“线性代数”的可视化教学案例探索

Visual Teaching Case Exploration of"Linear Algebra"

“线性代数”是理工及经管类大学本科生必修的一门数学课程,该课程概念和定理较多且抽象,是学生学习的难点。本文通过MATLAB软件可视化了线性代数中若干核心概念的教学设计,以线性变换为纽带,将矩阵、矩阵的行列式、线性方程组解的情况等知识点串联,形成了三个典型教学案例,旨在帮助刚接触线性代数的学生建立起对这些基础概念的直观理解,把握各个知识点之间的内在联系,并为他们进一步理解和掌握其他概念和高维空间的内容奠定坚实的基础。

"Linear algebra"is a compulsory mathematics course for undergraduate students in science,technology,business and management.It has many concepts and theorems that are abstract,which makes it difficult for students to learn.This paper visualizes the instructional design of several core concepts in linear algebra using MATLAB software.Taking linear transformations as the link,it connects such as matrices,determinants of matrices,and solutions to systems of linear equations,forming three teaching cases.The aim is to help students who are in the initial stages of learning linear algebra to build an intuitive understanding of these basic concepts,grasp the intrinsic connections between various knowledge points,and lay a solid foundation for them to further understand and master other concepts and the content of higher-dimensional spaces.