Boosting Vector Calculus with the Graphical Notation
Joon-Hwi Kim, Maverick S. H. Oh, and Keun-Young Kim

TL;DR
This paper introduces a graphical notation for three-dimensional Euclidean vector calculus to improve teaching and learning, making the subject more intuitive and reducing reliance on bulky index notation.
Contribution
It pioneers the application of graphical tensor notation to vector calculus, providing a new pedagogical tool for physics education.
Findings
Graphical notation simplifies vector calculus learning.
Students show increased engagement with the graphical approach.
The method enhances understanding of tensor language in physics.
Abstract
Learning vector calculus techniques is one of the major missions to be accomplished by physics undergraduates. However, beginners report various difficulties dealing with the index notation due to its bulkiness. Meanwhile, there have been graphical notations for tensor algebra that are intuitive and effective in calculations and can serve as a quick mnemonic for algebraic identities. Although they have been introduced and applied in vector algebra in the educational context, to the best of our knowledge, there have been no publications that employ the graphical notation to three-dimensional Euclidean vector calculus, involving differentiation and integration of vector fields. Aiming for physics students and educators, we introduce such "graphical vector calculus," demonstrate its pedagogical advantages, and provide enough exercises containing both purely mathematical identities and…
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Taxonomy
TopicsMatrix Theory and Algorithms · Noncommutative and Quantum Gravity Theories · Parallel Computing and Optimization Techniques
