Boosting Vector Calculus with the Graphical Notation
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 threedimensional 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 practical calculations in physics. The graphical notation can readily be utilized in the educational environment to not only lower the barriers in learning and practicing vector calculus but also make students interested and selfmotivated to manipulate the vector calculus syntax and heuristically comprehend the language of tensors by themselves.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.00892
 Bibcode:
 2019arXiv191100892K
 Keywords:

 Physics  Physics Education;
 High Energy Physics  Theory
 EPrint:
 11 pages, 2 figures