复变函数论”中研究型教学模式的探索与实践

摘要

近些年，以培养学生创新能力为导向的研究型教学模式受到了广泛关注。在高校，科研是重点，教学是基础，教学和科研的有效结合正是研究型教学的出发点。笔者基于复变函数论中的幂级数展开定理（Taylor定理和Laurent定理），探索研究型教学的有效性，并在教学内容、教学方法和教学反馈方面进行了具体实践。结果表明：研究型教学有利于提升学生学习的主观能动性，尤其在培养学生的创新能力方面有明显的优势，是一种值得借鉴的教学模式。

Abstract

In recent years, the research-oriented teaching mode guided by cultivating students' innovative abilities has received widespread attention. In universities, scientific research is the focus, and teaching is the foundation. The effective combination of them is the starting point of research- oriented teaching. This article explores the effectiveness of research- oriented teaching based on the power series expansion theorem (Taylor's theorem and Laurent's theorem) in the theory of complex functions. Moreover, specific practices are carried out in teaching content, teaching methods and teaching feedback. The results indicate that the research-oriented teaching is beneficial for enhancing students' subjective initiative in learning, especially in cultivating their innovative abilities, and the teaching model is worth learning.

关键词

创新能力 / 研究型教学 / 复变函数论 / Taylor定理 / Laurent定理

Key words

innovative abilities / research-oriented teaching / the theory of complex functions / Taylor's theorem / Laurent's theorem