so is it a highway heading north bound or like subway... maybe a interstate?
@kaizhang68011 жыл бұрын
Patrick, I just want to take my time to thank you for all the great videos on your channel. I am a struggling engineer but thanks to your videos, i've been passing all my math classes with ease. I really wish that you have more advanced contents or covered more topics beyond simple calculus such as fluid mechanics or statistic analysis so that i can breeze through all my courses. It literally takes me 5min to fully cover a topic compared to 2-3 hours by looking through my textbook. Anyway keep doing what you do.
@Magnawulf10 жыл бұрын
For anyone wondering why it's not Cn = Co/(n+1)! Look at his equations. For example he determined that C3 = Co/3! which is indeed Cn = Co/n!. He also determined that C4 = Co/4! which follows Cn = Co/n!
@bangargaurav16367 жыл бұрын
Magnawulf thanks for explaining
@TheRevival886 жыл бұрын
Here starting level of numeral too matters
@Vyantri4 жыл бұрын
When you say C3, that subscript 3 does not represent just n, but n+1. So I think that the final result can be written as C subscript n+1 equals C sub naught over (n+1)! and I think that this is equivalent to Cn=C0/n! You can replace the n with anything because they are the same thing in both the left and right hand side of the equation.
@tonystank13094 жыл бұрын
My man, @PatrickJMT is helping a lot of people.... Especially during their exams!!! Thanks man.
@magaliebravo66799 жыл бұрын
I'm pretty sure its suppose to be c/(n+1)! either way, thanks for uploading PatricJMT!!! I've been following you since my algebra days.
@vaultvon21268 жыл бұрын
Same here. He is the master. from the very start to ....
@sayanmondal45708 жыл бұрын
Magalie Bravo Actually for n=m-1 we get the value of Cm = Co/(m!)
@johnnysv76466 жыл бұрын
It would have been better to "Re-index" or change the name of the variable "n" to "k" to avoid confusion because to determine the pattern you look at the consecutive Cn values. So for C1=C0/1! , C2=C0/2! , C3=C0/3! we can clearly see that the pattern is in fact Cn= C0/n! or Ck=C0/k! which is how I write it to avoid confusion.
@Peter_19865 жыл бұрын
PatrickJMT, Professor Leonard, Khan Academy, blackpenredpen and Michel Van Biezen are my favourite applied science channels.
@MichaelSmith-rh9ok3 жыл бұрын
@@Peter_1986 The organic Chemistry tutor is really good too!
@hampsternips10 жыл бұрын
my lecturer is a potato, Patrick you are awesome!
@mathadventuress3 жыл бұрын
Hahaha
@shaquillchole8042 Жыл бұрын
😂😂😂wow
@moosaabbas8310 Жыл бұрын
Lk1hlIU
@Ammaray12 жыл бұрын
Would you be willing to post a couple more examples of Power Series solutions of DE with initial conditions, possibly in a term-by-term method? Thanks for all you have done. You have helped me so much already! I have been learning from your videos for a couple of years now.
@heilgid929 жыл бұрын
the man, the myth, the legend... patrickjmt
@syedubaid4116 Жыл бұрын
The man, the math , the legend
@heilgid92 Жыл бұрын
@@syedubaid4116 wow! A reply to my 7 year old comment!
@syedubaid4116 Жыл бұрын
@@heilgid92 lol, it's KZbin's new algorithm which brings old comments up
@heilgid92 Жыл бұрын
@@syedubaid4116awesome. Why are you learning differential equations? 7 years ago I was in college. Now I've been working as an engineer for over 5 years now!
@syedubaid4116 Жыл бұрын
@@heilgid92 good question, I completed all my engineering courses 6 years back apart from differential, couldn't get my degree ... That's why I'm studying differential... Me too I'm an electrical engineering on job since the past 6 years 😂
@MrSexyJem12 жыл бұрын
patrick, for the people who are going to have trouble in the near future, i really suggest that u put up another example one with x's and y's because those question really needs a next level of understanding. For example y'' - xy' - y= 0 really suggest you put up on any of these type of equations. it would really help us out alot.
@Zeeblog14 жыл бұрын
Thanks, this really helped, your teaching method is really clear and concise. I also like the way you make your summation signs, haha.
@mosulicwele18249 жыл бұрын
I passed the maths because of your efforts, may all the blessings be upon you. Thanks!!! You always make things easier so that we can understand.
@virginialikesyou12 жыл бұрын
patrickJMT you have helped me from Calculus I all the way through Differential Equations. I LOVE YOU!!
@JustinZymbaluk7 жыл бұрын
Thanks a lot Patrick, you've been a real life saver my entire college career. I also just want to say, I love the way you write your sigmas, they look so cool and sleek!
@Arwokid11 жыл бұрын
because (if im not wrong) ...a power series has to start with x^0 (
@patrickjmt15 жыл бұрын
differential equations - usually taken after calc 2 or 3
@bobyoco14 жыл бұрын
@patrickJMT I second the idea of another video even though I have my test soon. This was the hardest for me to learn/understand. As always, you're a lifesaver Pat!
@jossell91110 жыл бұрын
God Bless you patrickJMT. Just in time for my Diff Eq Quiz today!
@patrickjmt15 жыл бұрын
it is: QuickCam Orbit AF
@damienjamieson757711 жыл бұрын
Thanks Patrick for a clear reliable lesson.
@pamodakoggala4 жыл бұрын
patrickJMT thank you very much for uploading this video. It was really helpful
@tokkeekkot68746 ай бұрын
🎉
@JSSTyger13 жыл бұрын
@tfreed20 I can clear up your question. When he had Cn+1 = Cn/(n+1), the equation was in terms of Cn and not of C0. That is why the multipliers were not the same. Plugging in n = 1, you get C2 = C1/(2) = C0/2. It actually is the same.
@TazerBlaze11 жыл бұрын
When you differentiate a summation, imagine differentiating every term in the summation. He changed it because if not then, you would start at n=0 for all terms in the summation so the 1st term would be C0*x^-1 which would not be the derivative of ANY of the terms so it would not be in the summation, that's how it has to be rewritten (:
@Ammaray12 жыл бұрын
Question: What does it mean if an initial condition is given, such as in the following example: df/dt = f + t init. cond.: f(0) = 1. Thanks for all the other vids! You are a life saver.
@patrickalle13 жыл бұрын
Hey Pat. At the end of your video you're basically saying "oh, well this is basically e^x." Which brought Laplace Transforms to mind. Where you have to recognize what whatever the thing is and plug and chug. Are these related or just coincidences?
@Isou300811 жыл бұрын
You are always on point Patrick , thank you so much.
@patrickjmt12 жыл бұрын
you are very welcome
@Syruscleat15 жыл бұрын
Wow! You made my hat spin with all that algebra! As always, my hat goes off to the AMG! American Math Guru that is!
@aubreehuntley55885 ай бұрын
thank you your video is so much clearer than others!! Clutch for my calc 2 final❤️❤️❤️
@kagayakuangel58285 жыл бұрын
I am laughing when he said at the end, “hopefully this looks familiar to you” 😂 and I’m just like, “he means that’s e^x right?” Lol and lol yeah. I hope it looks familiar to me on that final exam next week LMFAOOOOO!!!!!!!!!!
@VelocityCCX15 жыл бұрын
Thank-you Patrick, this is my first of I hope many video's I will watch.
@QuackersForMath5 жыл бұрын
Really great explanation - something my university failed to achieve. Thanks mate :)
@geromegacrama2843 жыл бұрын
Wow ,amazing ,,thanks Teacher 😁😁🙏..God bless you 🙏
@DaveDruska15 жыл бұрын
Thanks for this, post that harder question! In your next video can you explain how to find the first few nonzero terms "about x=0"?
@JSSTyger13 жыл бұрын
I knew the answer right when I looked at it. :) I actually did not learn power series methods for solving diff eqs in college. I taught it to myself afterward in my spare time.
@patrickjmt15 жыл бұрын
thanks for the tip! i will do this
@PatWizard5 ай бұрын
bro thanking his own video. I can't even blame him, its that good
@vbballmaster11 жыл бұрын
its because the formula is kind of a shorthand to avoid doing the calculations, its not Cn, but C(n+1) originally, so n=2 gives C3 = Co/3!, which follows with Cn= Co/n!
@thies2us9 жыл бұрын
Patrick and others, do we always have to assume a solution of this kind? are there any other solutions to assume? thanks
@shaygahweh12 жыл бұрын
I got a 100% on the test thanks to you Patrick =) Last calc course. WOOHOO! =D
@benclark57479 жыл бұрын
why isn't it no cn=c0/(n+1)!
@socratiat_09 жыл бұрын
The question at any minute of the video .. so I can help
@maddywellsgarske7999 жыл бұрын
Ben Clark This is because he is NOT using the same (n) as he was using when plugging in values to find the coefficients. Look again at 8:35. When he was plugging in n=3 into the equation he was getting C4=Co/(4!) . The key point here is noticing the 4's! You can also look at the rest of the examples before that C3=Co/3!, C2=C0/(2!) and so on. Therefore he can say Cn=Co/(n!), you could also say C(n+1)=Co/(n+1)! if you wanted to use the same n in both ideas. Try plugging in (n) into your equation. Lets try n=1. With your equation C1=Co/(2!), is this correct? No, the answer should be C1=Co/1! or C1=Co. So you would either have to change your equation to C(n+1)=Co/(n+1)! or Cn=Co/(n!) in order for it to fit the pattern. Both are correct! Yours was a mixture of both. I hope that helps!
@cpt_shipard96985 жыл бұрын
@@maddywellsgarske799 Thx for pointing that out.
@anzatzi11 жыл бұрын
wow--that was awesome--was jest reading the same example in a book with no results--thanks
@DoggoWillink12 жыл бұрын
YES!! Patrick my exam was cancelled today because the "courier", if you will, never showed up with the exams haha. I might have a chance now. He said it was a first, just left now; too happy.
@Thexder014 жыл бұрын
@liquidstl Yes, you first shift indices to match the exponents in x. If after that, the sums start at different points, **do not** shift -- just write separately the few indices which are not in all the sums. That said, great video!
@da1booger1312 жыл бұрын
This is why I love this place. I'm sure to learn math and get a good laugh at the same time.
@johnnysv76466 жыл бұрын
His pattern is correct Cn= C0/n!. It would have been better to "Re-index" or change the name of the variable "n" to "k" to avoid confusion because to determine the pattern you look at the consecutive Cn values. So for C1=C0/1! , C2=C0/2! , C3=C0/3! we can clearly see that the pattern is in fact Cn= C0/n! or Ck=C0/k! which is how I write it to avoid confusion. I hope this cleared up any confusion
@coltennabers6349 жыл бұрын
if you go to TTU don't get Arne Ledet for Diffeq - just a heads up.
@iDanielSalmeron9 жыл бұрын
Wreck EM wreck EM wreck EM
@canyuksek42244 жыл бұрын
You are a great tutor, thanks!
@td-po5ik11 жыл бұрын
Patrick ! this question was on my exam. Thank you so much !
@reclusivewanker411912 жыл бұрын
that was really helpful but in my humble opinion you should do more complicated ones.
@rabeeaatif19844 жыл бұрын
YOU ARE AMAZING!!!!!!!
@abguitar999 жыл бұрын
Thank you patrickJMT :) Really helpful.
@liquidstl14 жыл бұрын
I'm taking an engineering math class this fall so I'm watching some of these videos as review. One thing I was never too sure of is. When shifting the index; is the point to have the index start at the same point for each series, or to have the same exponent so that you can factor out the Cn's and equate coefficients to solve for the recurrence relation? Also, Its slipping my mind at the moment, but other than inspection, what other way is there to solve this ODE?
@javierrubio188911 жыл бұрын
Thank you for your videos. This example is too obvious ( y' - y = 0, y' = y,....what's the proper function of the derivative, Dy=y ?....it is y = c exp x ). But it's nice to see that the method works! . JBcn
@carbon2735 жыл бұрын
how did you get C_n= C_0/n! if for example at n=3: C_4=C_0/4! ???? if n=3 and the subscripts are 4 shouldn't it be n+1 instead of n for the generalized form?
@patrickjmt15 жыл бұрын
no, there is no mistake!
@markkennedy97674 жыл бұрын
At 3:00 isn't the goal of shifting index to make the powers on the x the same (to allow us to add both sums) and not necessarily to have both sums to go from zero to infinity as you say in the video.
@zurchei11 жыл бұрын
that was helpfull indeed , and will be glad if u could put more vedios on differentials equations..they are realy gıving me headaches..
@ibrahimhelmi233512 жыл бұрын
Thank you very much,,looking forward to see example 2 :)
@DaveDruska15 жыл бұрын
You should turn off the auto brightness/contrast so the whole video doesn't flash brightness when your hand goes into view. Thanks!
@ujueije57627 жыл бұрын
Brilliant, really brilliant for this excellent video. Keep on the good job
@kellyblakmoffat7 жыл бұрын
my secrete tutor...you have been so helpful just from first year now am in my third year EEE
@patrickjmt7 жыл бұрын
time to go be a donor at Patreon :)
@ovsick12 жыл бұрын
Can you please put a video on how you get n+1 =n , lagging. When you have coefficients (c1, c2, c3...) equal to zero. How you do the lagging, and how you know how many times you need iterate the Sum. Thanks
@Peter_19865 жыл бұрын
My Linear Analysis class spent a whole lecture going through this stuff. I skipped that lecture and watched this video instead, lmao.
@kimkieu301010 жыл бұрын
Very helpful, thanks. But my DE homework is so much harder than this :/
@yorkeR17713 жыл бұрын
@evelelamayo I don't believe so. If you check, he arrived at the condition: C_(n+1) = (C_n)/(n+1). He then wrote his answer in terms of C_n, so (C_0)/(n!) is the correct answer. This is actually a famous example because y = ce^x (constant c) is the only function where y = y' (I think).
@wiselinkmarque394710 жыл бұрын
all the problems I find online are too simple compared to my differentials... I can't figure this stuff out. went to two college classes, tutors don't have a clue.... this sucks.
@magaliebravo66799 жыл бұрын
wiselink thats when its time to meet with the professor
@wiselinkmarque39479 жыл бұрын
Magalie Bravo That's all fine when the professor has time but my professor had grandkids to attend to a lot so he wasn't around much. I passed the class anyways though. I just don't see how it is going to help me with finding a job later on.
@maddywellsgarske7999 жыл бұрын
Magalie Bravo This is a reply to your earlier post and the reason behind why his equation is actually correct. I thought it wasn't at first just like you did. Here is my explanation. The n he is using in the end isnt exactly the same n as he was using before. Look again at 8:35. When he was plugging in n=3 into the equation he was getting C4=Co/(4!) . The key point here is noticing the 4's! You can also look at the rest of the examples before that C3=Co/3!, C2=C0/(2!) and so on. Therefore he can say Cn=Co/(n!), you could also say C(n+1)=Co/(n+1)! if you wanted to use the same n in both ideas. Try plugging in (n) into your equation. Lets try n=1. With your equation C1=Co/(2!), is this correct? No, the answer should be C1=Co/1! or C1=Co. So you would either have to change your equation to C(n+1)=Co/(n+1)! or Cn=Co/(n!) in order for it to fit the pattern. Yours was a mixture of both. I hope that helps!
@ayuparpe15806 жыл бұрын
how are u r doing ENGINEER WISELINK
@Nothing-ui7pj4 жыл бұрын
To check wether they are fundamental we take the wronskien at the singular point right?
@ayadalhashimy49873 жыл бұрын
Q1. Solve the following differential equation using power series at x=0. Find the first few terms. y" + x²y + xy = 0
@dwilmer714 жыл бұрын
patrick didnt you say you did a more complicated example?? cant find it? thanks
@humphrec7313 жыл бұрын
a more complex example? Is it available yet?
@tejumadeolomola26273 жыл бұрын
I hope you living the life you want!. Cos you are a gem
@patrickjmt3 жыл бұрын
it is mostly good, with a few hiccups, but that is life :)
@liquidstl11 жыл бұрын
for my Intermediate Heat Transfer Class, I have to solve T''+mT^4=0 where M = 2epsillon*sigma/k = constant..... I am in the middle of an attempted solution using power series but I don't know what to do because I cant consolidate terms since one summation has X^k while another has X^4k. Where do I go from here? Are there any alternative solution methods, etc? Thanks!!!! -Chris Downs
@noodlefart10293847567 жыл бұрын
i was struggling with this all year then you taught me in 10 mins lol
@patrickjmt7 жыл бұрын
now you know where to come next time you get stuck :)
@RosatiSamuel7 жыл бұрын
Its been awesome getting this working out here, Ive worked a lot in class and not understanding! kudos tutor, but how did you factor out the second step of the summation, little bit confused over there
@Gobemoucheful12 жыл бұрын
So when you took the derivative of your first seires why did the summation start at n=1 instead of n=0?
@ummarfarooq41608 жыл бұрын
Awesome one thanks
@stanleyho249911 жыл бұрын
This video helped me a lot. Thank you!
@patrickjmt15 жыл бұрын
and the cam was a $100 webcam by logitech
@patrickjmt14 жыл бұрын
@dwilmer7 i had every intent to when i made this, but i never did yet
@patrickjmt15 жыл бұрын
nope! c_n = c_0 / (n)!
@moutzdx52558 жыл бұрын
what if we have y'-2xy=0. can u answer me plzz ?? How you will write it as a single submission ??
@ashwathamagaming77888 жыл бұрын
Sir ur vdos r very helpful... Can u please tell me if the method u showed in this vdo is known as Frobenius method??????
@wlthr8 жыл бұрын
no, that would be y_p=sum(a_n*x^(n+r)) with a0 != 0
@hashtagjules63112 жыл бұрын
you should do more video on power serious solutions and frobenius' theorem please :)
@jaybee96314 жыл бұрын
Hi Patrick, how would you solve if the equation was non-homogeneous?
@Blacksnowman12 жыл бұрын
Can anyone tell me how I am suppose to know when to use power series to solve a differential equation?
@kiddcamel Жыл бұрын
I wish I could thank you in person
@skipunkrich12 жыл бұрын
have you posted the more difficult one yet?
@sravanthysharma50328 жыл бұрын
Thanks a ton patrick ur videos are really helpful
@dwilmer714 жыл бұрын
thank you.. one more question.. after you take derivative of first summation (n=0 to n=infinity).. why does it then change to n=1 to n=infinity?? thank you
@rippen5263 жыл бұрын
Wow your comment was 11 years ago, 😨 .
@RedBar3D9 жыл бұрын
How do we know that y = Ce^ax is the only solution to differential equations like these, where y' = ay? Is there any way to verify that there are no other solutions?
@socratiat_09 жыл бұрын
I think that there are other ways .. but the problem is I do not speak English well
@RedBar3D9 жыл бұрын
Socrat AL-Baghdadi you could provide me with a link
@ostensiblyquerulous7 жыл бұрын
Simon Nylund The goal is to just find solutions that span the necessary solution set space. So it is very likely a different answer does exist, but that's irrelevant, because we don't have methods for solving for them.
@23youwatch13 жыл бұрын
is there a second example video?
@Prashanth-yn9zd4 жыл бұрын
Is C0.e^x the only solution for that equation?
@corbinsherman243812 жыл бұрын
It is not very useful if you have constant coefficients but if you have variable coefficients it is a way to find a solution to the DE
@patrickjmt15 жыл бұрын
do not be sorry! i make mistakes quite regularly!!! actually, i appreciate it VERY much when people point out my mistakes - i do not want incorrect videos! as i say, feel free to post comments or questions : ) this is how we all learn! : )
@jonasnghifewa5541 Жыл бұрын
when n=3 we are getting C0/4! is this not supposed to be C0/(n+1)!
@HattManDoo12 жыл бұрын
Excellent review! Thank you so much!
@math-tutor2 жыл бұрын
wow. that video was on 2009 :)
@roblecrystaljade4 ай бұрын
Sir, what book do you use as reference??
@patrickjmt13 жыл бұрын
@MizuPsi i only know how to do simple examples
@PTNLemay4 жыл бұрын
If Co acts like an initial condition, how would we have solved it if y(0)=0? In that case the sum would have had a zero multiplying the rest of it. Which feels like it would stopped everything in it's tracks.
@thephlebotomist14 жыл бұрын
could we see some of important ODEs that need this approach like a bessel or airy function?
@liquidstl14 жыл бұрын
Hey could you do a more complecated example of this? thanks