| 分段函数求导的一个简便而严谨的算法 |
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| 引用本文： | 龚谊承,李寿贵.分段函数求导的一个简便而严谨的算法[J].河池师专学报,2010(5):1-5. |
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| 作者姓名： | 龚谊承 李寿贵 |
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| 作者单位： | [1]武汉科技大学理学院信息与计算科学系,湖北武汉430065 [2]武汉科技大学冶金工业过程系统科学湖北省重点实验室,湖北武汉430081 |
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| 基金项目： | 科技部重大教研项目子课题：科学思维、科学方法在高等数学课程中的应用与实践（2009IM010400-1-25）; 湖北省教育厅教研资助项目：信息与计算科学专业的课程体系与专业定位研究（2008182） |
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| 摘 要： | 在处理＂分段函数在分段点处的可导性判断与导数值计算＂时,学生总想用简便方法,而教师则总要强调定义的严谨性.为了寻找解决简便与严谨之间矛盾的可行方法,首先将教师和学生的思想算法化,并结合算例分析了各自的优劣,接着提出了一个使简便算法严谨的充分条件,继而给出了一个当简便算法不严谨时的缓和算法,并基于此给出了一个简便而严谨的融合改进算法.
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| 关 键 词： | 函数 分段函数 导数 算法 简便性 严谨性 |
A Simple and Rigorous Algorithm for the Derivatives of Piecewise Functions |
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| GONG Yi-cheng,LI Shou-gui.A Simple and Rigorous Algorithm for the Derivatives of Piecewise Functions[J].Journal of Hechi Normal College,2010(5):1-5. |
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| Authors: | GONG Yi-cheng LI Shou-gui |
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| Institution: | 1,2) (1.Department of Information and Computation Science,Science College, Wuhan University of Science and Technology,Wuhan,Hubei 430065; 2.Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology,Wuhan,Hubei 430081,China) |
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| Abstract: | When dealing with the derivative of a piecewise function at its piecewise point,students usually prefer the simple and convenient skills while teachers insist on preferring the rogorious routine by the definition.To find a feasible method to solve the inconsistency,the techniques of teachers and students are firstly algorithmized respectivly,and their advanteges and disadvanteges are analyzed via examples.Then a sufficient condition for the correctness of the simple and convenient algorithms is put forword,and a demulcent algorithm is defined to palliate the acute contraditions between the teachers and students.Last but not the least,a modified algorithm is brought forward to combine the simplicity and conveninence of the students algorithm with the rigorousness of the teachers＇. |
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| Keywords: | function piecewise function derivative algorithm simplicity rigorousness |
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