多變數雙曲函數的偏微分問題

The Partial Differential Problem of Multivariable Hyperbolic Functions

余啟輝(Chii-Huei Yu)

《永達學報》 12卷2期 (2012/12) Pp. 1-12

https://doi.org/10.30179/BYTITC.201212.0001

摘要

本篇論文主要是研究四種多變數雙曲函數的偏微分計算。我們利用二項級數和逐項微分定理可以求出這四種多變數雙曲函數的任意階偏導函數，因此大大降低了求高階偏微分值的困難度。另一方面，我們舉出四個多變數雙曲函數的例子，實際的求出它們的任意階偏導函數以及它們的一些高階偏微分值，而這些高階偏微分值的答案都是以無窮級數的型式呈現出來。同時我們利用數學軟體Maple算出這些高階偏微分值以及它們無窮級數解的近似值。

關鍵字

多變數雙曲函數 ； 二項級數 ； 逐項微分定理 ； Maple軟體

並列摘要

This paper mainly studies the partial derivative evaluation of four types of multivariable hyperbolic functions. W can obtain any order partial derivatives of these four types of multivariable hyperbolic functions by using binomial series and differentiation term by term theorem, and hence greatly reduce the difficulty of evaluating their higher order partial derivative values. On the other hand, we propose four examples of multivariable hyperbolic functions to evaluate their any order partial derivatives and some of their higher order partial derivative values practically, and the answers of these higher order partial derivative values are presented in infinite series forms. Simultaneously, we employ the mathematical software Maple to calculate the approximations of these higher order partial derivative values and their infinite series forms.

並列關鍵字

Multivariable Hyperbolic Functions ； Binomial Series ； Differentiation Term by Term Theorem ； Maple