Abstract
This paper uses the mathematical software Maple for the auxiliary tool to study the partial differential problem of four types of multivariable functions. We can obtain the infinite series forms of any order partial derivatives of these four types of multivariable functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order partial derivative values. On the other hand, we propose some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.
Highlights
Differentiation Term By Term Theorem, Maple approximate values calculated and solutions to similar problems, as determined by Maple
In calculus and engineering mathematics curricula, evaluating the m -th order partial derivative value of a multivariable function at some point, in general, needs to go through two procedures: firstly determining the m -th order partial derivative of this function, and taking the point into this m -th order partial derivative. These two procedures will make us face with increasingly complex calculations when calculating higher order partial derivative values ( i.e. m is large), and to obtain the answers by manual calculations is not easy
This type of research method allows the discovery of calculation errors, and helps modify the original directions of thinking from manual and Maple calculations
Summary
Keywords Partial Derivatives, Infinite Series Forms, Differentiation Term By Term Theorem, Maple approximate values calculated and solutions to similar problems, as determined by Maple. We study the partial differential problem of the following four types of n -variables functions
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