# Final homework due May 3 by 5pm — MTH 429H

The final homework assignment is posted here.

# The Poincare Lemma

The Poincaré lemma is a generalization of the familiar fact that a curl-free vector field in ${\mathbb{R}^{3}}$ may be expressed as thee gradient of a function. In these notes we formulate and prove the Poincare lemma.

# Lectures on Stoke’s Theorem — MTH 429H

Stokes Theorem states that

$\displaystyle \int_{S}d\omega=\int_{\partial S}\omega \ \ \ \ \ (1)$

where ${S}$ is a ${j}$-surface in ${\mathbb{R}^{k}}$, ${\omega}$ is a ${C^{1}}$ ${j-1}$-form and ${\partial S}$ is a ${j-1}$ surface (or a collection of ${j-1}$ surfaces) in ${\mathbb{R}^{d}}$ that make up the boundary of ${S}$.

# Two Announcements

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.

# Lectures on Differential Forms — MTH 429H

We now turn to the study of hyper-surfaces in ${\mathbb{R}^{d}}$. A hyper-surface is something like a curve or a surface in ${\mathbb{R}^{3}}$ or their higher dimensional analogues. A differential form is the something we can integrate over a hyper-surface.