Calculus 2 Lecture 8.1: Solving First Order Differential Equations By Separation of Variables

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Professor Leonard

Professor Leonard

Күн бұрын

Пікірлер: 236
@Boxesandchips
@Boxesandchips 8 жыл бұрын
These are without a doubt the best Calculus videos on the internet, paid or unpaid.
@lilbrownie3344
@lilbrownie3344 8 жыл бұрын
Paid with ads thru monetization, donations and college facility.
@noddlexxx9161
@noddlexxx9161 5 жыл бұрын
The organic chemistry tutor is better
@noddlexxx9161
@noddlexxx9161 4 жыл бұрын
Google Account I can’t believe u have an acc name google account 😂😂
@danialvalentin5845
@danialvalentin5845 4 жыл бұрын
Do you know if he does lessons on Arc Lengths, Area of a Surface of Revolution, and Hooke's Law?
@namrin9006
@namrin9006 3 жыл бұрын
@@noddlexxx9161 On the contrary, these lectures are more in-depth and comprehensive. I use organic chemistry for introductions to the topic or review, when it comes to the nitty gritty, this is the best.
@Wura_ola
@Wura_ola 8 ай бұрын
It's 2024 and your videos are still saving me. You are a lifesaver. Thank you!
@darthboganis1356
@darthboganis1356 4 жыл бұрын
What is a differential equation? 1:00 Example of a 1st ODE 3:00 Functions in terms of x and y 5:00 Example 8:00 More on the differential Equation 14:30 The initial condition 17:00 Example 20:00 The initial value at zero gives the constant C 23:00 Separable differential equation 26:00 What is Separable and what isn't? 30:00 Example 35:00 Example 40:00 Example 56:00 A separable equation. A product (i.e. multiplication) of x and y >> separate them 1:01:30 Writing the C constant Initial value problem 1:09:00 1:13:00 U-Sub won't work, because the squared term isn't in denominator. Can you split the fractions? 1:15:00 using different subscripts for constants like c1 and c2 is really just making your life easier. > It works because they're essentially still constant. There are no unknown variables involved. The initial value gives a specific solution because it allows us to find the constant C, and the general solution is just a family of curves anyways Natural Growth and Decay 1:18:30-1:44:00 Example 1:44:00 proportionality, solve for e^k Decay 2:02:00 Law of Cooling 2:18:00 > the differential equation 2:26:30 Solve the differential 2:30:00
@MansoorAuto2k
@MansoorAuto2k 3 жыл бұрын
Some heroes don’t wear capes, thank you sir
@crazeladd
@crazeladd 3 жыл бұрын
Yo, bless up ❤
@Analys1s
@Analys1s Жыл бұрын
Does he not do linear differential equations?
@jarinmirza
@jarinmirza Жыл бұрын
Believe it or not, this is still very useful in 2023! Thank you, sir.
@1818soccerislife
@1818soccerislife 7 жыл бұрын
you teach like you ACTUALLY CARE about the students' learning and that is amazing. Wish there were more profs like you
@alityamusic
@alityamusic 6 жыл бұрын
You sir... you are a prime example of what a teacher should be. Thank you from the deepest confines of my heart.
@ILikeWeatherGuy
@ILikeWeatherGuy 9 жыл бұрын
all your lectures are very intuitive. thank you. the difference between the way that you teach and the professors here are like night and day.
@robbiebeenham5980
@robbiebeenham5980 7 жыл бұрын
completely agree... here it actually looks like he cares if his students understand and learn... as you could see genuine disappointment that the student didn't do his homework, and it was such a small one at that
@poetadetusnoches
@poetadetusnoches 8 жыл бұрын
This guy is my nigga. . . you should get an award for best professor/ tutor on youtube. I'm not even in your class and you are still the best professor have ever had by far. I click on your ads when I see them.
@jensmalzer6344
@jensmalzer6344 2 жыл бұрын
please dont use the n word if you're latinx, that word is reserved for black POC only
@Sam-y8f
@Sam-y8f Ай бұрын
I was avoiding Prof Leonard's videos before because they're so long but wow, these are very high quality lectures. Highly recommended! Thanks Professor Leonard!!
@thetrueslav9958
@thetrueslav9958 6 жыл бұрын
you are the type of teacher that every student would want, you go over the ideas, you ask for a show of hands to see how your students understand the certain topic, you are just like my Maths teacher, SUPERB! and thanks to you my weakness in D.E has become a strength
@noralyounes214
@noralyounes214 8 жыл бұрын
Just bring Mr Leonard to the next avengers movie " the infinity war", and he will differentiate the evil to ZERO.
@ellifontanilla1520
@ellifontanilla1520 7 жыл бұрын
Nor Jones this comment is dope.
@ricardoo6824
@ricardoo6824 7 жыл бұрын
Elli Fontanilla lmfao he's gonna bring Thanos to zero, by proving his power is convergent through the nth term test 😂😂
@Mewluver101
@Mewluver101 6 жыл бұрын
Best comment by a landslide! 😂
@Shadowfax2409
@Shadowfax2409 6 жыл бұрын
Professor Leonard is the real MVP of calculus. He makes everything make so much sense.
@paerful
@paerful 10 жыл бұрын
You explain it and make It really easy, I can't bear to go to class but I would just pay in my bed and watch your videos and easily pass my course. Plus you gotta hand out some workout routines sir.
@wilsanxubuzani3322
@wilsanxubuzani3322 9 жыл бұрын
my favourate lecturer...u make it simpler than the person I'm paying directly
@Techytecherson
@Techytecherson 11 ай бұрын
I hope you see this comment. When fearing my calculus exams and not knowing where to start, your videos saved the day. Not only did I pass the classes, but I understood the "why" in math. Thank you and hope we see more videos soon. Best wishes to you and your family.
@grahbuckfan6
@grahbuckfan6 6 жыл бұрын
I just got done with a summer semester of calc 1 with the hardest professor at my school and got an A thanks to you. Needless to say i'm back for calc 2.
@johnholme783
@johnholme783 7 жыл бұрын
Brilliant lecturer! crystal clear and very thorough. I wish I had a lecturer like this when was studying maths at college.
@Gabagool22
@Gabagool22 6 жыл бұрын
The best professor we don't deserve.
@georgesadler7830
@georgesadler7830 Жыл бұрын
Professor Leonard, thank you for an exceptional video/lecture on Solving First Order Differential Equations by Separation of Variables, Population Growth and Decay, Half Life and Newton Law of Cooling. I am familiar with these topics from Introductory Differential Equations and Applied Mathematics. A solid understanding of Techniques of Integration is needed to solve problems in Ordinary Differential Equations. This is an error free video on KZbin.
@joeeoj27
@joeeoj27 7 жыл бұрын
A video in a calculus 2 series taught me more about diffEqs than a week in a diffEq class.
@mohammedsaeed7241
@mohammedsaeed7241 8 жыл бұрын
the best professor in the world
@PLP0321
@PLP0321 7 жыл бұрын
"You're the teacher. You tell me." I am sure you will make it far in your career with that attitude, young lady. Great lectures by the way, Professor Leonard.
@sushio4357
@sushio4357 Жыл бұрын
If you watched the lectures she is actually pretty smart and proactive when he ask questions, I am sure she just wanted to be funny but came out pretty offensive lol.
@peterkonata3394
@peterkonata3394 9 жыл бұрын
I enjoyed your teaching approach. Very easy to understand the concepts fully.
@uhrrtax
@uhrrtax 8 жыл бұрын
OMG you have just saved my life. Studying for and engi. degree and my proff is so hopeless it is unbelivable and the thing is if i dont get it i fail not only this but also another 15 engi. subjects as everything prety much is based on differential equations. And altho english is not my main and i never had any math not ralculus en english i have no problems any more. BIG BIG thank you. (now i feel sorry for my group as 90% are probably going to fail big time)
@GHOSTRIDER4EVER
@GHOSTRIDER4EVER 3 жыл бұрын
My mind is always blown by his explanations. Wow!
@ParthPatel403
@ParthPatel403 7 жыл бұрын
Great lectures! The way he doesn't skip trivial steps makes it possible of even an highschooler to learn calc 2
@patrickkwong4651
@patrickkwong4651 7 жыл бұрын
He does the one thing every math teacher fails to do. Explain EVERY step. Taking this course in the summer is a fucking pain.
@Keepcalmliveon5
@Keepcalmliveon5 Жыл бұрын
56:24 "you're the teacher you tell me" yikes! You even handle conflict smoothly and with grace!
@tylersteffensen9268
@tylersteffensen9268 Ай бұрын
That lady has been insufferable this whole calc 2 series, so annoying!
@nicholasfarrington6221
@nicholasfarrington6221 9 жыл бұрын
Thanks for doing these dude. I can't imagine where I'd be without these. My calc class has 40 people and it's impossible to learn.
@amiraitkulov9532
@amiraitkulov9532 3 жыл бұрын
Thanks Mr. Leonard for such great explanations
@Bee-uy2cn
@Bee-uy2cn 6 жыл бұрын
Thanks man. This has been so helpful. I go to my lectures and then come home and watch your lectures and it realy sticks in my brain. Your a little bit more thorough than my professor so this really helps.
@mastovlox
@mastovlox 7 жыл бұрын
Start of second lecture 26:13.
@josuaalbertsson2665
@josuaalbertsson2665 3 жыл бұрын
professor swole always has the best jokes and im here for it
@vaugnalmeida7513
@vaugnalmeida7513 7 жыл бұрын
One of the best tutorial videos i ever watch.
@nathandyson3462
@nathandyson3462 6 жыл бұрын
I'm probably the only one, but this is the only instance of Prof. Leonard's classes where I understand the procedures, but not the full underlying concept.
@gentlemandude1
@gentlemandude1 5 жыл бұрын
1:01:46 Students are showing some attitude. They don't know how good they have it. Most of us don't have Calculus profs who will repeat an explanation multiple times until everyone understands, let alone take notice of the fact that some students are struggling to grasp a concept.
@erinmusarra2898
@erinmusarra2898 9 жыл бұрын
This guys a beast. Great lectures.
@briscomakhubela8738
@briscomakhubela8738 6 жыл бұрын
Best in the world,keep up the good work
@Jewelworld360
@Jewelworld360 8 жыл бұрын
Are you going to fully cover differential equations in the future?
@rainbows_rblx2114
@rainbows_rblx2114 8 жыл бұрын
he'd kind of have to teach a class on it, which is probably out of his control
@shensley011
@shensley011 6 жыл бұрын
I realize this was 2 years ago but I'm sure others are wondering. He's going to start putting them out this fall (Sept 2018). if you go to his patreon channel you'll see that he will put them out every MWF starting in September. if you donate a little money, like I do only 10 bucks a month, it supports him in putting them out faster. but the good news is that they are COMING! ! :-) FINALLY. He also has a Facebook page now and I believe he will also be posting them on there. Happy math learning ya'll!
@ILikeWeatherGuy
@ILikeWeatherGuy 8 жыл бұрын
little helpful blurb: this is the REVERSE of implicit differentiation
@antoniolee7330
@antoniolee7330 6 жыл бұрын
You should cover all differential equations class. I made it to calculus I, II, and III by watching your videos. Thank you in advance.
@shensley011
@shensley011 6 жыл бұрын
he's going to start putting them out this fall. if you go to his patreon channel you'll see that he will put them out every MWF starting in September 2018. if you donate a little money, like I do only 10 bucks a month, it supports him in putting them out faster. but the good news is that they are COMING! ! :-) FinallY!
@grudingOyster
@grudingOyster 8 жыл бұрын
Why the hell students start packing before he is done? If i was his student, I would have waited until he left the class!
@360Tinker
@360Tinker 7 жыл бұрын
These kids have no idea how lucky they are to have an instructor like this.
@robbiebeenham5980
@robbiebeenham5980 7 жыл бұрын
so damn true... I'm literally so unhappy he doesn't teach the rest of this subject on the internet
@Kybeline
@Kybeline 7 жыл бұрын
lol. I've thought the same. A pity he has so little on complex numbers... complex analysis would be fine.
@Fleurlean4
@Fleurlean4 7 жыл бұрын
This is an impolite habit that occurs all over college campuses everywhere. There needs to be an etiquette component of your grade so that people don't do this annoying shit.
@trouserpython3857
@trouserpython3857 7 жыл бұрын
@luigisf. An 'etiquette component of your grade' ????? You have lost the plot champ.
@khushisuri5783
@khushisuri5783 6 жыл бұрын
wow i literally LOVE you for this vid
@eliassafstrom757
@eliassafstrom757 2 жыл бұрын
There is always this guy sneezing, at least one time in every lecture XD. Very nice videos, keep up the work!
@amukomaina6285
@amukomaina6285 7 жыл бұрын
All your videos are always the best.....(from Kenya)
@harmanbans
@harmanbans 6 жыл бұрын
Fantastic lecture, but when you dropping that workout vid?
@ShivamYadav-ys3bp
@ShivamYadav-ys3bp 2 жыл бұрын
Thank you professor 👨‍🏫 thanks 🌹🌹🌹🌹🙏🙏🙏🙏🙏🙏
@fabbyszn3127
@fabbyszn3127 7 ай бұрын
Crazy to think that the students taking this class back then are in their late 20s or turning 30 soon
@Peter_1986
@Peter_1986 4 жыл бұрын
2:47:00 "I am a hot guy." LMFAO, savage. xD
@nuzhatazim8194
@nuzhatazim8194 3 жыл бұрын
doin hot guy shit
@kevinz8875
@kevinz8875 3 жыл бұрын
i don't know why there are 20 dislikes. probably they are the shill from those paid videos (like the ads in the beginning of every video :)
@imamalam4971
@imamalam4971 7 жыл бұрын
Much love Prof Leonard.
@instaminox
@instaminox 8 жыл бұрын
I am actually taking ODE and watching this video from cal2 thanks
@sflanagan3139
@sflanagan3139 7 жыл бұрын
Around 1:20: we're given y = k X T, and then dy/dT = k X y. If y equals a constant (k) times time (T), shouldn't the derivative of y with respect to T be k, rather that k X y? After all, at 1:30:00 we find out that ln abs val y = k X T + C
@mdsajedulislam4951
@mdsajedulislam4951 7 жыл бұрын
Hey Flanagan, In the equation y=k*T; T is a function of t itself that is T=T(t). For example, T(t)=4t+1 something like that. Now if you take derivative on both sides then it will give you dy/dt = k * y. How? just think of that if you differentiate function T(t), you will get another function of t; denote y=dT/dt=y(T). In a nutshell, just take derivative on both sides with respect to t not "T", then you will get the idea.
@siyandapete1762
@siyandapete1762 2 жыл бұрын
best teacher ever
@rednax3788
@rednax3788 8 жыл бұрын
"I don't care if it's c1, c2, or c3po"
@FB-tr2kf
@FB-tr2kf 7 жыл бұрын
LOOL
@tomneijman4212
@tomneijman4212 9 жыл бұрын
Very well explained professor! Thank you for that. No judgement here, misspelling is human and your teaching is marvellous, but you're reaction after misspelling separable a few times is very funny: just abbreviate it into "sep." (at 34:34)...
@ShivamYadav-ys3bp
@ShivamYadav-ys3bp 2 жыл бұрын
Pranam gurudev 🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
@taimooralibukhari
@taimooralibukhari 6 жыл бұрын
I thought after Calc 1 and Calc 2 no more from this page. But Diff Eq. Also here damn sir
@charlestodd2725
@charlestodd2725 6 жыл бұрын
I'm taking differential equations during summer 1 right now and I wish you had your DE course uploaded already, you're amazing!
@juanamorim8081
@juanamorim8081 3 жыл бұрын
thank you so much for the class teacher. really helped me
@abdullahmohammad5613
@abdullahmohammad5613 7 жыл бұрын
You did really good in explaining how to solve the questions but the concept ok ._.
@trusttrinity
@trusttrinity 7 жыл бұрын
you rock sir it is a thumbs up for you
@aketemamaebeneza3278
@aketemamaebeneza3278 6 жыл бұрын
Please, we need more videos on differential equations. Please ,save us.
@MrYawdennis
@MrYawdennis 10 жыл бұрын
you just wonderful pro!
@Operaatoors
@Operaatoors 9 жыл бұрын
Where do you teach? I want to change my University right now! :) Anyway, thanks for this explanations!
@punyamishra3628
@punyamishra3628 9 жыл бұрын
Sir.. can you please upload lectures on homogenous and linear forms of differential equations!
@jackalopetecumseh9127
@jackalopetecumseh9127 5 жыл бұрын
great videos
@7urbine
@7urbine 6 жыл бұрын
Thank you Mr. Swolo
@shep7484
@shep7484 8 жыл бұрын
Wonderful lecture but at around 30:00 I can't work out the relation dy/dx=g(x)• h(y) or g(x) dx + h(y) dy = 0. after the 'or', I keep getting dy/hy=g(x)dx which seems to lead to g(x)dx - dy/h(y) = 0. it's hard to see the jump from this to what you present. Probably something I am overlooking but either way, thanks for the lecture on differential equations. Jerry E Shepherd
@daswubs2383
@daswubs2383 7 жыл бұрын
Do you have more videos on chapter 8?
@gamersbaxe4052
@gamersbaxe4052 2 жыл бұрын
You the best
@abayoalainbertin8172
@abayoalainbertin8172 8 жыл бұрын
well explained
@robertosmiths5668
@robertosmiths5668 6 жыл бұрын
Very helpful, thank you
@jkp-qe4ty
@jkp-qe4ty 8 жыл бұрын
You blew my mind
@wagarimesfin4780
@wagarimesfin4780 6 жыл бұрын
thank you interesting video.I wish if you are my professor.
@lusekelolwesya4270
@lusekelolwesya4270 8 жыл бұрын
this is great
@walrusboy91
@walrusboy91 8 жыл бұрын
the guy who constantly yawns in all of these is starting to get to me. One day youtube will automatically mute yawns in lectures.
@Kybeline
@Kybeline 7 жыл бұрын
That doesn't mean he's not interested. He probaly needs a little more oxygen, that's all. If he'd got hickup or turret you wouldn't consider him unpolite, would you?
@trouserpython3857
@trouserpython3857 7 жыл бұрын
Wait until you get to the calc 3 playlist and meet kermit the frog.
@FB-tr2kf
@FB-tr2kf 7 жыл бұрын
Highfield, Calc 3 harder than 2?
@FB-tr2kf
@FB-tr2kf 7 жыл бұрын
Did you do all the vids or skipped a few? trying to see how long it will take me. Currently in the process of finishing off this vid...
@trouserpython3857
@trouserpython3857 7 жыл бұрын
@Perafin alkalistaar. At my university calc 3 was considerably harder and also included a lot more content in comparison to calc 2 but calc2 is a first year course and calc 3 is a second year course at my university so that might have something to do with it.
@umikohiromi6015
@umikohiromi6015 7 жыл бұрын
Absolutely brilliant lecture! I have a question. Why can't we just evaluate with initial condition y(0) = 1 and solve for C when we arrived at: y^2/2 - ln [y] = -e^x + C? We got rid of the derivative, so why must we go further? It looks like that would give a different value (e.g. C1 = 3/2) from the one when we go further and multiply both sides by 2 (e.g. C2 = 3). Can anyone please help me understand why is that so, and why is the latter the real solution and not the former, since in both cases y is in its implicit form? What am I doing wrong here?
@nickfeijoo7779
@nickfeijoo7779 6 жыл бұрын
THANK YOU PROF L
@amberdigiovanni
@amberdigiovanni 7 жыл бұрын
Please do a class on differential equations Professor Leonard!
@shensley011
@shensley011 6 жыл бұрын
he's going to start putting them out this fall. if you go to his patreon channel you'll see that he will put them out every MWF starting in September 2018. if you donate a little money, like I do only 10 bucks a month, it supports him in putting them out faster. but the good news is that they are COMING! ! :-)
@fisikalectures597
@fisikalectures597 7 жыл бұрын
He's probably raising America's educational system by like twice.
@joshuamendez425
@joshuamendez425 4 жыл бұрын
Yo the tortilla on the comal comment to figure out how much heat his fingers could withstand got me dead 💀
@williammendez5209
@williammendez5209 3 жыл бұрын
what's the time stamp lol
@szsolzel
@szsolzel 9 жыл бұрын
i think though that |y|=x means that y=x over the range interval of (0,∞), and y=-x over the range interval of (-∞,0), (and ofcourse (0,0) when x=0) so this would only be true, when C is [0,∞) ?
@lonewolf-yy2jh
@lonewolf-yy2jh 4 жыл бұрын
thaleeeeeeeeee vere levelll
@hafizsahib4351
@hafizsahib4351 6 жыл бұрын
Sir please upload the whole course of differential equation for undergraduates
@nostrasummit5785
@nostrasummit5785 6 жыл бұрын
appropriate that differential equations is lecture lucky #13
@netiamcintosh
@netiamcintosh 10 жыл бұрын
This is kind of helpful especially how i just moved to china and my chinese teacher don't care if the students understand. Now i have exams next week and might fail and all my life i failed at maths why is it forced on dumb people like me?!!!!
@grantedwards8546
@grantedwards8546 9 жыл бұрын
+Twin 2 Thats a great question. No one should have to take any calculus courses if they don't need/want to. If you don't find an appreciation for college level mathematics then switch your major to something that you find more practical.
@Peter_1986
@Peter_1986 4 жыл бұрын
Math is one of those subjects where you need to be very comfortable with the previous concepts in order to have an easier time with later concepts. You should definitely make sure that you are very comfortable with arithmetic and algebra, because those courses will _always_ be required for _everything_ that comes afterwards, and you will save yourself from a lot of trouble if you have truly nailed those courses.
@brianling9346
@brianling9346 3 жыл бұрын
love the puns!
@ShreyButle
@ShreyButle 6 жыл бұрын
5:54 I can just imagine Kylo Ren working on Differentials.... LMAO
@juliuskentbalagot4776
@juliuskentbalagot4776 7 жыл бұрын
Thank you
@AliMohammed-ly8lx
@AliMohammed-ly8lx 9 жыл бұрын
Mr, Leonard, i'm wondering if you have any videos about Multivariable calculus or deferential equations. i did not find any things that's belong to you, any way i wish if there 3 or 4 profs like you,
@cortez121219933
@cortez121219933 9 жыл бұрын
Ali Moe I don't think he ever will, if he does he will put every math professor in this country out of business. The gastapo will come and get him. lol
@benzola4808
@benzola4808 9 жыл бұрын
Mauricio Ruiz You're right.
@thomasrad6296
@thomasrad6296 9 жыл бұрын
Ali Moe he said he will plan on releasing them in 2016, its on his youtube disscussion.
@jessicaw766
@jessicaw766 9 жыл бұрын
+Ali Moe He's supposedly adding them around or after Spring 2016.
@elainfei5163
@elainfei5163 6 жыл бұрын
lowkey using this video for my differential equations class... hahahahahaha
@ShytFerBraynes
@ShytFerBraynes 8 жыл бұрын
I might transfer from UCD to merced just to take his math class.
@roberthorcher4937
@roberthorcher4937 8 жыл бұрын
This one had a lot of funny quotes in it. :)
@wolfpatrol318
@wolfpatrol318 8 жыл бұрын
+Robert Horcher 1:29:35 got me good
@abelgonzalez5870
@abelgonzalez5870 7 жыл бұрын
Robert Horcher iii
@ptyxs
@ptyxs Жыл бұрын
Toward 32:20 it is "separable" not "seperable" !!
@aceflywings
@aceflywings 7 жыл бұрын
Hi Professor leo, where can i find the remaining lectures on chapter 8 cus i can't see them. thanks
@lorenzomarquezortiz9239
@lorenzomarquezortiz9239 7 жыл бұрын
ohh god, i wish we had a math teacher as goood as you professor Leornard. at our school we have nothing but garbage, smug conceited garbage that hates to be there teaching garbage students on the tax payers dime. or so is their atitude
@trouserpython3857
@trouserpython3857 7 жыл бұрын
Hey P.Len what Myer Briggs personality type do you identify with?
@nilminideen5296
@nilminideen5296 7 жыл бұрын
Prof Leonard have you got second order differential equations ??
@philasandedlamini9469
@philasandedlamini9469 3 ай бұрын
getting my degree and buying bro that segway
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