Extra credit projects

Here is your extra credit opportunity--20pts total.  The project will be three pages double spaced, 1 inch margins.  Projects will be delivered in pdf format to my inbox AND in my department mailbox (in Wexler Hall 231) before Wednesday May 4 at noon.  No credit will be given for projects that do not meet the format or deadline.  Each project will have statements clearly cited.  While I offer starting references in as Wikipedia pages, each project will require you to locate a minimum of two other published references; you may wish to speak to your engineering professors for suggestions.  Below I offer two topics, I'm open to adding other topics to the list if you can come up with one that has a compelling application of multivariable calculus.



Topics:

1) The use of divergence, curl and gradient in electrodynamics.
Some starting references:

A) https://en.wikipedia.org/wiki/Electromagnetism
B) https://en.wikipedia.org/wiki/Classical_electromagnetism
C) https://en.wikipedia.org/wiki/Maxwell's_equations

Specific questions to answer:  What does the divergence of an electric field tell you?  What does the curl of an electric field tell you?  What does the divergence of a magnetic field tell you?  What does the curl of a magnetic field tell you?  What does the gradient of an electric potential tell you? Suppose that there is an electron sitting at the origin. What is flux integral over the sphere of radius 1?


2) The use of divergence, curl and gradient in fluid dynamics.
Some starting references:

A) https://en.wikipedia.org/wiki/Fluid_mechanics
B) https://en.wikipedia.org/wiki/Fluid_dynamics
C) https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

Specific questions to answer with regard to a velocity field of a fluid in motion: What does the divergence  tell you?  What does the curl tell you?  How are these related to pressure?  What are the properties of a potential flow?