以泰勒公式教学为例探索高等数学的教学改革

Taking Taylor’s Formula Teaching as an Example to Explore the Teaching Reform of Higher Mathematics

摘要: 高等数学是所有自然学科的基础，学科中的微积分、复变函数以及数理统计是研究自然现象，揭示自然规律，探索规模应用的理论研究工具。随着大规模科学计算与大规模工程应用的发展，越来越多的科学领域都比以往更加迫切地需要高等数学的理论与应用支持。如何上好《高等数学》这门课？如何让《高等数学》这门课适应时代的需要？如何让学生们学以致用？是每个《高等数学》教师必须考虑的问题。本文从泰勒公式课堂教学的实际出发，以泰勒公式教学为例从多方面探索《高等数学》课的教学改革研究与应用。

Abstract: Advanced mathematics is the foundation of all natural disciplines. Calculus, complex variable functions and mathematical statistics in the discipline are theoretical research tools for studying natural phenomena, revealing natural laws, and exploring scale applications. With the development of large-scale scientific computing and large-scale engineering applications, more and more scientific fields need the theoretical and application support of advanced mathematics more urgently than ever. How to teach advanced mathematics well? How to adapt advanced mathematics to the needs of the times? How can students apply what they have learned? It is a question that every advanced mathematics teacher must consider. Starting from the Taylor’s formula actual situation of classroom teaching, this paper takes Taylor’s formula teaching as an example to explore the research and application of teaching reform of advanced mathematics from various aspects.