• Review all the names of units, and their SI conversions
• Review all eqns of time constants
• “Amperian Loop”

AP Phys C Mech is an examination held by the CollegeBoard in mechanics.

Things to Study

• Permittivity of free space
• Impulse
• Springs! In general. Perhaps review old notes.
• How to be faster?

Kepler’s Laws of Planetary Motion

AP Statistics is an examination by the CollegeBoard.

See also crap to remember for AP Stats

Non-Focus Mistakes

• file:///Users/houliu/Documents/School Work/The Bible/APStats/APStats5Steps.pdf
• file:///Users/houliu/Documents/School Work/The Bible/APStats/APStats5Steps.pdf
• file:///Users/houliu/Documents/School Work/The Bible/APStats/APStats5Steps.pdf
• Interpretation of regression outputs

Backlog

• Chi-square
• file:///Users/houliu/Documents/School Work/The Bible/APStats/APStats5Steps.pdf
• file:///Users/houliu/Documents/School Work/The Bible/APStats/APStats5Steps.pdf

Notes

• confidence interval
• hypothesis testing
• t-statistics
• chi-square
• data inference
• binomial distribution

Show that:

\begin{equation} \dv t e^{tA} = e^{tA}A \end{equation}

We can apply the result we shown in eigenvalue:

\begin{equation} \dv t \qty(e^{tA}) = \dv t \qty(I + \sum_{k=1}^{\infty} \frac{t^{k}}{k!}A^{k}) = \qty(\sum_{k=1}^{\infty }\frac{1}{k!}kt^{k-1}A^{k-1})A \end{equation}

We do this separation because \(k=0\) would’t make sense to raise \(A\) (\(k-1=-1\)) to as we are unsure about the invertability of \(A\). Obviously \(\frac{1}{k!}k = \frac{1}{(k-1)!}\). Therefore, we can shift our index back yet again:

\begin{equation} \qty(\sum_{k=1}^{\infty }\frac{1}{k!}kt^{k-1}A^{k-1})A = \qty(\sum_{j=0}^{\infty }\frac{1}{j!}t^{j}A^{j})A \end{equation}