I would really like to tank MIT and Dr. Strang for uploading these videos to the public. Although my university is not as prestigious as MIT, and I will never receive a degree from a school such as MIT. It is amazing that i can just go online and learn from the brilliant minds that teach at MIT. This will probably be the closest thing to free education in my lifetime, and I cannot thank MIT enough for not locking these beautiful videos behind some sort of pay wall. My school often glosses over or completely skips many things that I have watched in MIT OpenCourseWare videos(especially Calc 3 and now ODEs), and I thoroughly enjoy how the math classes at MIT do not gloss over the theory and just say, "Use this formula for this and do this when you see that, ect." It is very frustrating to me when my teachers never take the time to explain why a formula works, or what is the underlying reason that you do this when you see that. I like to understand the inner workings of mathematics, and I just want to thank you one more time for posting these videos. They are very insightful, helpful and informative.
Yes MIT lecturers have a really unique way of making you appreciate the value and purpose of maths, they don't hide you from the real applications of maths which is the key to understanding. It gives you a real way to think through problems intuitively instead of being completely stuck because you don't understand what you are actually solving and why. Without context differential equations are just completely alien and most educators don't address this.
I’m very confused about why he is able to just solve the equations for the coefficients. Is he trying to get them to sum to zero, since that is the only way for sint=cost for all t? That seems like the justification, which really would have helped me with my homework last night...
The results for M & N seem suspiciously similar to the Laplace Transforms of sin(at) and cos(at). Is this just a coincidence or is there some underlying meaning behind this?
I'm confused when he solves for the m and n with cos and sine. Since cos and sine are interchangeable, is it safe to write the pair of function "-aM+omegaN = 1 ..." to find the solution? I don't think so. It could be that they sum to 1.5 and a -0.5 from sine part cancel out to be a 1 on the right.
So.. You do it substituting a column of the coefficients matrix [-a w; -w -a] by the independents terms matrix [1; 0], and then you divide the determinant of that one by the determinant of the original coefficients matrix.. In this case, M = det( [1 w; 0 -a] ) / det( [-a w; -w -a] ) N = det( [-a 1; -w 0] ) / det( [-a w; -w -a] ) *I just wrote that because even I dind't remember Cramer's formula
I would really like to tank MIT and Dr. Strang for uploading these videos to the public. Although my university is not as prestigious as MIT, and I will never receive a degree from a school such as MIT. It is amazing that i can just go online and learn from the brilliant minds that teach at MIT. This will probably be the closest thing to free education in my lifetime, and I cannot thank MIT enough for not locking these beautiful videos behind some sort of pay wall. My school often glosses over or completely skips many things that I have watched in MIT OpenCourseWare videos(especially Calc 3 and now ODEs), and I thoroughly enjoy how the math classes at MIT do not gloss over the theory and just say, "Use this formula for this and do this when you see that, ect." It is very frustrating to me when my teachers never take the time to explain why a formula works, or what is the underlying reason that you do this when you see that. I like to understand the inner workings of mathematics, and I just want to thank you one more time for posting these videos. They are very insightful, helpful and informative.
