Watching this video makes me really question why I even bother going to my lectures, I just spent an hour sitting in a lecture, bored out my mind and I left understanding none of it. I spend 20mins watching this video in the comfort of my home and I now understand it perfectly.
All coefficients must be zero on the left side, to ensure the polynomial is zero for all x values. Similar to comparing coefficients in certain types of algebra solutions (comparing coefficients in partial fractions, for example).
It is not about two things adding to be zero. It is about comparing coefficients for the power series. For a power series to be guaranteed to be zero, then every coefficient must be zero. Consider: a + bx + cx^2 + dx^3 = 0 for instance. If a, b, c, or d are not zero, then the left side is not guaranteed to be zero (depending on what you put in for x).
Spent over an hour in office hours with my prof + sat through class this was "taught" in + recitation it was "reviewed" in and I didn't understand until today with your video, my exams tomorrow thanks!
Lol @ 14:35 - "no more math," I actually find the recursion and patterning in these to be really remarkable. I just have a hard time making the recursion relation up at the end out of it, especially since often there isn't one that is really easy to identify. Like this one, it is y_1(x)=a_0*sum_(n=0)^\infty x^{3n} and y_2(x)=a_1sum_{n=0}^\infty x^{3n+1}, but I can't easily see a pattern to the coefficients within the terms. Do you know of a good material for finding out how to do this more easily? Or is there just no point in doing that, and if that is the case why does my professor keep doing that?? LOL
Watching this video makes me really question why I even bother going to my lectures, I just spent an hour sitting in a lecture, bored out my mind and I left understanding none of it. I spend 20mins watching this video in the comfort of my home and I now understand it perfectly.
Explained better in 18 minutes than my prof in two lectures.
Well done.
2 weeks of confusion solved in 20 minutes. Thank you very much!
@8:14 why is 2A_2=0 a possibility if its addition not multiplication?
All coefficients must be zero on the left side, to ensure the polynomial is zero for all x values. Similar to comparing coefficients in certain types of algebra solutions (comparing coefficients in partial fractions, for example).
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Tomorrow is my exam and you just saved my semester
How do you solve initial value problems?
God, my lecturer took entire week to explain this, still i couldn't understand the concept. You should be the professor in my university.
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Very helpful...finally cleared up the indexing issues I was encountering after reading numerous textbooks. Pretty clear now. Keep it up!
Love, love, LOVE this video. Very clear and concise. Thank you so much!
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The Lecture was really outstanding.Things are very clear now.Thanks for your effort.
8:04 you lost me here. If a sum of 2 numbers is zero, why must either of them be zero? That’s only true when multiplying not adding.
It is not about two things adding to be zero. It is about comparing coefficients for the power series. For a power series to be guaranteed to be zero, then every coefficient must be zero.
Consider: a + bx + cx^2 + dx^3 = 0 for instance. If a, b, c, or d are not zero, then the left side is not guaranteed to be zero (depending on what you put in for x).
@@HoustonMathPrep Ok, thanks, I think I'm seeing this now.
thank you so much this was really well explained! And used a pretty good example (Y)
Great vid! That re-indexing process had me so confused I really think I can do this now
Concepts got clear in the very first time (y)
Spent over an hour in office hours with my prof + sat through class this was "taught" in + recitation it was "reviewed" in and I didn't understand until today with your video, my exams tomorrow thanks!
fanatstıcly solved
ı couldnt understand from books
A black background with the perfect voice.
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I can't believe I spent almost two weeks trying to solve this with no success!!! Thank you sir.
I feel like I just ran a marathon
Thanks so much! You explained this so well!
Lol @ 14:35 - "no more math," I actually find the recursion and patterning in these to be really remarkable. I just have a hard time making the recursion relation up at the end out of it, especially since often there isn't one that is really easy to identify. Like this one, it is y_1(x)=a_0*sum_(n=0)^\infty x^{3n} and y_2(x)=a_1sum_{n=0}^\infty x^{3n+1}, but I can't easily see a pattern to the coefficients within the terms. Do you know of a good material for finding out how to do this more easily? Or is there just no point in doing that, and if that is the case why does my professor keep doing that?? LOL
i needed video like this.... and you are saver.........
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Finally,searched a lot for this topic...peace
Very clear explaination thnk yu :-)
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Houston math prep you are mathematician
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This is maaaaad long! Thanks though! :)
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OMG!!! Thanks to you I just aced my 4th diff eq test. you are truly a blessing. I finished with an overall grade of 91.3%
great video! but has anyone ever told you that you sound like Sheldon Cooper?