  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 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 self-motivated to manipulate the
vector calculus syntax and heuristically comprehend the language of tensors by
themselves.
