| 分析课程中若干重要概念与定理的教学探究 |
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| 引用本文： | 虞志坚.分析课程中若干重要概念与定理的教学探究[J].台州学院学报,2014(3):69-72. |
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| 作者姓名： | 虞志坚 |
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| 作者单位： | 台州学院数学与信息工程学院,浙江临海317000 |
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| 摘 要： | 对分析课程中导数与微分概念以及鲁津定理与富比尼定理的教学作了若干探究。首先，我们强调要将一元函数、多元函数以及向量值函数的导数和微分纳入统一的框架之中进行教学。其次，对于鲁津定理我们要突出定理的关键是用连续函数逼近可测函数时不能破坏函数总体性质。最后，关于富比尼定理我们指出定理的重点是先判断被积函数的可积性。
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| 关 键 词： | 导数 微分 鲁津定理 富比尼定理 教学探究 |
Teaching Explorations on Some Important Concepts and Theorems in Analysis |
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| YU Zhi-jian.Teaching Explorations on Some Important Concepts and Theorems in Analysis[J].Journal of Taizhou University,2014(3):69-72. |
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| Authors: | YU Zhi-jian |
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| Institution: | YU Zhi-jian (School of Mathematics and Information Engineering, Taizhou University, Linhai 317000, China) |
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| Abstract: | In this note, some teaching explorations on important concepts and theorems in analysis are done. Firstly,concerning the derivatives and differentials of single or several variable functions and vector-valued functions, it is important that we should teach them in the same frame. Secondly, as for Lusin＇s theorem it should be emphasized that we must keep the global properties of a measurable function when we use a continuous one to approximate it. Lastly, it must be pointed out that the key of Fubini＇s theorem is that we have to check the integrability of the integrands first. |
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| Keywords: | Derivatives Differentials Lusin＇s Theorem Fubini＇s Theorem Teaching Explorations |
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