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.
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!
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).
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
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).
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!
U r a blessing for all the students out here... :) Thanku for a clear explanation of the concept..!! Ur awesome..
God, my lecturer took entire week to explain this, still i couldn't understand the concept. You should be the professor in my university.
Tomorrow is my exam and you just saved my semester
Very helpful...finally cleared up the indexing issues I was encountering after reading numerous textbooks. Pretty clear now. Keep it up!
I can't believe I spent almost two weeks trying to solve this with no success!!! Thank you sir.
Love, love, LOVE this video. Very clear and concise. Thank you so much!
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!
I arrived 7 years after you posted this video. Thank you.
Do U know ?
U r a great man !!
wow :)
The Lecture was really outstanding.Things are very clear now.Thanks for your effort.
Great vid! That re-indexing process had me so confused I really think I can do this now
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%
How do you solve initial value problems?
My final is in few hours . This was really helpful and easy to understand u saved me . Thank you .
Concepts got clear in the very first time (y)
@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).
Finally,searched a lot for this topic...peace
This just made all of this make sense! Thank you!
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thank you so much this was really well explained! And used a pretty good example (Y)
This was unbelievably helpful! Thank you so much!!
A black background with the perfect voice.
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You have explained very well this course, thanks for your contribution in science
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I thank God for bringing you in this third planet
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Thanks for helping me understand this
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Very clear explaination thnk yu :-)
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Easy to understand
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
you are a god sir !!!
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THANK YOU
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.
I used to think PatrickJMT is best. My opinion is changed!
thanks man.....🙆🙆🙆🙆
that was good
Lifesaver
This is maaaaad long! Thanks though! :)
thank you
fanatstıcly solved
ı couldnt understand from books
great video! but has anyone ever told you that you sound like Sheldon Cooper?
I feel like I just ran a marathon
THANKS (with capital letters)
omg cant be better ,
nice
Houston math prep you are mathematician
Thank you 🌷