Week 1 March 20th 2020
\[\frac{d^2\psi}{dx^2}+\frac{8\pi^2m}{h^2}[E-U(x)]\psi (x)=0\]
We start off strong with the one dimensional \(\text{Schr}\ddot{o}\text{dinger Equation}\). An important equation for all of quantum mechanics, well at least in 1-dimension.
Week 2 March 30th 2020
\[P(A|B)=\frac{P(B|A)P(A)}{P(B)}\]
This week we are taking it back to the fundamentals. The Bayes Theorem, arguablly the most rudimentary and important in understanding probabilities. Useful for calculating your chance of contracting the coronavirus too.
Week 3 April 6th 2020
\[\frac{dy}{dx}+P(x)y=Q(x)\]
We continue with the basics this week. The Bernoulli differential equation. If you see an ODE in this form, why not try solving it with an integrating factor of form \(r(x)=e^{\int P(x)dx}\).
Week 6 April 20th 2020
\[\int_{\partial\Omega}\omega=\int_{\Omega}\partial\omega\]
Due to exceptional circumstances, last two weeks’ equations seem to be missing! But nevertheless, we have another beautiful one this week. Stokes Theorem of Differential Geometry, a beauty indeed, maybe you can learn more about it in our Vector Analysis course.
