基于实际应用背景构建《复变函数》课程的系统性教学框架——以代数运算与幂级数的教学方法为例

Building a Systematic Teaching Framework for the “Complex Variables” Course Based on Practical Context—Taking Teaching Methods for Algebraic Operations and Power Series as Examples

摘要: 《复变函数》是一门重要的大学工科数学基础课程。该课程理论体系完整，应用背景鲜明，特别是对电子、通信、自动化等专业的学生而言，该课程对后继专业课程乃至研究生阶段的学习都是非常重要的。教学过程中，将知识点与应用背景结合，会对上课效果起到积极的促进作用。本文主要探讨复数的代数运算与复变函数的幂级数的教学实施过程，主要介绍复数的加、减、乘、除的几何意义，以及幂级数讲解过程中配合趣味性例题，增强课堂的授课效果。

Abstract: “Complex Variable Functions” serves as a crucial foundational mathematics course for engineering disciplines in universities. Characterized by a comprehensive theoretical framework and distinct practical relevance, this course holds particular significance for students in electronics, communications, automation, and related fields. It provides essential groundwork for subsequent specialized courses and advanced studies at the graduate level. Integrating theoretical concepts with real-world applications during instruction significantly enhances classroom effectiveness. This paper examines the pedagogical implementation of algebraic operations of complex numbers and power series of complex functions. Specifically, it presents the geometric interpretations of addition, subtraction, multiplication, and division of complex numbers, and introduces engaging examples during power series instruction to optimize teaching outcomes.