assigned today:

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, \(\vec{F}=-\vec{\nabla}V\).

Due today:

- talked about the funk we're in after the election
- Quiz on comparing and contrasting the Laplace Transform and Eigen approach to a damped oscillator (with non-zero initial conditions).
- Asked them to write down the fundamental theorem of calculus
- most wrote \(\int_a^b f(x)\,dx=F(b)-F(a)\)

- I walked through the other three and we compared and contrasted (including a one-word story!)
- we talked about when you need a vector field and when you need a scalar field
- we talked about the arbitrary sign in the Stoke's version

- We talked about the given function in the 2nd problem
- We talked about the third problem and how they need to be able to go from one to any of the others.

They asked that I work a few problems, especially with div and curl