral and discrete wavelet transform are presented for purpose of electric power system protection, based on the analysis of wavelet transform for sampled digital signals under the Shannon sampling theorem.

从电力系统继电保护应用的角度，结合香农采样定理，深入探讨了连续信号和离散信号的小波变换的关系，给出了离散信号的积分小波变换和离散小波变换的数字计算方法。从理论上研究了信号小波变换的误差与尺度函数和小波函数的关系。

Limits, Continuity, Derivatives, and Integration of Single Variable, Integration Techniques, Applications of Derivatives and Integrals, Infinite Sequences and Series, Multivariable Function and Their Derivative, Multiple Integrals, Integration in Vector Fields.

课程内容：单变数函数之极限、连续、微分、积分，积分技巧，微分与积分的应用，无穷数列与级数，多变数函数之偏微分、可微性，多重积分，极值问题，向量场积分。

As an application of the interpolation criteria, the interpolation formula of bandlimited transmission signals which satisfied the condition of the Nyquist first criteria has been presented.

在信号插值问题上，首先利用基本的信号模型和Nyquist第一准则，导出了一个插值准则，作为插值准则的应用，对满足Nyquist第一准则的带限传输信号给出了一个通用的插值公式，以升余弦滚降函数为成形滤波函数的限带传输信号作为一个特例，通过计算机仿真验证了插值算法的可行性和有效性。

It gives a method in calculating belief function and belief interval of the whole simulation result.

将信任函数理论应用到了仿真结果评估问题中，给出了总体仿真结果的信任函数和信念区间的计算方法。

This dissertation firstly introduces the principles of four kinds of simple gridding methods, which are"Linear interpolation based on triangulation","Inverse distance weighted and averaged method","Modified Shepard's method"and"Multiquardirc method". Secondly, it researches the Ordinary Kriging method for geophysical irregular data, which mainly includes the base knowledge of region change and variogram and the principle of Ordinary Kriging method. Thirdly, it researches the Inverse Interpolation for geophysical irregular data, which mainly includes the principle of inverse interpolation and its iterative algorithm, and the principle of Inverse Interpolation to realize the gridding of geophysical data. Finally, it uses these gridding methods to grid theoretical model data of potential field and raw aeromagnetic data, and compares and analyzes the gridding results.

本文首先简单介绍了地球物理不规则分布数据的四种简单网格化方法(即基于三角网的线性插值法、反距离加权平均法、改进的Shepard方法和多元二次函数法)的方法原理；接着，重点研究了地球物理不规则分布数据网格化的普通克里金法，主要研究了区域变化量、变差函数的基础知识和普通克里金法的方法原理；之后，重点研究了地球物理不规则分布数据网格化的反插值法，主要研究了反插值法的方法原理和迭代求解算法，以及反插值法实现地球物理数据网格化的原理；最后，应用这些方法对理论位场模型和实际航磁数据进行了试验、对比和分析。

The theory of KEM for simple soils limit analysis is dissertated in detail. Based on this, KEM has been developed to complicated soils limit analysis for the first time. Appropriate functions and variables of different engineering practice are presented, and the minimization technique for functions is adopted the conjugate gradient method.

在详细论述了土体极限分析KEM的基本原理、对均质土体极限分析KEM研究的基础上，根据KEM的基本原理，在国内首次将KEM扩展应用到复杂土体的极限分析中，根据工程问题的实际情况找出了合适的KEM土体极限分析目标函数和自变量，对目标函数的优化方法采用了变尺度法。

Theorem of mean significance: The application derivative research function's nature wants directly or indirectly with the aid of Yu Zhongzhi,Specially Lagrange theorem of mean,Here is mainly from the equality proof, the inequality proof, existence asks some limits, the determination equation root and so on five aspects to carry on the discussion,so, The theorem of mean is transforms as the function in the sector research important tool, Must bring to the enough attention in the middle of ours study and the teaching.

中值定理意义：应用导数研究函数的性质都要直接或间接地借助于中值，特别是拉格朗日中值定理，这里主要是从等式的证明、不等式的证明、求一些极限、判定方程根的存在性等五个方面来进行讨论，因此，中值定理是转化为函数在区间上的研究的重要工具。在我们的学习与教学当中要引起足够的注意。

Based on specific requirement for the top-coal caving mining to the four-bar linkage ,a design method of the four-bar linkage is put forward in the paper in which the least difference function between the lemniscate locus and the power function curve is used as the main objective function.

基于综放工艺对支架四连杆机构的特殊要求，首次提出以双纽线与幂函数曲线之差值最小作为主要目标函数的数学模型，并在此基础上应用VisualBasic5 0编制了四连杆机构的优化设计程序，可以同时实现优化参数显示与优化结果的动态显

Support vector machines was introduced to structural reliability analysis as a tool for reconstruction of limit state function.

将支持向量机作为极限状态函数重构的工具引入结构可靠性分析问题中，并结合蒙特卡洛方法，分别给出了模式识别型和函数回归型两种支持向量机模型应用于结构可靠性分析的计算流程图。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。