(DiffEQ, Fall 23) 29 - Delta function and practice with ODEs

In this lecture we introduce the delta function (which is used to model instantaneous pulses in our differential equations). We also get a bit more practice in for using Laplace transforms to solve ODE equations.

0:00 Introduction to the delta function
3:51 Solving ODEs with piece-wise components
5:40 Example
15:53 Example
24:19 Example
34:35 Example
43:08 Example
56:58 Example

[mattnyte]

I got a question regarding the laplace of {u(t-a)}. I see from some of your videos (first video intro to this) being e^as / s. While this one and earlier one didn't include the /s, and became e^as. Is there a reason for that?