利用数学归纳法证明了一个关于正值函数的不等式，并举例说明了其应用。
This paper proves an inequality based on a positive function with mathematical induction and demonstrates its application with examples.
该文讨论傅氏变换中的二个时域积分特性，在求解频谱函数中的应用方法，并举例予以说明。
This paper discusses the application methods on solving frequency function and sets examples, in the two integral characters of time domain on Fourier conversion.
通过对两个求导例题的分析，归纳出求函数在某些特殊点导数的新的解法定理及推论，并举例说明它们的应用，最后对此求导方法进行总结。
Through analyzing two examples of seeking derivative, new theorem and deduction for solution to some functions derivation under the special condition are concluded, and examples are shown.
通过在积分换元、微分方程求解、多（一）元复合函数求全微分、偏导数及高阶偏导数中的应用举例，论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
Based on the theory of differential geometry and geodesy, the second order differential equation and the first differential relationship are derived on the regional earth ellipsoid in this paper.
通过在积分换元、微分方程求解、多（一）元复合函数求全微分、偏导数及高阶偏导数中的应用举例，论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
Based on the theory of differential geometry and geodesy, the second order differential equation and the first differential relationship are derived on the regional earth ellipsoid in this paper.
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