Variation of Parameters

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: ocw.mit.edu/RES...
Instructor: Gilbert Strang
Combine null solutions to find a particular solution for any right hand side. But it may involve a difficult integral.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@TheHamoodz]

Came in trying to study for differential equations exam, ended up learning stuff for my circuits exam... Nice!

[@ozzyfromspace]

Seeing him go from variation of parameters to the convolution of f(T) and the impulse response was soooo satisfying. I’m gonna do this for myself in full, just to enjoy the satisfaction/euphoria that results 😄☺️

[@bunkydunk7500]

Me too! I can't stop watching them both especially during this class at a
different school!

[@TheMehedi007]

God bless Dr Gilbert Strang .

[@BentoMontenegro]

Strang always clear, always simples, always the best!

[@mrvzhao]

For full derivation of the two equations at 3:10, check out this video: th-cam.com/video/IYKULUq6YPQ/w-d-xo.html

[@zizo-ve8ib]

Thanks alot that really helped ☺️

[@Kanya-qg8rk]

Thanks!helps alot!

[@DarkMonolth]

I learned this method completely differently using multiple determinants, it comes out a lot easier in my opinion.

[@spiderjerusalem4009]

mind sharing it?

[@a2sirarvindarorakibaate889]

Wronskian method

[@wsilva1051]

Nice presentation, Dr Strang. It couldn't be nicer. I just felt curious about the lower limit of integration set to zero. Was that arbitrary? I know it fits perfectly ok, especially when thinking physically in terms of causality of the Green's function and all that stuff, but I couldn't find any good reason for that choice if did not know in advance that a Green's function was going to shows up in the end. Could someone help me clarify this?

[@HosRo4161]

Thank you, Professor Strang! Thank you!

[@jonathansum9084]

For those people who don't know how the first two equations of rule come from, plz watch this old MIT video :th-cam.com/video/IYKULUq6YPQ/w-d-xo.html

[@lilibethcruz3284]

thanks!!!! This lecture really helped!

[@mazenjuma9165]

Lilibeth Cruz nice

[@georgesadler7830]

This professor really wants students to understand differential equations like the back of their hands.

[@DouglasHPlumb]

James Cook does a lecture on VP and during that or a couple after that he explains where that equation that is identically zero comes from. I think this is where the audio gets screwed up in his lectures on DE's.

[@hathuytu]

how can the coeff b,c be variable in time? they should be constants.

[@josephsabu9739]

I wonder where that 2 Equations come from...?

[@salwynmathew8545]

Which ones?

[@hwx5413]

3:00-3:58，how does these two equations come from?

[@Awesomepapercup]

thats the formula for variation of parameters

[@mengyuwang5159]

I had the same question too. But it turned out the first equ is only based on an assumption, and no certain evidence at that time can support the assumption. By assuming the establishment of the first equ, the second one can be derived. Later, you'll find it can work out under that assumption.

[@mzrba]

How would the two equations @4:03 look like if we have 3 null solutions for the system?

[@MuhammadShoaib-tm9no]

is he really teach at MIT?

[@earthlingsixbillionandsome406]

Don Music: Oh I'll never get it, never (bang)

[@debjyotichattopadhyay6679]

i wish my school teacher to see this video