The final homework assignment is posted here.
The Poincaré lemma is a generalization of the familiar fact that a curl-free vector field in may be expressed as thee gradient of a function. In these notes we formulate and prove the Poincare lemma.
where is a -surface in , is a -form and is a surface (or a collection of surfaces) in that make up the boundary of .
The MSU Math departments first undergraduate colloquium will take place at 4:10 PM Friday, April 5, 2013 in C304 Wells Hall.
The talk, entitled Recounting the Rationals, will be delivered by Neil J. Calkin from Clemson University. More details can be found here.
On Saturday, is our Tenth Annual Student Mathematics Conference meeting 9am to 5:15 pm in C304 Wells Hall — follow this link for a program. Come listen to what your fellow students have been working on.
We now turn to the study of hyper-surfaces in . A hyper-surface is something like a curve or a surface in or their higher dimensional analogues. A differential form is the something we can integrate over a hyper-surface.
From Rudin Ch. 10: 9, 15; and the following additional exercises.
These still need some editting, but you can find the notes here: