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1.
特别推荐     
《中学数学》2012,(20):2
《新课程函数问题研究》函数是高考的重点、热点,函数思想是教学思想方法中最为闪亮的一朵奇葩.《新课程函数问题研究》结合新课程标准,以高中数学中涉及到的函数问题为主线,对函数的定义域与值域、函数的性质及应用、函数中的数学思想方法探究、二次函数的重要作用、三角函数问题研究、高考中的分段函数、抽象函数专题  相似文献   

2.
函数是高中数学的核心和重点,函数板块中孕育着很多数学思想方法,诸如方程思想、数形结合思想、分类讨论思想等.思想方法渗透到函数试题中,使原本并不复杂的函数问题变得复杂起来.我们知道,单一的函数教学除了认知基本初等函数和函数性质之外,其难度并不大,但是随着知识整合度的提升、字母参数的渗透,解决问题的时候必须依赖更多思想方法的渗透才能解决.数学家熊庆来曾说过:“分类的思想是数学的瑰宝,我在解决很多复杂的数学问题时,总是将其分类为一部分、  相似文献   

3.
函数的思想是高中数学中最重要的数学思想方法之一,数列作为一种特殊的函数,更是与函数思想密不可分,因此,有些数列的问题可以构造函数,利用函数思想来解决.下面结合实例加以说明.一、构造函数,利用函数图像性质巧解  相似文献   

4.
<正>数列是一种定义在正整数集或其有限子集{1,2,…,n}上的特殊函数.所以在解决某些数列问题时,可以借助函数的思想和方法加以解决.但数列的自变量具有离散性.因此用函数的思想和方法解决数列问题时往往产生一  相似文献   

5.
利用历史比较和分析的方法,探讨波莱尔提出"关联函数法"的思想背景,分析了波莱尔利用该法研究函数奇点、函数解析开拓等问题的思想方法和意义.  相似文献   

6.
解斜三角形的应用范围非常广泛,是高考的热点之一.为了学好解斜三角形这一内容,除了掌握解斜三角形的基本理论、基础知识、基本方法外,还应对以下几个问题加以注意.1注意函数思想的应用函数思想是最基本的数学思想方法之一,运用函数思想是指运用函数概念和性质去分析问题、转化  相似文献   

7.
将不等式问题转化为函数问题,利用函数性质来研究、解决不等式问题.掌握不等式证明的一种函数思想方法,从而提高分析问题与解决问题的能力.  相似文献   

8.
数形结合是数学解题中一种重要的解题思想方法,利用函数图像的直观性,通过观察图像而获得对函数性质的认识,这是数形结合的基础依据,也是研究数学问题的常用方法.运用数形结合思想来解决常见函数问题大致有以下几个方面.一、利用图形对称性求函数的解析式  相似文献   

9.
研究函数切线问题是高考热点之一,导数与函数的切线有缘,因为f(′x0)的几何意义是曲线y=(fx)在点(x0,(fx0))处的切线的斜率.因此,利用导数求解函数问题,几乎是新课程高考每年必考的内容.在这类问题中,导数所肩负的任务是求切线的斜率,这类问题的核心部分是考查函数的思想方法和解析几何的基本思想方法,真正体现出函数、导数既是研究的对象又是研究的工具.  相似文献   

10.
王伟 《中学生数学》2012,(23):18-19
函数思想,是指用函数的概念和性质去分析问题、转化问题和解决问题.方程思想,是从问题的数量关系入手,将问题中的条件转化为数学模型:方程、不等式或方程与不等式的混合组,然后通过解方程(组)或不等式(组)来使问题获解.函数与方程犹如亲兄弟,彼此身上存在对方的影子,两者互相转化接轨,形成了函数与方程思想.本文将用函数与方程思想来解决三角函数的证明求值问题.  相似文献   

11.
We extend and solve the classical Kolmogorov problem of finding general classes of Kolmogorov equations that can be transformed to the backward heat equation. These new classes include Kolmogorov equations with time-independent and time-dependent coefficients. Our main idea is to include nonlocal transformations. We describe a step-by-step algorithm for determining such transformations. We also show how all previously known results arise as particular cases in this wider framework.  相似文献   

12.
An iterative gradient descent method is applied to solve an inverse coefficient heat conduction problem with overdetermined boundary conditions. Theoretical estimates are derived showing how the target functional varies with varying the coefficient. These estimates are used to construct an approximation for a target functional gradient. In numerical experiments, iteration convergence rates are compared for different descent parameters.  相似文献   

13.
Hyper-heuristics are high level heuristics which coordinate lower level ones to solve a given problem. Low level heuristics, however, are not all as competent/good as each other at solving the given problem and some do not work together as well as others. Hence the idea of measuring how good they are (competence) at solving the problem and how well they work together (their affinity). Models of the affinity and competence properties are suggested and evaluated using previous information on the performance of the simple low level heuristics. The resulting model values are used to improve the performance of the hyper-heuristic by tailoring it not only to the specific problem but the specific instance being solved. The test case is a hard combinatorial problem, namely the Hybrid Flow Shop scheduling problem. Numerical results on randomly generated as well as real-world instances are included.  相似文献   

14.
This paper develops a procedure for numerically solving continuous games (and also matrix games) using a gradient projection method in a general Hilbert space setting. First, we analyze the symmetric case. Our approach is to introduce a functional which measures how far a strategy deviates from giving zero value (i.e., how near the strategy is to being optimal). We then incorporate this functional into a nonlinear optimization problem with constraints and solve this problem using the gradient projection algorithm. The convergence is studied via the corresponding steepest-descent differential equation. The differential equation is a nonlinear initial-value problem in a Hilbert space; thus, we include a proof of existence and uniqueness of its solution. Finally, nonsymmetric games are handled using the symmetrization techniques of Ref. 1.  相似文献   

15.
This paper shows how to solve two-part sequencing problems in a three-machine robotic cell so as to minimize the cycle time. We start dealing with cycles whose associated part-sequencing problems do not have the structure of a travelling salesman problem (TSP). The idea behind our approach is to modify the waiting time formula and formulate the closely related modified problem as a generalized travelling salesman problem (GTSP). The other cycles to be tackled are those that have a TSP structure for their associated part-sequencing problem. The existence of common states between these cycles allows us to mix and mould all of them into a GTSP. The solution procedures, designed for both cycle classes, are merged into a single heuristic and evaluated. The computational results provided prove the efficiency of the approaches.  相似文献   

16.
In this paper we present a new approach to solve a two-level optimization problem arising from an approximation by means of the finite element method of optimal control problems governed by unilateral boundary-value problems. The problem considered is to find a minimum of a functional with respect to the control variablesu. The minimized functional depends on control variables and state variablesx. The latter are the optimal solution of an auxiliary quadratic programming problem, whose parameters depend onu.Our main idea is to replace this QP problem by its dual and then apply the barrier penalty method to this dual QP problem or to the primal one if it is in an appropriate form. As a result we obtain a problem approximating the original one. Its good property is the differentiable dependence of state variables with respect to the control variables. Furthermore, we propose a method for finding an approximate solution of a penalized lower-level problem if the optimal solution of the original QP problem is known. We apply the result obtained to some optimal shape design problems governed by the Dirichlet-Signorini boundary-value problem.This research was supported by the Academy of Finland and the Systems Research Institute of the Polish Academy of Sciences.  相似文献   

17.
Troesch’s problem is an inherently unstable two-point boundary value problem. A new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve Troesch’s problem. The underlying idea of the method is to convert the hyperbolic-type nonlinearity in the problem into polynomial-type nonlinearities by variable transformation, and the variational iteration method is then directly used to solve this transformed problem. Only the second-order iterative solution is required to provide a highly accurate analytical solution as compared with those obtained by other analytical and numerical methods.  相似文献   

18.
Average-optimal string matching   总被引:2,自引:0,他引:2  
The exact string matching problem is to find the occurrences of a pattern of length m from a text of length n symbols. We develop a novel and unorthodox filtering technique for this problem. Our method is based on transforming the problem into multiple matching of carefully chosen pattern subsequences. While this is seemingly more difficult than the original problem, we show that the idea leads to very simple algorithms that are optimal on average. We then show how our basic method can be used to solve multiple string matching as well as several approximate matching problems in average optimal time. The general method can be applied to many existing string matching algorithms. Our experimental results show that the algorithms perform very well in practice.  相似文献   

19.
利用中值定理证明方程解存在性问题时的关键步骤是构造合适的函数,通过一个具体的例题详细阐释了如何利用积分因子思想构造函数以证明与中值定理相关的过程.  相似文献   

20.
Renewable natural resource systems often represent examples of joint production. Optimal control theory is employed using the linear variational method to derive the general solution to the timber-forage joint production problem, with the objective of maximizing present value of revenue. The results indicate that optimal control theory can successfully solve such problems. The functional forms of the solution provide insight into how changes in parameters will influence the optimal joint production system.  相似文献   

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