Uniform Convergence was defined, and was illustrated by the odd and even expansion examples from last lecture. (The even one converged uniformly, but the odd one didn't.) The concept was further illustrated in Maple by plotting the Square Wave (non-uniformly convergent) and the Sawtooth (uniformly convergent).
Various theorems on uniform convergence were presented. Most of them are fairly obvious and are really saying "make sure there are no jump discontinuities".