Laplace Transform: Second Order Equation

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
Instructor: Gilbert Strang

The algebra problem involves the transfer function. The poles of that function are all-important.

License: Creative Commons BY-NC-SA

[trelosyiaellinika]

Answer to last example: y(t) = A*e^(s1*t) + B*e^(s2*t) + C*cos(ωt) + (D/ω)*sin(ωt)
Thanks for the lectures. It's very helpful to shed light on many of the nuances I could not get from other similar lectures.

[vishusharma]

I can binge-watch Prof. Gilbert Strang

[TheudosGauh]

Yeah...lost audio at the last part of this video. For this particular example, Laplace transform is indeed much more complex than the usual method... But i think the best thing about Laplace transform is that it provides us with a reliable algorithm to solve for differential equation, i.e., the formalist approach instead of relying on intuition or great moment of Eureka.

[johnkoatdungdit]

I really like the way MIT offers its lectures

[Choklad]

The sound gets cut at 16:09. But this lecture really helped me understand more about the laplace transform, thank you!

[mikyotsi]

Excellent Teacher!!Sir the new generations are grateful!!!

[WestOfEarth]

Thank you for these outlines. Really helps me understand Laplace. While audio cut-out was unfortunate, I feel sorry for Prof. Strang. He seems to have known it cut out too, and looks crestfallen that he wasn't able to end with a concluding remark.

[georgesadler]

These mathematical tricks are awesome. I am constantly trying to learn them.

[jungleb]

I wish my professors had been as clear as these lectures! What a great style of teaching.

[Chris-zzgm]

Congratulations, your course is perfect.
Everything is clear and simple
Thx

[eng]

Strang added his comment that its zero initial condition : 12:20 hence the initial values are zero at LHS

[jersonchuquimboques]

the kransfer function is G(s)=1/(s^2+Bs+c) only when initial conditions ( Y'(0)=0, Y(0)=0 ), is this really? if i am wrong, can you solve my doubt ? MIT OpenCourseWare

[blederman]

What confuses me is when Professor Strang takes a Laplace of a first or second derivative, he omits the y(0) and y'(0). What is his justification for doing that?

[johnchristian]

This is great nice, shame about the sound cut-off at the end though

[jarinorvanto]

History doesn't repeat itself, but it mimes.

[leonardosoto]

at 8:14 where did the y(0) terms go? i understand that the laplace transform of the derivative is s*Y(s) but there is an extra term that this guys omitted

[gjop-zkwi]

A sum of two logs is a product of a log.

[Cherem]

I'd like to learn how he does his partial fractions so fast

[hashhoomy]

During Re{} and Im{} treatment for cos(wt) as if he assumes 's' is real! This is shocking!

[pnachtwey]

I like this guy much better than the MIT guys. the MIT guys waste too much time on theory, not on technique,