An Pei

School of General Education and Foreign Languages, Anhui Institute of Information Technology

Abstract：

Green's formula is a core theorem in multivariable integral calculus, enabling the equivalent transformation between double integrals over plane regions and closed line integrals of the second kind, and it is also a key and difficult topic in advanced mathematics teaching. To address problems in traditional Green's formula teaching, this paper constructs a dual-driven teaching paradigm of traceability analogy and progressive problem chains, based on the unified idea in calculus of transforming internal integrals into boundary operations. Taking the extension of one-dimensional integration laws to two-dimensional planes as the logical main line, the study follows the cognitive sequence from special to general to complete the theorem's hierarchical derivation, rigorous proof, and gradient-based exercise training.

Key Words：

advanced mathematics; Green's formula; analogy teaching; line integrals of the second kind; teaching reform