Introduction to Initial Value Problems (Differential Equations 4)

[@ProfessorLeonard]

TOTALLY MADE A MISTAKE ON EXAMPLE 1..... Sorry guys, C=3. Accidentally divided for some reason, :)

[@david-yt4oo]

scared me there for a second man

[@stewartmoore5158]

:D You had me racking my brains on that one. Thanks for the clarification!

[@jneumanium]

He’s human after all lol

[@ProfessorLeonard]

Totally! I make LOTS of mistakes.... just ask my wife... hahaha

[@egoiisticprince7977]

Professor Leonard hahha... You Are So Good Your Wife Should Be Proud Of You

[@Handleoriginal12]

I have so much faith in this man that when he said C=1/3, I thought I was wrong.

[@zorinx6590]

😂

[@DucNguyen-tf3nj]

Me too! I just spent an hour trying to work out what I did wrong. I thought, “How did I get C=3? I did something wrong!” Until I looked at the comments 😂

[@ahmedlutfi4894]

math beats faith

[@Mbaaqail]

you should make a course on how to become a professor like professor leonard for our professors

[@max-pn8tt]

pls

[@mhtyphoon7524]

yes, please

[@loveconomics]

When I saw that he wrote C = 1/3, I questioned 27 years of learning math

[@torment6425]

@@saiketbd3592 why?

[@MuhammadIsmail-un3qd]

he is a legend...don't judge him on a single minor mistake...it happens to all...

[@enzoqueijao]

@@MuhammadIsmail-un3qd He's not judging Leonard for it, it's just a joke. I also thought for a second that I was dumb when I saw him write 1/3 lmao

[@MuhammadIsmail-un3qd]

@@enzoqueijao 😃👍🏻

[@Padthai_Shrimp]

Oh thank god it was an error. I was questioning my self as well.

[@ba924]

only youtube channel that I don't skip the ads because you deserve that youtube money sir

[@con_el_maestro3544]

simp energy

[@omoragan]

I whitelisted the channel but I hate the ads so much because they're about getting a tutor or using a website with tutorials. I already have Professor Leonard!!

[@lilchronics]

God bless you... you don't know how much help you are to some of us Africans without talented teachers

[@marcodeli9]

it is awesome being taught by someone who can fluently speak English, love you bro

[@imadetheuniverse4fun]

You have a way of pre-empting and heading off points of misunderstanding before they happen. Makes the learning process so smooth. I love your teaching style!

[@johncaruthers315]

@4:00 shouldn't C be equal to 3? When you enter 1/3, still is a good solution for the differential equation. 3 works as well i think. Feel free to double check.

[@TheTacticalDood]

"C = 1/3" is indeed a solution for the differential equation but it is not the particular solution that satisfies the initial condition.

[@ProfessorLeonard]

Yep, made a mistake, C=3. Sorry, was talking and not thinking ;)

[@Mordenperson]

Yea I Was doing the example and got C = 3 and kept going back over the video to see if I messed up but it became apparent I Was right. Ty for the comment Prof you can edit videos now maybe add a fix in?

[@abaundwal]

It is indeed a solution. In fact, any value of c works, that's why it's called an *arbitrary* constant. However, we want that particular value of c that makes y(x) go through (0, 3) and that's c = 3.

[@jc78607]

Your videos are incredible and have been an "integral" part of my success in school so far.

[@stvhwrd]

You speaking to the camera is sooo much better than us watching you speaking to the class. Thanks for doing this!

[@470bubbles]

Taking differential equations online for my upcoming semester and you will be my bread and butter to succeeding in this class.

[@toddsecor288]

I have watched lecture videos from various different universities like MIT and Stanford and I have to say your videos are much better. You are a great professor. Out of all my math professors from algebra up to calc 3 and linear algebra I have only had 1 professor that was in your league. Unfortunately he moved colleges after I took him for calc 2. I will be taking Diff EQ in the fall of this year, but first I am watching all of your videos. Definitely going to get an A :) Thanks for your help.

[@ThePerfect1077]

When you said videos won't be released often I was expecting ~2 weeks per video, so ~3 days is such a treat! TY!!!

[@tonya7517]

Professor Leonard you are a talented teacher, and may I say a god of maths. You know how to give us the informations and stress on the important stuff we need to know so that we can solve any problem we get with 0 difficulties. Your way of teaching is never boring I could watch all of your playlists in one time like I'm watching some kind of fun series. It's because of you that I passed Calc 1 and 2 and now hopefully Differential equations. No other teacher has ever done this they make maths look like a boring and hard subject. You have my respect. God bless you proff

[@nta699]

What, C = 1/3, I got C = 3.: Where did I go wrong with such a simple problem? Then, ahh, I was not alone. Thanks for all the comments that proved I had not forgotten all my math. I took this course over 40 years ago ;-). You are still the best, Professor Leonard.👍

[@abaundwal]

I love how you intentionally make mistakes to help us see what errors we are prone to making. Great video. :)

[@jh2519]

WHAT????? I had no idea Professor Leonard did a diff. eq. class! Perfect timing! I just started a couple days ago!!! WOOOOOO!!

[@aliberbey9359]

Shout out to the G.O.A.T. Prof. L , the homie for life. Your style of teaching is impeccable like Mike Tyson said. Thank You

[@SpencerRemy]

This series is the best explanation of Diff EQ. You sir, are a fantastic teacher. Many thanks!

[@main1608]

21:00. Even with the initial condition y(0) = 1. There will still be a family of solutions because C = pi/4 + k * pi where k is an integer. It might be nice to add 0 < C < 1 to the question. That ensures C = pi/4 is the only correct answer.

[@mgancarzjr]

Hehe. That first answer would have earned only partial credit. Never forget that + k*π where k ∈ ℤ.

[@fitwithgonz]

Yo Professor Leonard much love 💗,thanks for putting time in these videos they are really helpful 🙏

[@salomeolusoji7551]

I have looking for the best video to watch for ODE. I stumbled on this and I am loving it.

[@megilemonjava8111]

Thank you!!! Thank you for everything, what you are doing for us! I wish my lecturers were like you!

[@mhtyphoon7524]

You are a very good professor. Honestly, My mind was blown up with Differential but then I found your this series, going through it and it is easy now.

[@SteamPunkLV]

oh darn! I was watching calc3 and I just now realized Leonard is doing videos on DEs. That's amazing, Leonard!

[@Shadowbrothe]

I missed you dearly during linear algebra, so glad to have you back for DiffEQ!

[@payrollpaul7528]

so grateful for this, you saved me in college and now in university!

[@chantitilley1712]

I hope you see this. I really wanted to tell you that you made this concept so simple!!! I am going to go through all your stuff!! I a taking a Masters course over ODE’s and I feel like they are speaking Greek! You helped me out so much!! Thank you!!!

[@rwharrington87]

28:18 Was expecting a "raise your hands if you feel alright with this" here.

[@marklarryorigenes8782]

My Hero in this pandemic online class times...

[@martinarthurfleming9747]

I love your math videos. You explain and demonstrate it so it makes so much sense.

[@alieucoker7853]

my fav lecturer on YT

[@jamilkhan-dx6vo]

that c = 1/3 questioned my whole existence i was thinking if you get c = 3 you have to write c = 1/3 that is how much i trust prof leonard

[@EdieRoxUrSox15]

I'm so happy you did a Diff Eq series! Best professor ever!

[@AirwithAri]

Professor Leonard is THE MAN

[@TruthofKashmir]

Oh man! I was jus waiting when professor will say "raise your hands if you feel okay with this 🙋🏼‍♂️"

[@michaelgray7717]

I totally raise my hand. I think it's almost gotten me in trouble, when I was watching his lecture in public (I think people thought I was doing a nazi salute or something :D )

[@TruthofKashmir]

@@michaelgray7717 oh really!!! Datz nice

[@fanimeproductionst.v.3735]

@@TruthofKashmir Das nice*

[@omarellbad9779]

Sad 😢

[@michaelgray7717]

@@marka.1770 For real. I'm not a nazi, though, in case anyone is wondering (and I'm not directing this at you, Mark). It's such a shame that anyone would need to clarify that.

[@prideolea]

Prof Leonard you’re bad ass 💪🏼

[@onemanenclave]

3:14 "And C what happens" Get it?

[@Samantha-rc7pn]

dude you are the best you saved my life again!!!!!!!!!!!!!!!!!!

[@laminjarju4466]

best teacher so far

[@engineeringfitness795]

1st. Oh and your a god. I'm glad your doing diff eq right now cause I will take it next semester.

[@juniorcyans2988]

I'm depending on your videos this semester to get a decent grade in the differential equations class! Thank you!

[@Michael-ho2hl]

You're doing a very good job sir! You're going to get more blessings and money I tell you for you and all your posterity....God bless!

[@KateHuang-v2w]

In the 5th example (21:12), can C also be 5pi/4 or is there any sort of domain restriction?

[@mathprof7776]

I am a Math Teacher myself but Hats off Professor Leonard.

[@icee562]

God, I've always loved his formatting.

[@FingerThatO]

this is what ive been waiting for years. FFFFFFFFFFFFFFFFFFFFFFFFFFFF YES!

[@jabronimargaretti7315]

Informative playlist. Thank you! just started to revise DEs to get a master's

[@muhammadfathurrahman3726]

Thank you professor. I like the way you teach. The wordings and etc. It might be normal in some states of USA but for me It felt like I'm learning math in the gym 😂

[@thevegg3275]

Thanks for the great videos! Much faster getting through the material sans classroom. At minute 7:32 you cancelled out a -Ce^-x with another -Ce^-x. In order for them to cancel one of them has to be +Ce^-x. You only needed to cancel the +x with the -x. Thanks!

[@Emot10ns]

The reason they cancel out is because they're on different sides of the equation. You added Ce^-x to the other side so you ended up with 0

[@patch9908]

2:48 Another value for C would be 5pi/4, since the period of tangent is pi. Also because tangent is positive in both the first and third quadrant. This means that what you said is not fully correct, but only partially. But please, feel free to correct me if I’m wrong. Nevertheless, I really enjoy your videos and I’m currently watching your entire series for differential equations to learn how to solve them. Thanks for the help.

[@estebannavarrorojas3801]

What a marvelous class!!

[@PartScavenger]

I literally just sneaked out of bed to watch this.

[@haseebali47]

I woke up and just saw the notification

[@taekwondotime]

You sneaked or snuck out of bed? ;)

[@tedchirvasiu]

Sneackationed

[@PartScavenger]

Though "snuck" has become more common, "sneaked" is the proper verb; as it is the past tense of "sneak." "Snuck" is a vulgarity that will be the end of the English language according to my English professor. Haha!

[@PartScavenger]

@@Peter_1986 Nobody. That's why its funny.

[@yamikanibetha]

You are a very wonderful teacher 😢

[@mortalvamp4782]

Just a thank you on saving my exam that is literally tomorrow and I am in deep deep shit. You are a beckon of hope on getting at least a C (maximum a C?)

[@xzantxzant7710]

Nov 2022...what!...ALSO scratching my head!...your forgiven Prof.

[@nostoon4332]

I'm using these videos to learn differential equations before I take the course next fall.

[@anakinkylo.thepomenerianan9084]

Great lectures you putting engineers through university

[@gokayaygun812]

You are the best teacher I have seen. I feel better now when I see you are teaching Differential Equations. I passed from Calculus 3 because of your help and thanks a lot for that. Can you please also add the subtopics name (as written on the book) in the information part such as "separable equation, exact equation or numerical method" ?

[@joanrivera4897]

Thanks so much! Your videos give me hope for the future of education.

[@BrukTadesse]

I like to say talented teacher & you are uniqe from all maths teacher

[@lsjmartin6220]

ahhh ive been able to understand everything so far, hopefully it stays like this🙏

[@gabrieldayot4921]

Hoping that you’ll make videos about Laplace transform

[@mattmccuen3619]

As always, masterfully done. You rock

[@GG-jn9fx]

Thank you so much for this. Currently taking diffy q online and my instructor doesn't give any type of lecture notes/videos. Luckily I have your videos! haha

[@ericjuli6576]

Any particular reason in Ex 2. That you 5pi/4 won’t work for “C”??

[@TrainPlaneBoat]

Professor, at 21:30, Can we also use 5pi/4? since when you divide the sin&cos component of the unit circle you'll get 1 too

[@tonytom8432]

I think that works too

[@domenicolacanale7765]

Hi Professor Leonard, here I am watching this for calculus 2. Your videos are amazing and very straightforward. Would you consider to make videos about Introduction to Linear algebra? :) Thank you! Keep up the good work!

[@afsanamariya373]

Omg thank you so much for doing this! I'm currently taking math 209 so it's really helpful

[@ezatullahshinwari9316]

Thank you Prof. Leonard from you nice lessons it is really useful

[@FabulusIdiomas]

Really the solution that pass through x=0 when y=3 is 1/0.33333... e^2x not 1/3 e^2x. Which means that the constant is already 1/0.3333... = 3 not 1/3. The mistake in your calculations is done when you assume that in 3 = C.1 you can pass 3 below 1, when really what the equality is telling you is that you already hace C = 3

[@rebeccawelch3800]

Is it necessary to watch these in order? i understand that the first few are like a good foundation, but in my college class they are covering some of your later topics currently (which is the beginning of the semester).

[@toormalueth513]

So helpful to us the students of mathematics but seeing c=1/3 made me think that I am following a fine art prof but thanks that you realized the mistake.

[@luiz_ed76]

Now I understand why you're using a t-shirt of Superman, because you're a superprof!

[@meredithgriffith4278]

20:56 Would it be wrong to put 5pi/4 instead of pi/4 as your value for C? are we only looking in the first quadrant?

[@braytonsalinas1490]

You deserve my tuition more than my college professor does

[@marisolreveles2575]

4am during quarantine and Im here trying to spend my time wisely

[@mohamedramadanmohamed3744]

Really helpful, thanks Professor Leonard.

[@muhammadziaulhaq1454]

Thank u sir for these awesome lectures.

[@hristokalchev316]

Hi, thanks for everything! But, I gotta a question, at @25:00 why is negative one (-1), so cos(90) is 1? Would somebody explain that to me?

[@PedroOliveira-ez2ni]

same here, didn´t understand

[@amaizenblue44]

Thanks for helping me get an A in Calc 3, sir. On to DiffEQ!

[@norantarek7097]

Thank you so much .. I’m looking forward for the next videos ❤️😍.. can’t wait !

[@semajo.9514]

This series is great because I don't feel the shame of sitting in a high school math class as an undergrad like some of the in-class videos lmao

[@iknowthatdubin4877]

Great lecture, phenomenal!

[@maaan8494]

Quality content, I understood it straight away, thanks

[@jimstanley_49]

It's important to check that the general solution _is_ a solution because on the test, showing it's a solution will be worth a chunk of the points, or your professor may slip in a non-solution to trip you up. More pragmatically, the whole point of the course, in the end, is to be able to find these solutions yourself. This is Differential Equations, not Advanced Derivative Exercises. Proposing a solution is only going to be a fraction of the credit if you don't show it's the correct solution. It's a bit like derivatives and integrals were the arithmetic, and now Diff Eq is the algebra that lets us solve for unknowns.

[@floge1]

Why is it that at 21:31 , c = pi/4. Shouldn't it be c = n * pi + pi/4?

[@Phac197]

thanks f this course. made new videos on other topics

[@əliabdulkərimova]

God be pleased with you,inşAllah,Amen🤲

[@atiya5455]

May you live a happy life...

[@Ubayd-qp6tq]

What about number 1 at 20:04 sir? And why did we cancel e^rx at the end?

[@edisondoko9113]

Love this guy

[@caroe.3237]

Thank you so much for these! You're the best!

[@cookiesksu]

thank you, professor

[@josuegutierrez3906]

I can't understand the derivation of the 3rd problem at min 10:21, can someone tell me why the inside derivative of ln (x+c) is not 1+c??

[@madisoncombs1492]

@ 15:18 you said the derivative of C was zero, but in the example before that, y(x) = ln(x+c), you said that the derivative of C was just C. Now I am very confused.

[@TrainPlaneBoat]

Thank you professor ; Happy New Year !

[@fanimeproductionst.v.3735]

How did he get c=1/3? Shouldn't it be c=3?