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利用Mathematica软件编程,实现了用复化Simpson公式求数值积分的可视化,动态演示了算例的计算过程;设计了用逐次超松弛迭代法求解线性方程组的交互过程,分析了松弛因子的改变对近似解的影响;给出了用一类特殊的牛顿迭代法求非线性方程根的可视化展示,通过算例演示了方法的求解过程。数值分析课程中利用Mathematica软件,可增强教学内容的直观性、交互性,激发学生学习的兴趣和动力。
Abstract：Using the Mathematica software programming,the visualization of the compound Simpsonformula for numerical integration is realized,and the dynamic calculation process of an example ispresented. The interaction process to solve linear equations by the successive over- relaxation iterationmethod is designed,and the effect of the relaxation factor changes on the approximate solution isanalyzed. A visual display of the special Newton iterative method for nonlinear equation roots is given,and the method of solving process through a numerical example is demonstrated. Using the Mathematicasoftware in the course of numerical analysis,the intuitive and interactive of teaching content areenhanced,and the students′ interests and motivation in learning are stimulated.
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基本信息:
DOI：10.16389/j.cnki.cn42-1737/n.2016.01.015
中图分类号:O241
引用信息:
[1]孔祥强.Mathematica软件在数值分析中的动态可视化设计[J].江汉大学学报(自然科学版),2016,44(01):74-80.DOI:10.16389/j.cnki.cn42-1737/n.2016.01.015.
基金信息:
2013年菏泽学院重点课题组项目(201311)