Lec 28 | MIT 18.03 Differential Equations, Spring 2006

[@subhamadhikari]

These lectures are creating effect through the waves of time.

[@jacksonmadison9994]

In the recitation Trace-Determinant Diagram | MIT 18.03SC Differential Equations, Fall 2011 The instructor said they would cover borderline cases where Tr = 0 or Det = 0 in another recitation, but I couldn't find such material in any other recitation. I think the only cases left were - stability of fixed points - stability when Det = 0, tr = 0, and rank of A is either 0 or 1 - stability around the origin when Tr = 0

[@georgesadler7830]

Professor Mattuck, thank you explaining another method of solving differential equations using Fundamental Matrix.

[@iwonakozlowska6134]

Since linear algebra is not strange to me , it's nice to come back to this lecture.

[@aatucagg]

@ 32:00 or about, He explains that the -3 is the flow leaving tank x into tank y, the 3 is the flow entering tank y from tank x, the 2 is the flow entering tank x from tank y, and the -4 is the flow leaving tank y into tank x and the flow leaving tank y to the outside.

[@daehomango10000]

Just in case someone is confused why x = X*v and not x = v*X at 38:55, x can't be v*X because the dimensions won't match up with x. x is 2 by 1 while v*X is (2 by 1)*(2 by 2) which doesn't work. X*v on the other hand is (2 by 2)*(2 by 1) = (2 by 1) which matches up with x, which is also (2 by 1).

[@mostaf682]

+Dae Ho Mang He meant v as a row vector if it were to be on the left, but he does the multiplication out verbally and comes to the conclusion that it does not give us what we want.

[@aidanivesdavis]

BRILLIANT lecturer.

[@michaellewis7861]

Existence and uniqueness theorem. Superposition principle. determinant of the fundamental matrix is never zero. Matrix differential equation. Matrix representation. Useful for inhomogenous systems. (We have solved inhomogeneous systems with constant coefficients.) General solution=complementary+particular. 34:19 Variation if Parameters.

[@invaderjmgjerwin]

nice explanation with nice personality!!!! =)

[@dcampos0]

this guys is the best shit ever

[@longshot1710]

@nemo1620 its called a band-pass filter

[@harvesterofsorrow731]

All prisoners in prison should be required to pass this guy's class before they are released back into society.

[@torstenpietersz7745]

Problem is, he makes it soo clear. Wish all my professors were this good

[@amberalbritton2793]

Why were these videos edited to omit parts of the lecture? Was it simply to make it shorter? We are watching the video in the first place because we're very interested in it and we will not mind it being a few minutes longer. It really pains me to lose things he's saying in these videos where the edit occurs. Please reload these videos with the full lecture!

[@videofountain]

You probably have benefitted already. I think you would benefit more to focus on the abundant material ... rather then focus on what you perceive to be missing. The technical people who attend to the video load may be completely distinct from the professors. Education will always be imperfect for everybody at some small amount of random time. There is also related pdf documents and EdX version at the MIT site.

[@freeeagle6074]

It's always good to see what you've got. You'll live a much happier life. Sometimes, a section of the lecture was cut owing to copyright reasons. Sometimes, some technical problem arose.

[@Mantis454]

why does the matrix equal [-3,3 2,-4]

[@akhilanr1233]

i was about to reply.... but i realized the comment was 8 years old... lol do u need the answer now?

[@HoppoLOL]

I'll never be smart enough to understand this and it always pisses me off, that doesn't mean though that I don't enjoy watching these videos.

[@thomasrad6296]

Abstract Math: Bing Bing Da Da

[@jebyron3]

@dcampos0 No, you're the best shit ever David.

[@arshigtx]

out of**

[@MyChemicalBromance]

So I learned the exact same thing for $500, that these MIT kids paid (Sorry, their PARENTS paid) nearly $8000 for...

[@freeeagle6074]

First, students with parental income lower than somewhere around 50,000 dollars will probably get full scholarships in many American universities. Even if not, students can get a 20-year loan from the federal government. After graduation, they pay only 200 dollars one month. Second, students at MIT get more resources from recitation, group study, office hours, etc. to help them understand and master the courses. Third, they obtain a whole network of similar-minded alumni. They may establish businesses or careers after or before graduating from university. They will also find alumni to help them when seeking a job.

[@arshigtx]

aww man this guy just droooooonnnesss....i find that the home made videos are alot better than thes profs at the unis...even if it is MIT...They take the passion and beauty of mathematics...even my own profs at CU are the same :(