培养学生发散思维 提高解题能力

发散思维是创造思维的核心。美国著名心理学者吉尔福特认为,它具有三个品质特征:流畅性、变通性和独特性。 第一,培养学生发散机智,实现和提高发     

加强新旧知识联系的教学 培养联想思维能力

思维是人脑对客观现实概括和间接反映,而联想思维是一种创造性思维,在情态上是发散的,多层次的,多方向的。它既具有思维的发散性、能动性、创造性等方面的共性,又具有触发性、伴随性、仿变性等方面的个性;所以“联想思维法”已成为现代数学教育研究的一个新课题。在数学教学中把发展学生的思维提高到应     

从求点到平面的距离谈发散性思维

从求点到平面的距离的四种方法谈发散性思维。     

优化数学教学方法 注重培养学生的发散思维

发散型思维是一种创造性思维，它包含创造思维的实质．它可以从一点出发，运用所学过的基础理论进行放射性联想，追求多种多样的解题方法和答案，并可以由此及彼、由表及里、触类旁通，活跃学生的思维，拓宽学生的思路，在同题的深度和广度上进行挖掘。这对于培养学生的分析问题和解决同题的能力有很大的帮助。发散思维具有求异性、探索性、 些     

训练数学思维,让数学核心素养落地生根

在课堂教学中,要注重训练学生的逆向思维、发散思维、直观思维、简化思维、辩证思维和逻辑思维,培养数学思维的开阔性、独创性、深刻性、逻辑性和严谨性,逐步提升学生的数学思维能力和核心素养.     

线性代数中的一题多解与学生发散性思维的培养

探讨了线性代数教学中的一题多解与学生发散性思维的培养     

培养创新思维，激发课堂活力

创新思维是一种发散性思维，是指能够多角度思考问题、创新性解决问题的一种思维能力.创新思维的发展能够激发学生的想象力，促进学生将知识整合优化，融汇贯通，更加灵活地解决问题，从而促进学习能力和创新能力的提升.本文中从探究最优解法、问题情境创设和创新习题训练三个方面阐述培养学生创新思维能力的方法，以优化学生的思维品质.     

例谈初中学生数学发散思维的培养

课程标准指出,在数学教学中,要重视培养学生的发散思维,从而提高学生的发散思维能力.那么,什么是发散思维？发散思维（又称辐射思维）是对已知信息进行多方向、多角度的思考,不局限于既定的理解,从而提出新问题,探索新知识或发现多种解答和多种结果的思维方式.它的特点是思路广阔,寻求变异,     

从一道中考复习题谈学生发散思维的培养

发散性思维是不依常规,寻求变异,对给出的材料、信息从不同的方向、途径和角度去设想,探求多种答案,最终使问题获得圆满解决的思维方法.其特点是:不拘泥于常规,充分表现出思维的流畅、变通;追求独特新颖的设想,在解决问题的过程中,有所发现、有所创新、有所突破.教师在教学过程中需要有意识地去培养学生的这一思维能力.本文从一道中考复习题中引导学生灵活运用割补法求图形的面积这方面人手,谈谈如何让学生求变、求异,以培养他们的发散性思维能力.     

发散式教学：培养学生数学思维品质的有效尝试

发散式教学,是根据学生已掌握的知识信息,从不同角度、沿着不同的方向去思考问题;多层次、多角度、全方位地重新组合记忆系统中的信息,达到解决新的问题的教学形式. 高中数学习题课教学的目的不仅是让学生掌握已学的公理、定理,更重要的是掌握科学的思维方式、方法,培养和拓展学生的发散思维能力,对提高其数学素养有着举足轻重的作用.怎样培养学生的发散性思维呢?     

慢扩张旋转流的稳定性分析（Ⅰ）—理论研究

本文研究了无粘不可压慢扩张旋转流的稳定性问题，采用多重尺度展开法对有慢扩张的旋转流的非对称扰动进行浅化稳定性研究，导出了零阶及一阶扰动模所应满足的微分方程及由于慢扩张引起振幅变化的控制方程，将Ｐｌａｓｃｈｋｏ关于慢扩张喷流的结果推广到具有慢扩张的旋转流情况。     

On integrals of equations of unstable nearly self-similar flows : PMM vol. 39, n 6, 1975, pp. 1060–1067

One-dimensional or nearly one-dimensional unstable motions of perfect gas are considered. Integrals admitted by the system of equations defining such motions are examined. Since the existence of integrals is associated with some law of conservation, i. e. with some divergent form of presentation of equations of the input system, it is possible by examining all divergent equations of gasdynamics to derive certain new integrals not previously considered.     

Schwarzschild-anti-de Sitter时空中Dirac场的统计熵

利用brick-wall方法,计算了Schwarzschild-anti-de Sitter时空中Dirac场的统计熵,讨论了Dirac粒子的自旋对统计熵的影响.结果表明,忽略远离围绕系统的真空的贡献,Dirac场的统计熵包含与黑洞视界面积成正比的平方反比发散项和对数发散项,整个表达式的结构与黑洞熵的结构不一样.对应于|∧|r²_h 的不同取值,对数发散项的贡献可以为正、负或零.     

A divergent system of non-stationary equations of motion of viscoelastic media in euler coordinates

A system of divergent equations of non-stationary motions of viscoelastic media is presented. It is shown that for continuous flows it is equivalent to the well-known system of equations in /1/. Divergent equations are preferable, for instance, from the viewpoint of their utilization in calculational algorithms. On the basis of the divergent forms obtained, relationships at discontinuities are analysed.     

线性代数课堂中的“教”与“学”

结合教学实践经验,从人才培养的角度阐述线性代数课堂教学中的思维培养问题.指出课堂教学中要善于创设和营造和谐民主、积极向上、与学生心理相融的良好的课堂氛围;设置有利于学生参与认知的教学环节,通过采用灵活的教学方式,激发学生思考;尊重学生主体地位,让他们在教学活动中获得最大的情感体验;充分利用直观形象思维,教学中贯穿直观的几何形象,激发学生学习的兴趣,激发他们的求知欲.     

Stability of a transonic profile arising from divergent detonations

We establish the existence of viscous profile of an undriven divergent detonation wave. The structure of the wave is a viscous shock followed by a reaction zone containing a sonic point. So the divergent detonation wave profile is a transonic profile.

We further establish the existence of classical global solutions of the Cauchy problem. The proof consists of establishing a priori estimates for the solution by a maximum principle and using Hölder estimates for solutions of parabolic equations. Finally, the nonlinear stability of the viscous transonic profile is established. The main reason for the stability is that there is a damping term due to the divergent nature of the problem.     

On low Reynolds number optimization of non-linear partial differential equations for convergent–divergent engulfment: A numerical result

The flow field in a convergent–divergent engulfment along with the installation of infinite cylinders as an obstacle results in non-linear partial differential equations and the scientific computation in this regard remains a challenging task. The present attempt is the numerical motivation in this direction to evaluate the flowing liquid stream in the convergent–divergent channel at a low Reynolds number. From the left wall, the liquid stream move with the parabolic profile and have interaction with the case-wise installation of infinite cylinders in the left vicinity of the convergent–divergent throat. The differential system is constructed for the flow field in the channel and hybrid meshed finite element method is utilized to report the numerical solution. A comparative study is enclosed for the hydrodynamic forces faced by obstructions in the left region of the convergent–divergent throat. The drag coefficient for a triangular cylinder acting as an obstruction is higher than that of a circular hitch. In comparison to both triangular and circular hitches, the square-shaped obstacle suffered the most drag force. Considering drag coefficient one can extend this work to obtain information for the real behavior of the vehicle toward air flow and may conclude findings toward reduction of fuel consumption.     

Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. Part II

Under a certain restriction, singular first-order linear partial differential equations of nilpotent type with two variables are divided into two classes. In the previous paper Part I, we dealt with the one class, and comprehended that there was a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients. In this Part II, we give a similar consideration on the other class. More precise global estimates than those given in Part I for coefficients will be required to prove the Borel summability of divergent solutions.     

Quantum entropy of Dirac fields in black holes

We use the brick-wall model to study the quantum entropy of the Dirac field in a static black hole with a global monopole or a cosmic string. We show that the entropy of the Dirac field contains a quadratically divergent term and two logarithmically divergent ones and it is not proportional to the entropy of the scalar field. The contribution of the logarithmic term to the entropy depends on the black-hole characteristics and is always negative. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 1, pp. 60–64, October, 2006.     

Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. Part I

This article part I and the forthcoming part II are concerned with the study of the Borel summability of divergent power series solutions for singular first-order linear partial differential equations of nilpotent type. Under one restriction on equations, we can divide them into two classes. In this part I, we deal with the one class and obtain the conditions under which divergent solutions are Borel summable. (The other class will be studied in part II.) In order to assure the Borel summability of divergent solutions, global analytic continuation properties for coefficients are required despite of the fact that the domain of the Borel sum is local.