assigned today:

Due today:

- standard-Fourier series:
I can explain, calculate, and use Fourier Series

- Any problem from 11.1.16-11.16.21 (calculate Fourier Series)
- 11.2.12 (inverted parabola)
- Any problem from 11.3.13-11.3.16 (damped, driven)

Due today:

- standard-fundamental theorems of calculus:
I can explain and use the fundamental theorems of calculus.

- Compare and contrast the 1D, grad, div, and curl versions of the fundamental theorem of calculus.
- For \(\vec{f}=(2xz+3y^2)\hat{y}+(4yz^2)\hat{z}\) check both Stoke's theorem for a single loop with 2 different surfaces and gauss' theorem for an interesting volume.
- Show that the following are equivalent:
- \(\vec{\nabla}\times\vec{F}=0\) everywhere
- \(\int_\vec{a}^\vec{b}\vec{F}\cdot\vec{dl}\) is independent of path, for any given end points.
- \(\oint\vec{F}\cdot\vec{dl}=0\) for any closed loop.
- \(\vec{F}\) is the gradient of some scalar, \(\vec{F}=-\vec{\nabla}V\).

- Quiz on gauss and stokes \(v(x,y,z)=\hat{i}\)
- Asked what they knew of Fourier series
- not much (as Guetter warned)

- asked them to plot a periodic function
- asked them to plot a cosine or sign with the same periodicity
- Showed them a Fourier Series
- integrated each term
- we talked about how doing the antiderivative was a waste of class time

- briefly discussed the use in damped/driven situations