基于Maple的理论力学教学实践

利用Maple强大的符号与可视化功能,方便、快捷、形象、直观地求解了理论力学中的几个具体问题,实现了基于Maple的理论力学可视化教学.Maple在数值计算和数据可视化方面具有较强的能力和特色,能简单、快捷地处理理论力学中自由落体偏东微分方程的求解,有限长度线段引力场的场强和引力势的计算问题,并同时绘制出数值解的2D、3D图形.列举了傅科摆的运动轨迹、洛伦茨方程求解计算的可视化结果,给出了洛伦茨方程求解的Maple程序.具体实例表明,用Maple来完成微分方程的求解和数值计算,实现复杂运动过程和计算结果的形象直观化,便于对各种初始条件下各变量的关系进行比较分析.对于物理教学提供了一种方便、快捷地实现可视化教学的方法.     

圆形镜平面腔数值迭代计算

从菲涅尔-基尔霍夫积分衍射方程出发,推导了圆形镜平面腔所满足的自再现模迭代方程,给出了数值迭代方程的具体形式和TEM00、TEM01、TEM10 3个模式的具体迭代方法。分析计算了3个自再现模的形成过程、单程损耗及相位等特性,并比较了不同菲涅尔数时各模式的本征值和衍射损耗。该方法为研究圆形平面镜谐振腔的激光模式、损耗特性及相位提供了可靠的理论方法,具体的数值迭代方法也可推广应用到其他类型的谐振腔。     

Investigating the relationship between pre-service physics teachers' professional knowledge,self-concept,and interest

This study investigates the relationships between professional knowledge, self-concept, and interest of pre-service physics teachers. In order to support student learning and interest development alike, teachers need a profound professional knowledge and respective motivational orientations. Developing both professional knowledge and motivational orientations in teachers is therefore a key challenge of teacher education. Prior research has focused on the development of content knowledge (CK) and pedagogical content knowledge (PCK) within teacher education, but the role of motivational orientations such as self-concept and interest have mostly been neglected areas of study. As individuals develop domain-specific motivational orientations, they compare their achievement in an external frame to the achievement of their peers, and they compare their achievements in an internal frame across domains. The effects of these psychological processes on domain-specific motivational orientations are described by the generalized internal/external frame of reference model (GI/E model). We assessed the professional knowledge (CK and PCK) and motivational orientations (self-concept and interest) of N = 200 pre-service physics teachers from 12 teacher education institutes in Germany. To investigate the predictions of the GI/E model, we utilized structural equation modeling. In line with the GI/E model, the analysis revealed that pre-service teachers use social comparisons. Pre-service teachers with a higher CK/PCK also showed a higher CK/PCK self-concept. We also identified instances of internal comparisons as we found that a high level of CK corresponds with a lower PCK self-concept. While we could not identify the same effects from professional knowledge on interest, self-concept mediated the effects from professional knowledge on interest. The results suggest that interdependencies between professional knowledge and motivational orientation should be given more consideration in teacher education research and should also be addressed more explicitly in teacher education.     

Unpacking teachers’ intentions to integrate technology: A meta-analysis

The Technology Acceptance Model (TAM) is a key model describing teachers' intentions to use technology. This meta-analysis clarifies some of the contradictory findings surrounding the relations within the TAM for a sample of 45 studies comprising 300 correlations. We evaluate the overall fit of the TAM and its structural parameters, and quantify the between-sample variation through meta-analytic structural equation modeling. The TAM fitted the data well, and all structural parameters were statistically significant. On average, the TAM variables explained 39.2% of the variance in teachers' intentions to use technology. Several sample, measurement, and publication characteristics, including teachers’ experience and the representation of the TAM variables, moderated the relations within the TAM. Overall, the TAM represents a valid model explaining technology acceptance—however, the degree of explanation and the relative importance of predictors vary across samples. Implications for further research, in particular the generalizability of the TAM, are discussed.     

微波消解-微分电位溶出法测定淡水鱼中镉含量

为镉的检测寻求一种快速、简便的新方法。通过玻碳悬汞电极测定淡水鱼中镉含量,考查了电沉积电位、电沉积时间、平衡电位、平衡时间对测定结果的影响。结果：当pH值为1.0～2.5、电沉积电位为-1.25V、电沉积时间为60s、平衡电位为-1.0V、平衡时间为30s时,测定结果最好。测定镉的线性范围为0～16ng,检出限为0.24ng/mL,回收率为98.6%～101.2%,相对标准偏差为2.4%。该法操作快速、简便,结果准确、可靠。     

数学建模在高等数学教学中的应用实例

数学建模的思想已经渗入理科各个学科,而数学建模真正走进课堂还需要认真探讨与实践。分析了高等数学教学中结合数学建模思想的重要性与可行性,联系高等数学教学中的一个内容即微分方程问题,探讨了高等数学教学与数学建模的有机结合.     

关于费马解的一个同余方程

设p为奇素数,a为整数,若ap-1≡(1mod p2),则a名为费马解。根据华罗庚给出的几个特殊的费马解,可以探求费马解的一般方法。利用初等方法及原根的性质研究同余方程xp-1≡(1modpl),l≥1的可解性,可以得到该同余方程的一切正整数解和费马解。     

一类带有线性边值条件拟线性微分方程解的存在性

应用不动点指数定理,研究了一类带有线性边值条件的拟线性微分方程{φ(x'));+a(t)f(x(t))=0,t∈(0,1){x(0)-βx'(0)=0,应用不动点指数定理得出该微分方程至少有一正解的充分{x(1)-δx'(1)=0条件.     

基于偏微分方程的线性函数数据建模应用研究

通过线性函数数据建模,以偏微分方程理论为依据,使用Visual C#作为编程设计语言,通过串行通信口送入大量实验数据,并对海量数据进行实证分析,由此获取线性方程的数据建模方法,得到相应程序算法模型,在Visual C#环境下编写程序进行调试分析与测试,并详细介绍了该方法的具体设计过程,给出了关键程序代码,同时给出了利用该方法进行数据处理的一个实例。对于利用采样的海量数据获得线性函数的相关研究有一定的参考价值。     

关于Mordell方程y^2=x^3＋k

设l,l1,l2,…,ls为任意整数,n为正整数,n1,n2,…,ns为任意非负整数．用初等数论方法证明了：如果k满足k=（4l＋2）^3-Пi=1^s（4li＋1）^2ni或k=（4l＋3）^3-2^2nПi=1^s（4li＋1）^2ni,则Mordell方程y^2=x^3＋k无整数解．