线性代数视角下的高等数学傅里叶级数教学探索  

Teaching Exploration of Fourier Series in Advanced Mathematics from the Perspective of Linear Algebra

作　　者：方敬轩 FANG Jingxuan(College of Science,Minzu University of China,Beijing 100081,China)

机构地区：[1]中央民族大学理学院,北京100081

出　　处：《中央民族大学学报（自然科学版）》2024年第4期84-89,共6页Journal of Minzu University of China(Natural Sciences Edition)

基　　金：国家自然科学基金(12301126)。

摘　　要：本文聚焦于高等数学教学,从线性代数的视角出发进行了傅里叶级数的教学探索与实践。首先剖析了线性代数的部分核心概念,并与傅里叶级数的原理进行了对比,以揭示两者之间的紧密关系。接着探讨了如何有效地将这种内在联系融入高等数学教学之中,旨在帮助学生更好地理解和掌握傅里叶级数的本质。这样的教学方法能够提升学生的数学素养,并为他们后续的学习和研究打下坚实的基础。This paper focuses on the teaching of advanced mathematics,specifically exploring and implementing the teaching of Fourier series from the perspective of linear algebra.Firstly,we ana-lyze some core concepts of linear algebra in detail and compare them with the principles of Fourier series to reveal the close relationship between the two.Then,we further explore how to effectively integrate this connection into higher mathematics teaching,aiming to help students better understand and grasp the essence of Fourier series.Through this teaching method,we hope to enhance students'mathematical literacy and lay a solid foundation for their subsequent learning and research.

关 键 词：高等数学 线性代数 傅里叶级数 教学探索 

分 类 号：O13-4[理学—数学]