# The 3 stooges of vector calculus and their impersonators: A viewer's guide to the classic episodes

@article{Buskin2013The3S, title={The 3 stooges of vector calculus and their impersonators: A viewer's guide to the classic episodes}, author={Jennie Buskin and Philip Prosapio and Scott A. Taylor}, journal={arXiv: History and Overview}, year={2013} }

The basic theorems of vector calculus are illuminated when we replace the original 3 stooges of vector calculus: Grad, Div, and Curl, with combinatorial substitutes. In addition to providing simple proofs of Green's theorem and the equivalence of the integral and derivative definitions of curl, we also provide a brief introduction to cohomology theory.

## One Citation

### APPROACHING GREEN ’ S THEOREM VIA RIEMANN SUMS

- Mathematics
- 2013

We give a proof of Green’s theorem which captures the underlying intuition and which relies only on the mean value theorems for derivatives and integrals and on the change of variables theorem for…

## References

SHOWING 1-10 OF 15 REFERENCES

### Div, grad, curl, and all that : an informal text on vector calculus

- Mathematics
- 1973

This advanced calculus text is suitable for mathematicians, engineers and physicists. For this second edition the artwork has been completely revised and there is a new section on simple…

### A Geometric Approach to Differential Forms

- Mathematics
- 2006

Preface.- Guide to the Reader.-Multivariable Calculus.- Parameterizations.- Introduction to Forms.- Forms.- Differential Forms.- Differentiation of Forms.- Stokes' Theorem.- Applications.-…

### Advanced Calculus: A Differential Forms Approach

- Mathematics
- 1994

This is a textbook, complete with examples, exercises, and solutions, for an advanced calculus course in which differential forms can be used to introduce the subject andMathematicians who teach the subject will find it enriching reading for its modern viewpoint and techniques.

### Algebraic Topology

- Mathematics

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.

### Vector Calculus

- Mathematics
- 2014

Four different vector fields on (x,y)-plane A vector field on a sphere ♣ Curves. A smooth curve is a continuous curve (no gaps or discontinuities) with no corners (no abrupt changes in slope at a…

### Analysis On Manifolds

- Mathematics
- 1991

* The Algebra and Topology of Rn * Differentiation * Integration * Change of Variables * Manifolds * Differential Forms * Stokes Theorem * Closed Forms and Exact Forms * EpilogueLife Outside Rn

### Boston

- History
- 1906

Regular stagecoach travel could be accomplished between Boston and New York by the mid 1740s, but the journey was an uncomfortable one. In the summer, dust filled the inside of the coach, and those…