MATLAB在“张量分析”课程教学中的应用  

Some Notes on the Application of the MATLAB Language to the Tensor Analysis Course

作　　者：汪建军[1,2] 许才军[1,2] WANG Jianjun;XU Caijun(The school of Geodesy and Geomatics,Wuhan University,Wuhan,Hubei 430079;Key Laboratory of Geospace Environment and Geodesy,Ministry of Education,Wuhan,Hubei 430079)

机构地区：[1]武汉大学测绘学院,湖北武汉430079 [2]地球空间环境与大地测量教育部重点实验室,湖北武汉430079

出　　处：《科教导刊》2024年第1期130-132,共3页The Guide Of Science & Education

基　　金：2019年“湖北名师工作室”项目(201902)。

摘　　要：张量分析是一种重要的数学工具,它在相对论、电磁场论和连续介质力学等诸多学科都有着广泛的应用。掌握这种数学工具,已成为从事相关科学研究的必备基础。然而,张量分析中非欧几里得空间局部切标架的存在,增加了张量计算和分析的复杂性。学生在学习“张量分析”课程时面临着抽象概念和复杂公式的理解上的困难。本文提出利用MATLAB工具在绘图、脚本编程和符号推导等方面的强大功能,从旋度分析、坐标变换和定理辅助证明这三个方面,并结合MATLAB脚本代码,展示MATLAB工具辅助于该课程教学的重要作用。教师借助该工具开展课程教学,将帮助学生有效提高对张量分析知识的理解。学生掌握了该课程的基础知识后,便能进一步使用MATLAB的张量工具箱或Pytorch深度学习库进行张量运算操作。Tensor analysis is a crucial mathematical tool with broad applications in fields as diverse as relativity,electromagnetic field theory,fluid mechanics,continuum mechanics,and so on.Mastery of this technique has become an essential skill for individuals engaged in scientific research.However,the presence of varying local tangential frames in non-Euclidean space adds more complexity to the tensor operation,compared to its operation in traditional Euclidean space,where the basis vectors are simple and uniform throughout space.This complexity blunts students'intellect to deduce intractable formulae and comprehend abstract concepts when studying the course of tensor analysis.To address this challenge,here we highlight the use of the MATLAB as a tool to help students grasp the fundamentals of tensor analysis.We employ the rich functionalities of the powerful tool,including plotting figures,coding scripts,deriving symbols,and computing tensors.We demonstrate the role that the tool plays in teaching the course in terms of curl operation,coordinate transformation and auxiliary proof of theorems with the addition of script codes.We believe that incorporating this tool into the course will sharpen students'comprehension on the course.It is also expected that they will be able to manipulate tensors proficiently using either the tensor toolbox in MATLAB or the Pytorch deep learning library,based on clear thinking about tensor analysis.

关 键 词：张量分析 坐标变换 定理辅助证明 MATLAB 

分 类 号：G424[文化科学—课程与教学论]