一类迭代微分方程解的存在唯一性定理

利用Picard逐步逼近法研究一类迭代微分方程解的存在唯一性,体现了Picard逐步逼近法在迭代微分方程中的应用。     

解的存在唯一性定理蕴涵的数学思想

常微分方程在数学学科的发展中具有很重要的地位,它是许多数学分支产生的动力.常微分方程蕴涵着丰富而深刻的数学思想与方法,通过对解的存在唯一性定理蕴涵的数学思想进行探讨和分析,阐释微分方程本身就是一种数学思想.     

常微分方程课中的线性微分方程组的解的存在唯一性定理的教学改革探讨

以建构主义的学习理论为基础，结合学习的实际情况和已有的经验背景，创建合适的学习情境，对常微分方程课程中的线性微分方程组的解的存在唯一性定理的教学过程进行了改革，具体做法是，减少讲授时数，将讲课时间控制在10min之内，而将大部分时间用于学习自己练习及以学习之间、学生与教师之间的交流的探讨，使学生能够综合贯通，形成 完整的知识结构。     

高阶线性微分方程解的存在与唯一性

用逐步逼近法和泛函分析中的压缩映射原理方法证明了高阶线性常微分方程柯西问题的解是存在并唯一的。     

常微分方程解的存在和唯一性定理中Lipschitz条件的弱化

常微分方程解的存在和唯一性定理是常微分方程的理论基础,但因其条件——Lipschitz条件太强,定理仅适于部分初值问题。为从应用上解决更多的初值问题,从理论上逐步向存在但暂且未知的必要条件逼近,本文对Lipschitz条件作一定程度的弱化。     

一类非线性常微分方程解的存在唯一性

在适当的自然结构条件下证明了完全非线性常微分方程F(t,u(t),u(′t))=0的周期粘性解的存在唯一性.     

一类迭代微分方程解的存在性与唯一性

研究了一类迭代微分方程解的存在性与唯一性问题,给出了存在唯一性定理,推广了已有的结果.     

一类微分方程周期解的存在性与唯一性,稳定性

利用线性方程组解的估计式和不动点定理,讨论了一类微分方程周期解的存在性与唯一性,稳定性。     

利用微积分证明不等式

不等式证明方法很多,利用微积分的知识证明不等式,使不等式的证明过程简单化,本文列举了8种常用方法.     

An aesthetic approach to the teaching of science

The role of aesthetic curiosity in the manipulation of materials is often ignored or considered irrelevant in most science curricula. Contemporary practice in curriculum design emphasizes an approach that views science and art as separate types of explorations. Some historians of technology and science suggest that basic discoveries arise out of an aesthetic curiosity fostered by play with materials or ideas. Experience with certain familiar materials of aesthetic interest suggest that children will sustain play for long periods and easily mix metaphors of art and science in developing an understanding of the phenomena that are a part of the experience. Several examples are given of how this might be accomplished.     

生物教学中的问题教学初探

新课程教学是以学生主动参与、乐于探究、交流与合作为新学习方式，以教师作为教学的组织者、策划者、引导者为新教学思想，以问题教学为新生物教学模式的中心．问题在生物教学中起着穿针引线的作用．教师只有充分认识问题教学在实践中的重要作用，通过创设问题情景，培养问题意识，鼓励学生大胆质疑、科学探究，养成自主学习的习惯，勇于探索、创新，才能顺利实现教学目标．     

基于Internet的网络教学模式探讨

本文阐述了基于Internet网络环境下的教育体制及主要网络教学模式，评价了个别化、协作学习、发现式、讨化式等主要网络教学模式的特点。     

定价多资产美式期权的半线性Black-Scholes偏微分方程的唯一解

In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.     

An inquiry approach to science and language teaching

The purpose of this study was to determine the effectiveness of an inquiry approach to science and language teaching to further develop classification and oral communication skills of bilingual Mexican American third graders. A random sample consisting of 64 subjects was selected for experimental and control groups from a population of 120 bilingual Mexican American third graders. The Solomon Four-Group experimental design was employed. Pre- and posttesting was performed by use of the Goldstein-Sheerer Object Sorting Test, (GSOST) and the Test of Oral Communication Skills, (TOCS). The experimental group participated in a sequential series of science lessons which required manipulation of objects, exploration, peer interaction, and teacher-pupil interaction. The children made observations and comparisons of familiar objects and then grouped them on the basis of perceived and inferred attributes. Children worked individually and in small groups. Analysis of variance procedures was used on the posttest scores to determine if there was a significant improvement in classification and oral communication skills in the experimental group. The results on the posttest scores indicated a significant improvement at the 0.01 level for the experimental group in both classification and oral communication skills. It was concluded that participation in the science inquiry lessons facilitated the development of classification and oral communication skills of bilingual children.     

研究性学习教学初探

研究性学习教学目标是培养创新型人才，教师应当把研究性学习，教学渗透到必修课教学过程中去，老师在教学过程中作示范研究，根据学生身心发展规律，探索研究性学习的教学模式和研究层次。