| 数学期望在高等数学教学中的应用 |
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| 引用本文： | 詹婉荣,于海.数学期望在高等数学教学中的应用[J].洛阳师范学院学报,2011,30(5):22-23,32. |
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| 作者姓名： | 詹婉荣 于海 |
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| 作者单位： | 洛阳师范学院数学科学学院,河南,洛阳,471022 |
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| 摘 要： | 本文讨论了数学期望在高等数学教学过程中几个方面的应用,为学习高等数学提供了概率背景.首先,给出了积分第一中值定理以及推广的积分第一中值定理的概率解释.接着,证明了平面薄板的重心坐标实际上可以看作二维随机变量的数学期望.最后,用数学期望重新给出了凸、凹函数的定义以及詹森(Jensen)不等式.
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| 关 键 词： | 数学期望 积分中值定理 重心 凸函数 凹函数 |
Applications of Mathematical Expectation in the Teaching of Advanced Mathematics |
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| ZHAN Wan-Tong,YU Hai.Applications of Mathematical Expectation in the Teaching of Advanced Mathematics[J].Journal of Luoyang Teachers College,2011,30(5):22-23,32. |
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| Authors: | ZHAN Wan-Tong YU Hai |
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| Institution: | ZHAN Wan-rong,YU Hai(College of Mathematics and Science,Luoyang Normal University,Luoyang 471022,China) |
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| Abstract: | In this paper,the applications of mathematical expectation in the teaching of advanced mathematics are discusses.The probability backgrounds are provided for the study of higher mathematics.First of all,the probability interpretations of the first integral mean-value theorem and the first generalized integral mean-value theorem are given.Secondly,we prove that the coordinates of the thin plane's center of gravity can actually regarded as the mathematical expectations of a two-dimensional random variable.Fin... |
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| Keywords: | mathematical expectation integral mean-value theorem center of gravity convex function concave function |
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