If someday in future I achieve something in mathematics then I'll give all the credit to you for making my base strong enough to deal any kind of mathematical problem. Thank you so much Sir.
@husamobaid859 Жыл бұрын
I can't thank you enough. Your efforts are changing people's lives for the better.
@scorpionedge4 жыл бұрын
Best prof on the planet! Never stop this incredible talent of yours!
@GaryTugan5 жыл бұрын
Hi Prof Leonard! I found your vids a few months back. They've been extremely helpful in reminding me of specific problem types and their solutions since its been a LONG time since I got my engineering degree from VA Tech (1987). Yeah, so it's been awhile, and since I am now working with students in math and engineering and the like, I like to keep myself fresh in the know. So, thanks for these vids!! In watching this particular vid, I found an interesting point in the 2 different ways you went about solving the integral. At 22:35, you've just shown the u-sub method. And then you go into the other really cool way. In doing both methods, I noticed a difference in the two answers... U-sub gives "v+1- ln(v+1) = x + C", but the 2nd method you showed gets the same thing, but without the +1 part on the left hand side. I realize you can bring the 1 you get when using the u-sub method over to the other side to join the constant and it simply makes a new constant. But still I am most intrigued as to why the two different methods give seemingly "different answers". I imagine you noticed this as well?
@lanefrasier38905 жыл бұрын
I was wondering the same thing
@GaryTugan5 жыл бұрын
@Erik Hamidullin that was my evaluation also as to why it works out. But it still doesn't exactly explain why the two methods create different answers that are a constant (out of phase) so to speak.
@Frostasy5 жыл бұрын
I've learnt so much from you over the years. You're helping me so much in my EE program.
@lacelulaqueimplota39554 жыл бұрын
I swear to God I will pay you back the day I am able to. Unfortunately, right now I am a poor bastard. I cannot thank you enough Professor Leonard. Thanks for everything man. :')
@aaronguerrero5927 ай бұрын
So this is like "Reduction to Seperable"... AWESOME!
@geethapillai47014 жыл бұрын
Never knew it was possible to understand calculus to this extent, thank you so much Prof Leonard ^^
@darkcry26826 жыл бұрын
your making the world a better place sir, thanks for yours videos
@CHRISTIANZEGARRA20186 жыл бұрын
Question: How far are you in the course of differential equations? Up to this video is this considered half way through the course or beginning? I’m taking differential equations next semester. Couldn’t have passed calculus 1-3 without your videos.
@habeebijaz59076 жыл бұрын
It's only 20 %
@Peter_19865 жыл бұрын
@@habeebijaz5907 He said in a comment section for one of the earlier videos in this playlist that the Laplace Transforms "will be covered later" or something like that.
@AmitKumar-oq6qu6 жыл бұрын
I will meet you one day just to say you "THANK YOU SIR" .......
@supernovae99906 жыл бұрын
Will you upload solving homogeneous and non-homogeneous differential equations using power series technique? Also the Laplace transform ?
@alrayyaniQtr5 жыл бұрын
I've noticed you've been stressing yourself over this course. Dont burden yourself with a big promise such as a complete course on DE. The load will be stressful and you'll hate cause it will feel like a job. Just make a video on a topic when you feel like it. You'll find yourself actually enjoying it not stressing it.
@ProfessorLeonard5 жыл бұрын
Thank you for that :) I've taken a small step back and it's made a difference. Family is happier too!
@alrayyaniQtr5 жыл бұрын
@@ProfessorLeonard glad to hear it :)
@itsamarmot3 жыл бұрын
@@ProfessorLeonard Hey I noticed it's been a while since your last Diff Eq video but I want to reiterate what an impact you've made on so many people. I've always had a rough time with math (especially DiffEq), often getting frustrated and spinning my wheels. It's been an uphill battle with my engineering classes until now. I'm so grateful to have found your channel, you do an unmatched job of explaining these difficult concepts. You literally change people's mindset about math and that is very, very unique. None of my professors have even come close to explaining concepts this well. Please keep doing what you're doing. I'd be overjoyed if you complete the DiffEq playlist. The world seriously needs more educators like you.
@diyartok25182 жыл бұрын
@@itsamarmot so he hasn't completed yet ? I thought that is all
@thomasjefferson6225 Жыл бұрын
@@itsamarmot hes caused me to love a subject that I loathed before. DE's are fun now!!!
@mausplunder53136 ай бұрын
really nice video... i think u can drop the abs value on the last answer because sqrt(v)+1 can never be less than zero.
@theoendre64845 жыл бұрын
the substitution in the last example is better to be v^2= x+y+1, it will make the integral a lot easier, you just need to be careful when taking the derivative of v^2 after solving for y, also be careful at the last step when you want to replace the v's, because your sub was v^2 & not v. Hope this will help
@garethpienaar31194 жыл бұрын
24:47 When I use the u sub method for that integral, I end up with the whole integral equating to (v+1 - ln(v+1). And this is different to the (v-ln(v+1)), which is what Professor Leonard got. Which one of these answers is actually correct, because when I google it, I keep getting different answers.
@marklando3034 жыл бұрын
Was wondering this too. It's both correct, because when simplifying the C constant can absorb the 1. Hope this helps
@garethpienaar31194 жыл бұрын
@@marklando303 Oh okay, thank you very much, now I understand.
@MikoPellas4 жыл бұрын
ran into the same problem, worked out in the end anyway using the constant
@volkanulker64323 жыл бұрын
can we use trig sub for 33:00 ? We can rewrite equation as 1/ v ^(1/4)^2 + 1^2 and gets arctan
@r1e2y45 жыл бұрын
I'm sorry but I'm a bit confused about the sub technique @22:08 if you let u=v+1 and after you integrate you will get u-ln|u|=x+c1. Replacing u with v+1 I'm getting (v+1)-ln(v+1)=x+c1 and putting back v=(x+y), I end up getting (x+y)+1-ln(x+y+1)=x+c1 which is different from your answer doing the other technique. Someone help.
@bloodyadaku14 күн бұрын
When you take the derivative of your substitution, shouldn’t dv/dx technically be a partial derivative since it’s a function of two variables? Is it ever going to make a difference? Obviously in these examples it didn’t matter because the x’s and y’s were separate but if you had something like v=sin(xy), y=arcsin(v)/x, then when you take the derivative your dv/dx would then have to be a partial, no?
@BoyleFrancis6 жыл бұрын
Going to the fitness center worked out...thousands of more subscribers.
@borisstrunjas86125 жыл бұрын
Professor do you can divide videos and make playlist 1 and 2 for calculus 2 and 3? I need transcript because english my second language. I learning math and english langauge through your videos:-)) Thanks a lot!
@mesutbakhtyari6 жыл бұрын
Definitely you gonna helps me a lot next semester
@Peter_19865 жыл бұрын
So basically this is a more general version of the "v = y/x" scenario?
@ProfessorLeonard5 жыл бұрын
a very similar idea
@bonbonpony3 жыл бұрын
So, once we get such an implicit solution, how can we verify it now that it is indeed a solution to our original differential equation? :q I mean, if it's not solved for y, we can't calculate its derivatives and substitute them back into the ODE to check if they satisfy the equation :/ Is there any other way to verify this? (Maybe something involving implicit differentiation?)
@karimaessatty11686 жыл бұрын
thank you professor .. I
@Pete17116 жыл бұрын
Very helpful, thank you!
@santiagoblandon30223 жыл бұрын
You should have a course to teach teachers how to teach :D
@b0711395 жыл бұрын
I like it !!! Take it to the other level !!!!💪🏽💪🏽💪🏽💪🏽
@AlphaNiner-yk8kh5 жыл бұрын
That moment when the marker died tho lololol 23:05
@nicksardelli890 Жыл бұрын
if you do a u sub then you get v + 1 - ln|v + 1|. So there's an extra + 1 in the equation
@yashrajjaiswal60516 жыл бұрын
Eagerly waiting for it
@Festus20223 жыл бұрын
why did he get 2 different answers for the integral ofV/V+1: using u-sub (@ 22minutes)-->V+1- ln(V+1), vs. the alternate way --> V - ln(V+1). Presumably, the +1 by the u-sub method is incorporated into the C of the alternate method.
@haakonkk5 жыл бұрын
Can you make a video on the wave and heat equation?
@Peter_19864 жыл бұрын
You could always check out Chris Tisdell's channel. He has several videos on PDE equations - including things like D'Alembert's Equation and applications of the Fourier Transform etc - and he shows the same genuine passion for teaching as Professor Leonard, and is just as likeable.
@oorjitgupta8 ай бұрын
in the root(x+y+1) problem, taking the entire root as v, then squaring both sides, and THEN differentiating makes the problem a cakewalk
@wesseljooste4144 жыл бұрын
In the first example problem, when working with 1/v^2 + 4 , is it incorrect to divide the bottom by 4 to get 1/4 (v^2 /4 + 1) ?
@shaheer_ghazi4 жыл бұрын
That is not incorrect. Going along with that step, v^2/4 can be rewritten as (v/2)^2. So, the integral would be tan^-1(v/2) multiplied with a factor of 2 to cancel out the chain rule of the v/2. You would have gotten the same exact result as the Professor so your method is just correct as the Professor's.
@nikolozperadze48872 жыл бұрын
Awesome!
@aaronguerrero5927 ай бұрын
36:25 ... answer as to why there is an extra +1 in the first option (u sub) 22:08
@rohanpradhan56693 ай бұрын
Yeah, I have the same problem
@rohanpradhan56693 ай бұрын
v+1-ln absolute value of v+1
@cheesecake74342 жыл бұрын
23:22 Pardon my french but holy shit that's beautiful
@godblessamerica93136 жыл бұрын
Yo proffesio love ur video thank you for dummin it down for students. I have not seen u in a while
@kaizen94516 жыл бұрын
God bless America he’s not dummin it down, he’s explaining it well!
@godblessamerica93136 жыл бұрын
@@kaizen9451 we all have our opinion to you it appears his explaining it well. I say his dummin it down. Teachers cant even explain it as he does
@dk-xn9el5 жыл бұрын
Sir u a really a good teacher but what about differential eqns of second order you didnt talk about them
@ProfessorLeonard5 жыл бұрын
We will get them
@dk-xn9el5 жыл бұрын
Like when because we are soon to finish diff eqns this semestre
@dk-xn9el5 жыл бұрын
And l really like to watch yo videos ,the way u teach is too good
@DemiHalf Жыл бұрын
can't we just not seperate anything and take the integral of 1/(x+y+1)^(1/2) dy? no? ok.
@hafizsahib43516 жыл бұрын
Please upload lectures of complex variable and transforme
@duckymomo79355 жыл бұрын
the words obvious and trivial are hilarious in math.
@Peter_19865 жыл бұрын
I hate when a math book keeps saying "obviously" when everything is a confusing mess, lol.
@duckymomo79355 жыл бұрын
@@Peter_1986 apparently r^2cos(θ)sin(θ)
@Peter_19865 жыл бұрын
@Mi Les "Obvious" is a bold statement, but it becomes obvious when you realise that the term sin(θ)cos(θ) can never have a value greater than 0.5, since sin(θ)cos(θ) = 0.5sin(2θ)
@Peter_19865 жыл бұрын
+Mi Les I noticed that I didn't mention that the maximum value for the left-hand side could be either +0.5r^2 or -0.5r^2, depending on which angle you pick (+45° or -45°), but either way, both of them will give a value that's less than r^2.
@shubham19996 жыл бұрын
Sir, can you tell me how to use the method of multipliers to solve linear PDEs?
@taekwondotime6 жыл бұрын
If you do the u-substitution at 22:00 and you get u - ln|u| + c, how does it equal what you get using the other method? Using the first approach, u = v+1, so you get: u = v+1 ---> v = u - 1 du = dv = u - ln|u| + c = v+1 - ln |v+1| + c whereas the other method gives you: v - ln|v+1| + c What happens to the +1?
@taekwondotime6 жыл бұрын
EDIT: Never mind. He answered my question later in the same video! :)