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关键词： 数学分析   现状   教学改革  

摘要： 长期以来,《数学分析》课是教师教得最累,学生学得最苦,效果却不太如意的课程。计算机和大学英语等级考试冲击了包括数学分析在内的专业课程的平时学习和期末考试。本文介绍了我们关于《数学分析》课程教学内容和教学方法改革的理论探讨与教学实践,以及进行分段教学与考试改革的经验。

关键词： 数学分析   问题链   设计原则  

摘要： 数学知识的内部结构是一个纵横交错的“问题链”结构,面对数学问题,寻求其与横向或纵向知识有联系的若干问题,必须符合数学学科特性、知识结构、严谨思维之需要的原则。其中问题链设计原则包括:数学化原则、可行性原则、层次性原则、探索性原则、模块化原则。

ISBN: (纸本)7040187515

关键词： GROUND-STATE   ENERGIES   HELIUM  

摘要： Bohr proposed in 1913 a model for atoms and molecules by synthesizing Planck's quantum hypothesis with classical mechanics. When the atom number Z is small, his model provides good accuracy for the ground-state energy. When Z is large, his model is not as accurate in comparison with the experimental data but still provides a good trend agreeing with the experimental values of the ground-state energy of atoms. The main objective of this paper is to provide a rigorous mathematical analysis for the Bohr atom model. We have established the following: (1) An existence proof of the global minimizer of the ground-state energy through scaling. (2) A careful study of the critical points of the energy function. Such critical points include both the stable steady-state electron configurations as well as unstable saddle-type configurations. (3) Coplanarity of certain electron configurations. Numerical examples and graphics are also illustrated. (c) 2006 American Institute of Physics.

关键词： counter-current chromatography   gravitational force   large-scale separation   mathematic analysis  

摘要： The gravitational force exerts an important effect on the counter-current chromatography (CCC) and has been used to retain the stationary phase and improve the efficiency in the various CCC separations. This paper deals with the effect of gravitational force on type-J CCC, one of the most popular CCC methods by the mathematical analysis for the first time. The theoretical analyses reveal a close relationship between the effect of gravitational force, the placed orientation of type-J CCC apparatus, and the revolutional speed. Two placed orientations are more suitable for preparative CCC separation: one is common horizontal, and the other upright. Thus, there are three optimum conditions for type-J CCC separation, the first using horizontal apparatus at very low revolutional speed around 10 rpm in the gravitational filed, the second by use of upright apparatus at moderate revolutional speed around 100 rpm in the three-dimensional complex force field composed of centrifugal and orthogonal gravitational force, and the third employing the apparatus placed at any orientation including horizontal and upright CCC apparatus at high revolutional speed above 300 rpm in the centrifugal force field. Therefore, we should consider the effect of gravitation force on CCC at the selection of proper operational conditions according to properties of two immiscible phases, the desired revolutional speed and the parameters of apparatus in order to utilize efficiently the effect of gravitational force. These analyses and results will benefit to improve the efficiency of CCC separation, especially large-scale industrial preparation. (c) 2005 Elsevier B.V. All rights reserved.

关键词： boundary integral equation method   boundary element method   annular plate   spurious eigenvalue   degenerate kernel   Fourier series   circulants   SVD technique of updating term   Burton and Miller method   CHIEF method  

摘要： In this paper, the spurious eigenequations for annular plate eigenproblems by using BIEM and BEM are studied in the continuous and discrete systems. Since any two boundary integral equations in the plate formulation (4 equations) can be chosen, 6 (C-2(4)) options can be considered instead of only two approaches (single-layer and double-layer methods, or singular and hypersingular equations) which are adopted for the eigenproblems of the membrane and acoustic problems. The occurring mechanism of the spurious eigenequation for annular plates in the complex-valued formulations is studied analytically. For the continuous system, degenerate kernels for the fundamental solution and the Fourier series expansion for the circular boundary density are employed to derive the true and spurious eigenequations analytically. For the discrete system, the degenerate kernels for the fundamental solution and circulants resulting from the circular boundary are employed to determine the true and spurious eigenequations. True eigenequation depends on the specified boundary condition while spurious eigenequation is embedded in each formulation. It is found that the spurious eigenvalue for the annular plate is the true eigenvalue of the associated interior problem with an inner radius of the annular domain. Also, we provide three methods (SVD updating technique, Burton and Miller method and CHIEF method) to suppress the occurrence of the spurious eigenvalues. Several examples were demonstrated to check the validity of the formulations. Copyright (c) 2005 John Wiley & Sons, Ltd.

关键词： 解析数论   手册   初等数论   离散数学   数学分析   工具书   概率论   论题   密相  

摘要： 本书是一部关于数论的大型资料性工具书，本卷和第一卷（1995年出版）一样，着重论述数论中的一些重要方面（偏重于初等数论和解析数论），特别是与离散数学紧密相关的以及与代数、几何、数学分析和概率论有交叉性的论题。与第一卷相比较，虽然后者涉及的内容较全面，但罗列的公式占了很大的篇幅，本卷对第一卷中一些论题作了专门而深入的论述，可以看作是第一卷的补充和深化。

关键词： synchronization   chaos   simplest linear   simplest quadratic   Ueda   communications  

摘要： A master-slave concept of chaotic system synchronization is examined and applied in secure data transmission. In most situations when examining this type of synchronization one considers the asymptotic stability of the particular system via Lyapunov's direct method, or conditional Lyapunov exponents are considered. In this paper Lyapunov's direct method is employed to show the asymptotic stability within the simplest piecewise linear master-slave chaotic flow. Also, however, in this paper, primarily the master-slave synchronization properties of the simplest quadratic chaotic flow and Ueda chaotic system are examined directly by means of mathematical manipulation of their dynamics equations, where possible, as well as via numerical simulations. In order to achieve this, in conjunction, numerical simulations and theoretical analysis are made use of. In this way it is shown that the synchronization error of the two aforementioned chaotic master-slave systems can indeed be predicted for certain driving signals, without the need for either analytical or numerical evaluation of the conditional Lyapunov exponents or employment of Lyapunov's direct method. Finally, a digital communication system based on the initial condition modulation of the chaotic carrier by the binary message to be transmitted, in the presence of noise, is proposed and evaluated for the three chaotic systems investigated. (c) 2005 Elsevier B.V. All rights reserved.

关键词： 变式教学   课本习题   数列   通项   数学分析  

摘要： 文[1]例谈了an=pan-1+f(n)型数列的通项求法,让笔者受益匪浅.但文[1]中变题2,3,4,7最后在方法点评上似有不妥,今冒昧提出,与大家讨论.我们先看变题2:已知数列{an}中,a1=1/2,an=4an-1-3n-1,求an.

关键词： 数学分析   中学数学   应用  

摘要： 将高师数学分析运用于中学教学数学,可以使许多由于受知识的局限而无法深入讨论的问题得到解决,起到了改变思维方式、拓宽解题思路的作用。