Power Series Solution for a differential equation

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  • Опубліковано 15 лис 2024

КОМЕНТАРІ • 199

  • @csegura26
    @csegura26 5 років тому +113

    The first second of this video is really remarkable

  • @damian.gamlath
    @damian.gamlath 6 років тому +94

    definitely cool.
    I love your way of teaching because you address the little doubts along the way, and explain why we are doing something, and why it makes sense to even think about doing it in the first place..
    Something that alot of other youtubers don't do as well as you do. Thank-you :)

    • @blackpenredpen
      @blackpenredpen  6 років тому +9

      27kdon I am glad to hear that! Thank you.

    • @ameerzain6857
      @ameerzain6857 3 роки тому

      you all probably dont care at all but does someone know of a trick to log back into an Instagram account..?
      I was dumb forgot the password. I love any tricks you can give me!

    • @btiabdes
      @btiabdes Рік тому

      222222222222222222222222222222222222222222222222222222

  • @HolyHubcap
    @HolyHubcap 7 років тому +56

    Did anyone else notice his awesome 1 handed marker switching skills? Great video, very helpful !

  • @Arycke
    @Arycke 7 років тому +64

    I have a degree in mathematics and I would have to say that it is always good that two methods yield the same answer for a problem 👍the power series derivation I'm sure will help those seeking to understand how to find a power series solution to a differential equation :D plus power series are so important in analysis so this is a good introduction to that as well. Great video!

    • @JoQeZzZ
      @JoQeZzZ 7 років тому +1

      How have you never studied power series solutions to n-th order differential equations while getting your math degree?

    • @skateboarderlucc
      @skateboarderlucc 6 років тому +11

      you misread...he said the video would be a good starting point for beginners (obviously not referencing himself).

    • @abda7184
      @abda7184 6 років тому

      Thank you very much for this informative explanation 👌👌👌👍

  • @m.abdullah4518
    @m.abdullah4518 10 місяців тому +4

    Bro your teaching method is goooood. Got my semester final today and this cleared power series for me which I wasn't able to understand the whole dam semester

  • @Acoustic_Mutale
    @Acoustic_Mutale 6 місяців тому +65

    2024 Engineers where you at?

  • @randys2669
    @randys2669 10 місяців тому +1

    Recently got back into studying math, this is such a beautiful method for differential equations

  • @josemaringarcia3335
    @josemaringarcia3335 4 роки тому +2

    Thanks for making the re-definition of powers so easy to follow.

  • @SuperDreamliner787
    @SuperDreamliner787 7 років тому +9

    I´m currently attending a differential equations class and I have to solve one with the powers series method. Thank you for putting this up! Greetings from Germany! :)

  • @jammcrusader1981
    @jammcrusader1981 4 роки тому +8

    dude honestly you are the man - i bought a shirt cause of how much you helped me

  • @seanfraser3125
    @seanfraser3125 7 років тому +9

    I think its great that you can find the solution in two very different ways. Yes, obviously the power series analysis is much more involved, but it also shows you another way of finding the general solution to the ODE. One of my favorite things about math is that there is almost always more than one way to approach a problem and find the same solution.
    Of course, if the problem on an exam was to find the power series solution to the ODE, I would just find the exact solution and find its power series. Saves a few minutes :)

    • @blackpenredpen
      @blackpenredpen  7 років тому +5

      Yea, I like it whenever we can solve a problem with multiple ways. This could also be done with integrating factor as well.

  • @blackpenredpen
    @blackpenredpen  7 років тому +91

    Hi!

    • @indrada-rf2vu
      @indrada-rf2vu 7 років тому +1

      blackpenredpen hi :)

    • @batubulgur
      @batubulgur 7 років тому

      blackpenredpen I just gave my math101 final and it went pretty well. Just learned Taylor and stuff like that. And seeing its usage to solve diff eq's is pretty cool. Love maths, still a lot to learn.
      I have a question, don't you have to calculate the remainder and show that it approaches zero? I mean, it looks just like e^x that gives us confidence but still...?

    • @jordancastaneda7027
      @jordancastaneda7027 7 років тому

      "It's just like excel!" yes, yes it is indeed, thank you so much for helping me see it this way ! This is the easiest explanation I have came across so far.

    • @alienmoondudes8071
      @alienmoondudes8071 7 років тому

      I laughed when seeing that xD

    • @lalitverma5818
      @lalitverma5818 6 років тому

      Hi

  • @jennieferadombire926
    @jennieferadombire926 5 років тому +2

    Thanks so much. I really enjoy your way of teaching, it makes the math so easy

  • @Ballzdippedincheese
    @Ballzdippedincheese Рік тому

    You really helped me out i was stuck with this question for the past 5 or 6 minutes.....thank you

  • @Skull2121
    @Skull2121 7 років тому +1

    I needed this 4 days ago for my differenials final :,( i was searching all over youtube for a great video like yours! Keep it up!

  • @syaoransakura8839
    @syaoransakura8839 4 роки тому

    Wow, thank you. Your explanation save my TASK

  • @ryujinryuk
    @ryujinryuk 7 років тому +102

    19:40 when u activate the asian mode........

    • @marouanechokri3970
      @marouanechokri3970 5 років тому +1

      LOL

    • @tomatrix7525
      @tomatrix7525 3 роки тому

      But he is Taiwanese

    • @Hyperdrive
      @Hyperdrive 3 роки тому

      @@tomatrix7525 Yeah Taiwan isn’t in Asia

    • @tomatrix7525
      @tomatrix7525 3 роки тому +1

      @@Hyperdrive I just got a notifcation with ur reply. I have no recollection commenting that so Idk what I was thinking. Of course it is jn Asia

  • @shayanmoosavi9139
    @shayanmoosavi9139 5 років тому +3

    The power series solution is starting to click for me. Thank you very much :)
    P.S : 10:26 e cosine, e cosine, e cosine😁😁

  • @Collinator02
    @Collinator02 Рік тому +2

    this guy is single handedly teaching me diff eq. ive had 3 teachers so far. 1st dude i withdrew from, graded ridiculously hard. made up stuff that only he understood. talked in an accent and wouldn't help. 2nd and 3rd taught the class together split in the middle. 2nd guy was alright just ranted about random stories sometimes. 3rd guy. sheesh. tiny asian dude who whispers. cant understand a thing he says, and when he does talk about something really important he just starts talking 20 times faster WHILE STILL WHISPERING. love you blackpenredpen

  • @gaming_boga
    @gaming_boga 5 років тому

    Sir finally found a maths teacher in my life plz keep uploading videos thnks!!

  • @EngSeifHabashy
    @EngSeifHabashy 10 місяців тому

    Man I love how you save me!!❤❤
    I'm having my ODEs final exam after 2 days and I forgot all the methods and watching your videos right now

  • @hidude1130
    @hidude1130 7 років тому

    Dude you're by far the most talented bloke i've seen in youtube

  • @Prxwler
    @Prxwler 3 роки тому +3

    Woah, I haven't finished my calc 1 course and I find the first method overwhelming. Seems cool to be able to understand it AND replicate it, but knowing the second method exists made me feel a little relieved lol

  • @ahmadalrjoub7352
    @ahmadalrjoub7352 10 місяців тому

    thank you, Very clear and easy explanation

  • @rosemarybereket
    @rosemarybereket 6 місяців тому

    The you explain everything is so amazing ❤❤❤❤

  • @deligentchacha5420
    @deligentchacha5420 5 років тому +1

    this guy is a genius. Its an automatic distinction if you practice with Blackpenredpen

  • @KadeW10
    @KadeW10 6 років тому

    Thank you so much! I was never any good with series solutions and this video helped me significantly! Thank you

  • @Play-cn1ck
    @Play-cn1ck 7 років тому

    Thank you for your detail explanation.

  • @JacobKennedyowuor
    @JacobKennedyowuor 4 роки тому

    Wonderful. This has made sense to me for the first time. Thank you @blackpenredpen. I am writing an exam on Monday for Planetary Physics. Power series has been a nightmare. Not any more.

  • @davidhart1322
    @davidhart1322 5 місяців тому

    Test in 5 hours. Thanks man.

  • @BernhardMetz-u1f
    @BernhardMetz-u1f 6 місяців тому

    Man, this one I can do exactly in my head and not need a series solution 😮

  • @maryam_ahli
    @maryam_ahli 6 років тому

    THANK YOU SO MUCH!!! literally this saved my life!!

  • @sjoerdwiesmeijer7231
    @sjoerdwiesmeijer7231 4 роки тому

    That was really fun and insightful!

  • @hatsinze
    @hatsinze 8 місяців тому

    Thanks for the explanation

  • @ВладКузь-з7ч
    @ВладКузь-з7ч 7 років тому +22

    if only I saw this 3 weeks ago...

    • @Abdu_401
      @Abdu_401 5 років тому

      I can feel the sad energy behind this comment ...

  • @abdulrahmanalaqeel1720
    @abdulrahmanalaqeel1720 3 роки тому

    the old way is about 1 million times better than this journey, thanks for the video very helpful.

  • @emmanueladdo1430
    @emmanueladdo1430 7 років тому

    this video helped me in my math exam...thanks alot

  • @hichamitani6433
    @hichamitani6433 4 роки тому

    excellent explanation: keep it up prof

  • @usmanjaved2350
    @usmanjaved2350 4 роки тому

    Outstanding dear.... I cleared my every point... Love you dear ♥️♥️

  • @jayt675
    @jayt675 Рік тому

    Awesome teacher!

  • @aylin_spg
    @aylin_spg 6 років тому

    Thank you so much!!! You really help me
    I could understand it so well 👍

  • @wagsman9999
    @wagsman9999 6 років тому

    Love your videos. Very clear. Help me with my calculus tutoring. Thanks.

  • @FrankMarquez-cc2ye
    @FrankMarquez-cc2ye 6 місяців тому

    Thanks dude!!

  • @gregorio8827
    @gregorio8827 6 років тому +2

    Doing this integrating (using dy/dx notation) is extremly easy

  • @amin2468
    @amin2468 7 років тому +1

    Thanks alot, helpful as always.

  • @user-se1hj5vx3k
    @user-se1hj5vx3k 7 років тому

    Very insightful

  • @chritophergaafele8922
    @chritophergaafele8922 4 роки тому

    I never see you solve a math problem that fast

  • @willilow
    @willilow 3 роки тому

    eres un crack amigo,, gracias ,, saludos desde Chile

  • @meedumdarshana1591
    @meedumdarshana1591 4 місяці тому

    Thank You So Much

  • @thobilesikakane6113
    @thobilesikakane6113 2 роки тому

    You are the best at explaining the harder stuff. I wish you could do pdes, i guess its a bit late for me though.

  • @ostdog9385
    @ostdog9385 7 років тому +3

    Awesome I love it

  • @JoanneCheptoo
    @JoanneCheptoo 4 роки тому

    Bless your heart.

  • @gamingwolf3385
    @gamingwolf3385 Рік тому

    thank you a lot you are a great teacher , i love your style , and i start watching your videos instead of being present in my teacher boring classes hhh , i am kidding only , thank you a lot

  • @codedragon6237
    @codedragon6237 7 років тому

    Great videos! Keep it up!

  • @mokouf3
    @mokouf3 4 роки тому

    It is the Normal distribution curve!

  • @ennjoseph7311
    @ennjoseph7311 2 роки тому

    You are really remarkable ,, if only we could meet ,,you've been of so much help

  • @axlortega2881
    @axlortega2881 8 місяців тому +2

    why is a1 equal to zero at 6:33

  • @peerless3538
    @peerless3538 3 роки тому

    Awww you are so cute.....🥺.......thanks for the precious help......Almighty bless you.....🙌🏻

  • @masterenglish7838
    @masterenglish7838 6 років тому +2

    awsome
    i love your way of teaching...thank you

  • @amandabrandao3266
    @amandabrandao3266 3 роки тому

    this guy is a GOD

  • @MirryKay
    @MirryKay 2 роки тому

    Helpful

  • @araf-b
    @araf-b 2 роки тому

    Just awesome 🥰❤️

  • @pawankumarbehera2963
    @pawankumarbehera2963 10 місяців тому

    you rock

  • @Kurtlane
    @Kurtlane 7 років тому

    Your videos are great, including this one. Just one correction; here you say several times "to compromise it." I'm not sure what is the right word here, maybe "to counterbalance it" or "to restore the original meaning," or something else, but it's definitely not "to compromise."
    It's not depressing, it's excellent!

    • @blackpenredpen
      @blackpenredpen  7 років тому +1

      Kurtlane hi there! Thanks for the comment. My idea was like this: suppose u and I are making a deal, I give u two dollars, which means If i lose 2 then gain 2. Just like a trade. When I said this in my face to face class, my students understood it.

    • @oqardZ
      @oqardZ 7 років тому +1

      Expression you are looking for is "to compensate for it".

    • @blackpenredpen
      @blackpenredpen  7 років тому

      oqardZ that's for $ tho lol!

    • @blackpenredpen
      @blackpenredpen  7 років тому

      oqardZ but I might also use that next time

    • @davidgould9431
      @davidgould9431 7 років тому +3

      English can be a wretchedly difficult language. I am a 56 year old native speaker with only a rudimentary grasp of any second language, so I am totally in awe of people who manage to be 98% fluent in English, so please don't take this as a criticism of the videos: they are all perfectly understandable but, while we are talking about English rather than maths, I may be able to cast some light.
      The problem here is that compromise has gradually taken on two different meanings, depending on how it's used exactly (grammar alert: transitive versus intransitive usage):
      "to compromise *something* " means to make that something worse or to create a bad effect: if you have a container of water and you make a hole in it, you compromise its water retention (because it will leak). If you say that someone has a bad temper, or is lazy or something bad, you compromise their ability to get a job: you make it work less well. You might say you compromise *them* in that case.
      "to reach a compromise" or just "to compromise" (but no object: " we disagreed, but we compromised."), which is what you are doing with your trading example, is to make a deal that is part way between the two parties' starting positions: if I want to sell you my car for $1000 and you want to buy it for $500 we might compromise on $750. Or if I want to go to the cinema and my wife doesn't want to see the film, we might compromise by going out for a meal: we both get an evening out, but not our ideal evenings. As long as we both enjoyed it, we reached a good compromise.
      To wheel out some gratuitous grammar, when "to compromise" is transitive (that is, it takes an object: you compromise *something*), you are making that thing worse. When "to compromise" is intransitive (no object: you just compromise with each other, say), you are reaching an agreement.
      As oqardZ says, in this case a native speaker would use "to compensate": you have made a change in one place and, therefore, you need to make a change in another place to compensate for that first change.
      Sorry: this is far too long a comment. As I said initially, the videos are great and easy to understand: it's just that , in this case, what you said doesn't mean what you think it means.

  • @albajasadur2694
    @albajasadur2694 4 роки тому +1

    Sir, you showed in another video lecture that a Laplace transform is in fact a continuous analogue of Power series. By using this example, can you demonstrate and explain why it is more handy to solve this ODE by using Laplace transform ?

  • @zavionw.8052
    @zavionw.8052 5 років тому +2

    Me: *looks at thumbnail*
    Also me: "whitetextredtext"

  • @charliewilson3234
    @charliewilson3234 6 років тому

    Excellent stuff def not depressing.

  • @hassanalihusseini1717
    @hassanalihusseini1717 7 років тому

    A nice week to solve it with a power series, as power serieses are very important to make calculations easier.
    Of course it would be much faster to solve this problem by separation of variables:
    y' + 2xy = 0
    y/y' = -2x
    lny = -x^2 + c1
    y=ce^-x^2
    (with c := e^c1)
    I like your videos a lot, because they make me understand calculus deeper. Are you considering to make other videos on other subjects in mathematics, too?

  • @MegaPruddy
    @MegaPruddy 4 роки тому

    awesome 👏👏 👏

  • @zhylerliebesleid9771
    @zhylerliebesleid9771 4 роки тому

    This is so interesting

  • @jay1435
    @jay1435 5 місяців тому

    God bless you soldier

  • @luckybruno5827
    @luckybruno5827 4 роки тому

    Thank you so much, way better than my professor (:

  • @xrisku
    @xrisku 7 років тому

    I am watching this wondering why none of it looked quite familiar, until you did the old way. then a neural circuit instabtly lit up. :)

  • @raphaelseitz805
    @raphaelseitz805 7 років тому +2

    thanks a lot for your videos blackpenredpen :)
    the only point i did not get was why a1 has to be 0. couldn't it be anything?

    • @JerezMario
      @JerezMario 4 роки тому +1

      I also found it weird that we assumed a1 was 0

    • @souravchakraborty6766
      @souravchakraborty6766 Рік тому

      It's zero bc the right hand side is 0. That is why he set everything to zero. I hope this helps ;)

  • @pratishamishra4142
    @pratishamishra4142 6 років тому

    Thank u

  • @jackkalver4644
    @jackkalver4644 10 місяців тому

    Didn’t even take me a minute! y=Ce^-x^2=Σ((-1)^n C x^(2n)/n!

  • @dahazz
    @dahazz 7 років тому +1

    Hey! Can you do an IVP and finding the singular points?
    THANKS!

  • @charlesrothauser1328
    @charlesrothauser1328 4 роки тому +1

    I find the youtube commercials during this video a terrible distraction

  • @AdesanyaAyodejiCeg
    @AdesanyaAyodejiCeg 9 місяців тому

    really good video. but my exams are objective questions.

  • @inothernews
    @inothernews 7 років тому +1

    Great video! I have not done power series solutions in a long while so this is a good refresher! May I know what your academic background is?

  • @john-athancrow4169
    @john-athancrow4169 6 років тому

    I liked you finally said a .

  • @kgotlelloramatsetse2162
    @kgotlelloramatsetse2162 3 роки тому

    beyond cool!!!!!

  • @Juanksv09
    @Juanksv09 4 роки тому

    Jedi Marker Master

  • @FuhrerShattercore
    @FuhrerShattercore 7 років тому +1

    Will you be able to teach us the method of Frobenius? It just appeared in my Mid-term exam and I've concluded that my professor is a sadist... and that it will appear again the finals. Thanks for the video anyways. :D

  • @calebe16
    @calebe16 7 років тому

    Power series are interesting in some specific cases.
    I would like to know how to do with power series for non homogeneous differential equation.

  • @miguelbarbosa1583
    @miguelbarbosa1583 7 років тому

    that ending was crazy, Both are legal i guess!!

  • @yifengwang790
    @yifengwang790 5 років тому

    what a god

  • @digbycrankshaft7572
    @digbycrankshaft7572 3 роки тому

    Nice

  • @hlamzar
    @hlamzar 6 років тому

    you're awesome

  • @w.a.domski
    @w.a.domski 4 місяці тому

    watching this at 12am before my math test in 8am, and i haven't even studied power series yet (yes im an idiot), wish me luck

  • @sh6700
    @sh6700 2 роки тому

    That is so cool!

  • @cencenpolinar3085
    @cencenpolinar3085 2 роки тому

    for the second equation isn't n = -1 to make it x^n? thanks

  • @jarikosonen4079
    @jarikosonen4079 3 роки тому

    a1=0 & series-sum=0, so it's all 0 then.
    But if series-sum=-a1, will it be all 0 then also?
    a1=5 & series-sum=-5, how would it work?
    Maybe nothing that need be proven.

  • @ehtuanK
    @ehtuanK 7 років тому +1

    that was less than one minute, in fact it was exactly 42 seconds!

  • @N8TheGr8M8
    @N8TheGr8M8 4 роки тому

    Why do some people start the series at n=1 and some people start it at n=0 for the y' series?

  • @lorenzolevy4708
    @lorenzolevy4708 5 років тому

    Can you hypothetically use series to solve any ODE?

  • @kelvinadimas8851
    @kelvinadimas8851 Рік тому

    F A S C I N A T I N G

  • @drosos_strength_coaching
    @drosos_strength_coaching 3 роки тому

    Proper video title: why not to solve differential equations with power series even if your life depends on it

  • @jeanphillippes2196
    @jeanphillippes2196 4 роки тому +1

    Why take the bus if you've got a round-the-world ticket?

  • @SomeOne-gh3tw
    @SomeOne-gh3tw 5 років тому

    i LOVE U