Vorticity in Basic Multivariable Calculus [F]

Increasingly, engineers and scientists are talking about topological insulators. What they call the “vorticity” of a nonvanishing planar vector field is not its curl but its “degree.” The degree is continuous, but (unlike the curl) it is an integer. Therefore the degree does not change if conditions are slightly perturbed, so it might be used to store information—this is why people are interested in it. This talk will show how to introduce and practice vorticity in basic multivariable calculus without adding any new material, merely by replacing old examples, exercises and homework problems with new ones at the same level.