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整套试卷注重考查了数学的基础知识,继续加强几种基本技能、基本能力的考查力度,增强了数学在实际生活中的应用性,突出了数学的探究、建模思想,注重与新课改教材的接轨,反映了数学的终结目标———应用于生活.一、试题特点1.继续保持稳定,突出考查学科知识的主干内容所考内容尽量做到全面、适度,又突出支撑学科的知识体系的主干,卷中作为初中数学最基本内容的题有1、2、3、4、5、6、7、11、12、13、14、15、16、17、19、21、22、23,约占47%.代数约占54%,几何约占46%,分配合理.方程思想、函数思想、分类思想、数形结合思想在试题中有所反映,… 相似文献
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提起华润,你首先想到的是华润万家、苏果、欢乐颂,还是雪花啤酒、怡宝饮料、华润食品,抑或是华润地产、电力、新能源、水泥、燃气、医药、金融,甚至是微电子、纺织、化工?粗略数算,顿觉华润的多元化真是名副其实。 相似文献
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巧用统一代数替换法证明三角形不等式 总被引:1,自引:1,他引:0
众所周知,数学奥林匹克中三角形不等式证明试题屡出不穷,三角形不等式,包含三角形的各种元素(三边a、b、c,内角A、B、C及三角式,半周长s,外接圓半径R,内切圆半径r,旁切圆半径a、r_b、r_c,高h_a、h_b、h_c、中线m_a、m_b、m_c,角平分线t_a、t_b、t_c,面积s_△),可谓千姿百态,但往往有其共同特点:条件简单,结论复杂;因而证法灵活多变,颇有难度。 相似文献
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三位数凑“20”数——指三个数字之和为“20”的数列,如:3、8、9,4、7、9,7、7、6,8、8、4。……等,这些数列去乘二个同数,三个或四个同数,均有一些简便的巧妙方法,这是多年经验总结,也是合乎数学原理,是把笔算、心算、珠算有机她结合起来,加也灵活运用,因此它省力、省心、省时间、快速、好忆、启迪智力,具体如下。 相似文献
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“课题学习”类试题在近几年各地中考试题中频频出现,2011年尤为凸出,如北京、贵阳、盐城、南京、苏州、江西等省市的试卷中都有这类考题.此类试题通常以阅读理解、探索研究、实验操作等不同形式呈现,或以恰当的数学知识为素材,或以几何图形为题材,或以数学问题为背景等,通过对相关问题的描述、观察、操作(包括数据分析、整理、运算或作图、证明)、归纳、探究等,由问题再发现问题,并创新性地解答问题.试题在注重考查相关基础知识,基本技能、方法的同时,更注重考查考生对相关知识理解、联想、探究、发现、归纳、总结及创新的能力,是近几年特别是2011年中考命题中出现的新题型、新亮点. 相似文献
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Mehdi Dehghan Akbar Mohebbi 《Numerical Methods for Partial Differential Equations》2009,25(1):232-243
In this article, we introduce a high‐order accurate method for solving the two dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivatives of linear hyperbolic equation and collocation method for the time component. The resulted method is unconditionally stable and solves the two‐dimensional linear hyperbolic equation with high accuracy. In this technique, the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method give a very efficient approach for solving the two dimensional linear hyperbolic equation. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
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Magda Rebelo 《Journal of Computational and Applied Mathematics》2010,234(9):2859-2869
This work is concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation. Owing to the singular behavior of the solution near the origin, the global convergence order of product integration and collocation methods is not optimal. In order to recover the optimal orders a hybrid collocation method is used which combines a non-polynomial approximation on the first subinterval followed by piecewise polynomial collocation on a graded mesh. Some numerical examples are presented which illustrate the theoretical results and the performance of the method. A comparison is made with the standard graded collocation method. 相似文献
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Akbar Mohebbi Mehdi Dehghan 《Numerical Methods for Partial Differential Equations》2008,24(5):1222-1235
In this article, we introduce a high‐order accurate method for solving one‐space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivative of linear hyperbolic equation and collocation method for the time component. The main property of this method additional to its high‐order accuracy due to the fourth order discretization of spatial derivative, is its unconditionally stability. In this technique the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method produce a very efficient method for solving the one‐space‐dimensional linear hyperbolic equation. We compare the numerical results of this paper with numerical results of (Mohanty, 3 .© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
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Mehdi Dehghan Akbar Mohebbi 《Numerical Methods for Partial Differential Equations》2008,24(3):897-910
In this article, we apply compact finite difference approximations of orders two and four for discretizing spatial derivatives of wave equation and collocation method for the time component. The resulting method is unconditionally stable and solves the wave equation with high accuracy. The solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. We employ the multigrid method for solving the resulted linear system. Multigrid method is an iterative method which has grid independently convergence and solves the linear system of equations in small amount of computer time. Numerical results show that the compact finite difference approximation of fourth order, collocation and multigrid methods produce a very efficient method for solving the wave equation. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
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《Journal of Computational and Applied Mathematics》1997,79(2):289-297
A new approximation method is proposed for the numerical evaluation of the nonlinear singular integrodifferential equations defined in Banach spaces. The collocation approximation method is therefore applied to the numerical solution of such type of nonlinear equations, by using a system of Chebyshev functions.Through the application of the collocation method is investigated the existence of solutions of the system of non-linear equations used for the approximation of the nonlinear singular integrodifferential equations, which are defined in a complete normed space, i.e., a Banach space. 相似文献
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In this paper, a collocation method based on the Bessel polynomials is introduced for the approximate solution of a class of linear integro‐differential equations with weakly singular kernel under the mixed conditions. The exact solution can be obtained if the exact solution is polynomial. In other cases, increasing number of nodes, a good approximation can be obtained with applicable errors. In addition, the method is presented with error and stability analysis. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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The purpose of this study is to implement Adomian–Pade (Modified Adomian–Pade) technique, which is a combination of Adomian decomposition method (Modified Adomian decomposition method) and Pade approximation, for solving linear and nonlinear systems of Volterra functional equations. The results obtained by using Adomian–Pade (Modified Adomian–Pade) technique, are compared to those obtained by using Adomian decomposition method (Modified Adomian decomposition method) alone. The numerical results, demonstrate that ADM–PADE (MADM–PADE) technique, gives the approximate solution with faster convergence rate and higher accuracy than using the standard ADM (MADM). 相似文献
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We prove quasioptimal and optimal order estimates in various Sobolev norms for the approximation of linear strongly elliptic periodic pseudodifferential equations in two independent variables by a modified method of nodal collocation by odd degree polynomial splines. In the one-dimensional case, our method coincides with the method of nodal collocation when odd degree polynomial splines are employed for the trial functions. The convergence analysis is based on an equivalence which we establish between our method and a nonstandard Galerkin method for an operator closely related to the given operator. This equivalence is realized through a crucial intermediate result (which we now term the Arnold-Wendland lemma) to connect the solution of central finite difference equations and that of certain nonstandard Galerkin equations. The results of this paper are genuine two-dimensional generalizations of the results obtained by ARNOLD and WENDLAND in [2] for the one-dimensional equations. 相似文献
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Adjoint Error Estimation for a Pseudo-Spectral Approach to Stochastic Field-Circuit Coupled Problems
This work is concerned with the numerical approximation of random differential-algebraic equations (DAE), arising from electric field-circuit coupled problems. Using the adjoint DAE, the stochastic collation error is analyzed. The error can be evaluated using a collocation method of the same polynomial degree for the adjoint DAE. In particular, there is no need for constructing a solution of higher polynomial degree. The accuracy of the estimator is illustrated by a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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非线性积分方程迭代配置法的渐近展开及其外推韩国强(华南理工大学计算机工程与科学系)ASYMPTOTICERROREXMNSIONSANDEXTRAPOLATIONFORTHEITERATEDCOLLOCATIONMETHODSOFNONLINEARI... 相似文献