Research on Teaching Methods of the Three-Dimensional Stokes’ Theorem Based on Fundamentals of Calculus and Linear Algebra

本文提出一种基于微积分和线性代数基础的三维空间Stokes定理的处理方法，兼顾理论严谨性与实用性的同时融入课程思政。从矛盾论与辩证法出发，采用初等方法解释微分形式，进而揭示外微分与积分的统一性，为高等数学的教学与研究提供新思路。This paper proposes a method for the treatment of the three-dimensional Stokes’ theorem based on the fundamentals of calculus and linear algebra, taking into account the theoretical rigor and practicality while integrating into the course politics. Starting from the theory of contradiction and dialectics, the elementary method is used to explain the differential forms, which reveals the unity of exterior differentiation and integration, and provides new perspectives for the teaching and research of advanced mathematics.