I show how to rederive and prove Weierstrass's definition for the Gamma function. This is accomplished through multiplication, reduction formulas, asymptotics, limits, and the Euler Mascheroni constant.
Rederiving the Legendre Duplication formula. You have to use the Beta function and relate it to the Beta function with different arguments. It can also be done through multiplication.
Analyzing the parallel RC circuit through a transient analysis. We use diagrams and circuits with full explanations throught the process of analyzing this circuit.
Solving for the current in a RC transient circuit. This has been done before on highvoltagemath, but this time, we have used Laplace Transforms with contour integration to do it.