Lecture 6, Systems Represented by Differential Equations | MIT RES.6.007 Signals and Systems

[@abhishekmittal7213]

Everything finally makes sense now. I wish all professors could be as amazing he is

[@UAE1VTC]

He's a legend ...

[@nicholasestrella339]

The solution at 12:30 can be found pretty easily using Laplace transforms and partial fraction expansion. I'm not sure if there's an easier way.

[@haideralishuvo4781]

It can be also easily found using integrating factor

[@ahmedatifabrar7698]

কুর্নিশ জানাই। এটা পাঠ্যসূচিতে ছিল না, তবু দেখে ফেললাম। এতটা প্রশান্তিদায়ক ভাষণ!

[@saldelgadillo6233]

he is so good on this class

[@pedrovictor8666]

I've been watching the series and I couldn't follow along this lecture. Which subjects concerning ODEs do I need to know so I can understand this? Thanks.

[@dabulls1g]

ODEs

[@BRYANDKING03]

undetermined coefficients

[@liberaboit]

What is ICBS at 12:30?

[@adityakashyap6440]

"It can be shown"

[@pstark4]

at 19:08 the homogeneous solution to the difference equation Az^n cancels. Why? because it's just a constant and therefore can be called a_k?

[@esepecesito]

I had also problem with that. The thing is, you have terms composed of (coeficient * exponential) because the exponential is the same in all terms, you can take it out of the sum, as a common factor. Once it is out, you can divide be the same exponential A zˆn (you can divede by whatever you want, because on the other side there is a 0). After dividing by that, they all turn into "1", so they dissapear. Does it help?

[@pstark4]

@@esepecesito thanks, finally found Lathi's book, so I can concentrate on the ideas rather than the jumps.

[@u2bacount]

At 16:30 doesn't the impulse response not satisfy the initial conditions?

[@yougoog1]

This bothers me. I do not understand why the causality of the LTI is equivalent to the condition of initial rest. Can a LTI system be causal, but at the same time has some non zero initial conditions, meaning at time zero, the system is not at rest. For example, a LTI electronic system consists of a inductor and a capacitor. At time zero, the capacitor already holds some charges and the inductor already has current flowing through it. Does this none zero initial condition make the system not causal? If the causality is a property of a system, then why does this property depends on an initial condition? I must miss something about this causality property. Please help, thank you!

[@lounes9777]

@@yougoog1 have you find any answer ?

[@shalumail23]

Can someone please explain how do I carry out the solution at 12:30

[@marvinprakash1612]

solve the linear differential equation to get this solution

[@mohannadmahmoud6674]

did you get it?

[@sauravti]

Awesomeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 😎

[@srinadhj2638]

can you tell me what are M and N are in difference eaquation

[@faizanazam981]

Index of summation

[@nadiodib434]

They are length of input and output vectors, aka 'x' and 'y'.

[@sternowl2345]

order of the equation

[@babak-ssh]

epic!!!

[@gaybeerboy1]

12:30 a ???????

[@gregypooh]

Watch from 11:55

[@SanduniPremaratne]

How is the solution carried out at 12:30 to obtain the particular solution?

[@saranshgupta9119]

Wanna time travel with me ???

[@mujtabahassan7925]

U r class apart....

[@eurscher1]

08-31-2012; But seriously elders...why does this seem like a 1965 exposure ,trust ! Having problematics'inherent to time-constraint-sensitivity coupled to structural time expansion makes arbitrable the definitions' potential league of manipuable data inherent to differentiation intrinsics' susceptable to integral incursion .Equitable,yet sparklin' tardy ,trust .Unkle Allen don't look nuttin' like that ,now ! -Seclusionos .

[@mrnarason]

???

[@nevis2769]

wtf

[@VARUN-zn2nx]

lisan al gaib