摘要
高等数学是近代数学的基础,它具有高度的抽象性、严密的逻辑性和广泛的应用性。作为各类非数学专业必修的基础课,高等数学的学习对理工科后置课程的学习与理解起到了至关重要的作用。在电学的相关课程特别是《电工与电子技术》《电路基础》等专业基础课程中,本文从高等数学与电学的交叉视角出发,阐述高等数学的概念和方法如何帮助构建交流电路模型,提高分析的效率和准确性[2],探讨复数、微分方程、傅里叶变换、拉普拉斯变换等数学工具在交流电路建模与分析中的应用。通过建立电路行为的数学描述框架,揭示数学抽象与物理现象之间的内在关联,为复杂电路系统的设计与优化提供理论支撑。通过数学工具的灵活应用将抽象复杂的电路分析简单化,让知识的融合更加生动,不仅便于学生理解,而且在增加课堂的趣味性上发挥了作用。
Advanced mathematics is the foundation of modern mathematics,which has a high degree of abstraction,rigorous logic,and wide applicability.As a compulsory basic course for various non mathematics majors,the study of advanced mathematics plays a crucial role in the learning and understanding of post courses in science and engineering.In the relevant courses of electricity,especially in professional foundation courses such as"Electrician and Electronic Technology"and"Fundamentals of Circuits",this article starts from the perspective of the intersection of advanced mathematics and electricity,and elaborates on how the concepts and methods of advanced mathematics can help construct AC circuit models,improve analysis efficiency and accuracy[2],and explore the application of mathematical tools such as complex numbers,differential equations,Fourier transform,Laplace transform,etc.in AC circuit modeling and analysis.By establishing a mathematical description framework for circuit behavior,the intrinsic relationship between mathematical abstraction and physical phenomena is revealed,providing theoretical support for the design and optimization of complex circuit systems.By flexibly applying mathematical tools,abstract and complex circuit analysis is simplified,making the integration of knowledge more vivid.This not only facilitates students'understanding,but also plays a role in increasing the fun of the classroom.
作者
付亚坤
于晟伟
何永明
Fu Yakun;Yu Chengwei;He Yongming(China Fire and Rescue Institute,Beijing 102202,China)
关键词
高等数学
正弦函数
傅里叶级数
复变函数
交流电路
Advanced mathematics
Sine function
Fourier series
Complex function
Communication circuit
