# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Fri, Nov 11, 2016 9:10 AM (1 year ago)

### Fourier analysis

assigned today:

Due today:
• standard-fundamental theorems of calculus:

I can explain and use the fundamental theorems of calculus.

1. Compare and contrast the 1D, grad, div, and curl versions of the fundamental theorem of calculus.
2. 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.
3. Show that the following are equivalent:
1. $$\vec{\nabla}\times\vec{F}=0$$ everywhere
2. $$\int_\vec{a}^\vec{b}\vec{F}\cdot\vec{dl}$$ is independent of path, for any given end points.
3. $$\oint\vec{F}\cdot\vec{dl}=0$$ for any closed loop.
4. $$\vec{F}$$ is the gradient of some scalar, $$\vec{F}=-\vec{\nabla}V$$.

# in class

• 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

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