Boosting vector calculus with the graphical notation

@article{Kim2019BoostingVC,
  title={Boosting vector calculus with the graphical notation},
  author={Joon-Hwi Kim and Maverick S. H. Oh and Keun-Young Kim},
  journal={arXiv: Physics Education},
  year={2019}
}
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… 

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References

SHOWING 1-10 OF 19 REFERENCES

Spinors and space-time

In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant

Asian physics olympiad (1st-8th) : problems and solutions

This book compiles all of the test problems and solutions from the 1st through the 8th Asian Physics Olympiad. Test questions of every paper consist of two parts, a theory section and an experiment

Jim Blinn's Corner: Notation, Notation, Notation

This is Jim Blinn at his best—now even better, with the "Director's Cut" of the articles: revised, expanded, and enhanced versions of the originals.

On A Diagrammatic Proof of the Cayley-Hamilton Theorem

This note concerns a one-line diagrammatic proof of the Cayley-Hamilton Theorem. We discuss the proof's implications regarding the "core truth" of the theorem, and provide a generalization. We review

is decomposed into three invariant combinations under SO(3) action: divergence, curl, and "shear

    Cf. the "machine" view of tensors, such as in Misner, Wheeler, and Thorne's book

      This is related to Schur's lemma or Wigner-Eckart theorem in essence

        Problems and solutions on graphical vector calculus