Solving Multiple Integrals Using Maple

Bing-Huei Chen,Chii-Huei Yu

doi:10.13189/wjcat.2014.020401

Abstract

The multiple integral problem is closely related to probability theory and quantum field theory. This paper uses the mathematical software Maple for the auxiliary tool to study three types of multiple integrals. We can obtain the infinite series forms of these three types of multiple integrals by using differentiation with respect to a parameter, differentiation term by term, and integration term by term. In addition, we provide 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

As information technology advances, whether computers can become comparable with human brains to perform abstract tasks, such as abstract art similar to the paintings of Picasso and musical compositions similar to those of Mozart, is a natural question
This study introduces how to conduct mathematical research using the mathematical software Maple
For the three types of multiple integrals in this study, we provide some examples and use Theorems 1-3 and Corollaries 1-3 to determine the infinite series forms of these multiple integrals

Summary

Introduction

Whether computers can become comparable with human brains to perform abstract tasks, such as abstract art similar to the paintings of Picasso and musical compositions similar to those of Mozart, is a natural question. Whether computers can solve abstract and difficult mathematical problems and develop abstract mathematical theories such as those of mathematicians appears unfeasible. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. Maple provides insights and guidance regarding problem-solving methods. ∂f ∂ρ (ρ, x1, x2, x3,⋅ ⋅ ⋅, xn )dx2dx3 ⋅ ⋅ ⋅ dxn for all ρ ∈ (c1, c2 )

Main Results

Examples

Conclusions