I’m not even in Diff Eq anymore, just stopping by to say hi lol. Sending good vibes from Florida!
@kingarth0r4 жыл бұрын
bro this is A MILLION ZILLION TRILLION GAZILLION TIMES LESS CONFUSING THAN MY BOOK THANK YOU!!!!
@mikdamronoue31762 жыл бұрын
Totally
@pedrolotti452 жыл бұрын
I agree, but you could write this as a constant lol
@newmanhiding23142 жыл бұрын
Wow that’s a lot.
@itsninjagecko95864 жыл бұрын
I am an electrical engineering major and I can legitimately say you saved my life and kept me from having to repeat my Calc 4 class. Thank you so much for the explanations!
@abdallababikir91542 жыл бұрын
y'all call it calc 4, differential equations
@Syndicalism2 жыл бұрын
@@abdallababikir9154 Yeah that's pretty weird. I've heard some schools mix linear algebra with ODE and call it Calc 4. Calc 4 at my school is just Vector Analysis.
@Immadeus Жыл бұрын
im sorry Calc 4?
@warwick802 Жыл бұрын
Didn't know Isaac Newton made a 4th sequal
@Immadeus Жыл бұрын
@@warwick802 Calculus 4: Revenge of the Limit
@jumex_mango3 жыл бұрын
So I watched this video and the other homogeneous equation video yesterday night and this morning and was able to figure out 3 of my 4 exam problems (open notes). I want to thank you Professor Leonard for your videos because I would definitely have not been able to do my exam without your in depth explanations and tips 🙌🏽❤️
@cadencemaynard24492 жыл бұрын
bruh I would kill for an open note DE exam
@abdulhusseinalsultani9222 Жыл бұрын
Please see my Chanel (Abdulhussein Alsultani) to see the differences between my method in solving th e examples) Thank you very much.
@questionetics3 жыл бұрын
I'm taking Calc3 and Diff Eq at the same time currently, and if it weren't for your videos, I know I'd be failing this year, because my professors are basically reading the textbook to us. I just wish I knew your channel existed when I took Calc1 and 2, I would have gotten better grades. I'm sharing your channel with everyone I know.
@jeandreswanepoel37274 жыл бұрын
Professor Leonard, you are the reason why I will pass my Calculus 3 class and my Differential Equations Class. Thank you very Much! I wish my Professors were as good as you at explaining the work, you make math fun! I Wish I could have been in your classes. Kind regards from South Africa.
@maybe93575 жыл бұрын
I just love you man Youre the best maths teacher, would be a pleasure studying from you
@jarvisty36404 жыл бұрын
This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.
@rudnam2 жыл бұрын
I'm so so thankful for this really. My prof introduced diff eqs, its properties, separation of variables, linear DEs and integrating factors, and bernoulli's equation all within a span of 40 minutes and i could barely understand anything. You're a lifesaver
@nabilamehreen60545 жыл бұрын
might as well send you my degree when i graduate since you're the only reason ill pass most of my courses lmao
@Addictive_Gamers4 ай бұрын
🥰
@LOG20073 жыл бұрын
Played all your videos at the speed of 1.5 and really enjoyed your marvel. I absorbed everything you imparted like a sponge Professor Leonard. You have helped me get a straight A in Math courses. Keep up your excellent work, Professor!
@zanti41324 жыл бұрын
For this presentation he's wearing a long-sleeved shirt without the sleeves rolled up. Good idea - this is serious subject matter, and we students can't be distracted by those biceps.
@TalkswithJinesh3 жыл бұрын
Thank you professor for the video. Looks like there is a typo at 24:05, Ce^(-2x) - 1, but you wrote + 1
@moussapascalkone70733 ай бұрын
He rectifies it later at 24:54
@lindseytreweek87713 жыл бұрын
Today I did the second example by myself when a few days I had no clue what any of this was including a foggy idea on u-sub. It's crazy how many leaps in knowledge I'm experiencing from just following these videos. Thank you thank you thank you. Can never be overstated how much your help guides people like me who thought they were hopeless. You're the best!
@mpmndza2 жыл бұрын
Just a thought for the first problem at (6:24). If v = y^(-2), then dv/dx = -2y^(-3)dy/dx. If you divide the whole equation by y^3 you will be able to substitute in (-1/2)(dv/dx) directly. From there you can put it in linear form and solve. Saves you from all of the fraction exponents. Hard to explain in text but you essentially do two substitutions that gets you to dv/dx +2v= -2 in less steps. That's actually the brilliant thing about using substitution methods.
@parsingh5595 жыл бұрын
Fan for life. Leonard is the GOAT
@studywithankitadas5 жыл бұрын
I scored pretty good marks in maths in my initial semesters because of him... when he had stopped making vedios i had no choice so left maths and took another subject as minor.. my syllabus for this sem was differential equations even though I dont have the subject anymore I still watch his vedios 😁😁
@jarvisty36404 жыл бұрын
This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.
@daltoncarlson24024 жыл бұрын
Yes..., yes you make sense!!!! The hand-waving is yet explained again!!! Thank you, Sir!!! This beats the heck out of a zoom white board where all we get is a non-rigorous proof (because coming from Calc III Students know what that is....not at all), of Bernoulli's DE's, then thrown into examples where the product rule is bypassed when we learned it, LIKE, yesterday. As a student, I do not need five shorthand examples in chicken-scratch on a digital whiteboard over zoom, I need 1 or 2 examples that dive into the details as you do in your videos. You're the Clark Kent of Mathematics, yet be the one who has found the Kryptonite of college paid professors that lack a basic understanding of how to actually teach what they understand themselves!
@NeverendingAbyss5 жыл бұрын
Even after I'm done with the diff eq class this semester, I will anxiously wait for the rest of your lecture videos. Hands down the best explanation anyone has given on Bernoulli's.
@Siawash777 Жыл бұрын
I am a Mechanical Engineering major at UNF. I find your videos extremely helpful. I do tell everyone to watch your videos when I saw an opening
@jackpeters20383 жыл бұрын
I just spent 6 hours trying to work through this one math problem on homework not including the 4 hours spent the day prior. I looked at videos, notes, re-watched lectures, and asked peers, but I just was not getting anywhere. Finally, after all that stress and pulling my hair, I was able to follow the process, know what I was doing, and FINALLY get the correct answer. I cannot thank you enough. My grades are everything to me right now. Thank you.
@WilliamMansfield-w3h8 ай бұрын
Thank you Prof Leonard! This class has been a lifesaver. Hoping you come back soon and give us a Linear Algebra course! Taking it next quarter and don't know how I'll make it without your help.
@olivermogga69565 жыл бұрын
This is the most effective lecture on Bernoulli Differential Equations I have ever had.
@jakeb1103 жыл бұрын
this absolute unit of a man is going to be the reason I pass my differential equation class god bless you good sir
@loves2blumkin3 жыл бұрын
You have a gift for teaching and explaining complex topics. Thank you for providing these lectures for free to everyone
@Explorer9824 жыл бұрын
Long but useful and necessary. I tried learning this with quick 10 min videos but it wasn't cutting it. This is the kind of step by step explanation that works for complex topics.
@alsah-him15715 жыл бұрын
You are a seriously fantastic teacher! The detail and depth you provide with each new topic answers almost any question a student could possibly have. You also organize the information is such a way that it is easy to memorize the concept structure and problem solving structure.
@tanvirtscientist6084 жыл бұрын
i have never ever a teacher like you after my school! you just awesome! thank you a lot!
@integrateapproximate40008 ай бұрын
I love you. Thank you for being great. You make so happy every time because you explain everything so clearly. I hope you have a wonderful and fulfilling life that gives you everything you want Professor Leonard. You really do make a difference. Thank you. ❤
@ILikeWeatherGuy5 жыл бұрын
"leveraging the derivative of the power rule to undo a power rule inside of a product rule to undo that to find your original equation"= this video.
@tommulvey47525 жыл бұрын
this is the only one on youtube that doesnt make you remember the general solution. thank you
@scorpionedge4 жыл бұрын
11:35 "that garbage" lmao i love this prof
@EpicMathTime5 жыл бұрын
Was told about your channel today by a math major at my school. You're my hero.
@basilhsxatzhkostas2 жыл бұрын
Just watched the whole thing and I finally understood Bernoulli!, thank you so much superman!
@crazyirishman1214 жыл бұрын
Your videos are amazing. Also the way you have placed the ads on you videos are also great.
@davidxguitar3 жыл бұрын
Very helpful. With much gratitude Professor Leonard! You rock 🚀🎸🎯🏆
@RealLoveDragon5 жыл бұрын
I need this man leading me into combat
@jarvisty36404 жыл бұрын
This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.
@Juan_Carl0s4 жыл бұрын
Amazing, you've taught me all Cal classes + some stuff we didn't cover in my Differential Equations class (like in this video). A little comment I have is that I feel that you could've maybe done the work for all n to show how it always simplifies to a linear ODE. Keep up the good work!
@jarvisty36404 жыл бұрын
This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.
@jc-td4cc5 жыл бұрын
This helped me immensely. Thank you so much, sir!!
@abdellatifbourhim87214 жыл бұрын
These computations can be simplified. Indeed, set v=y^{-2}, you get that dv/dx=-2y^{-3}dy/dx. Then divide both sides of the equation dy/dx - y =y^3 by y^3. You get y^{-3} dy/dx -y^{-2}=1. So, (-1/2)dv/dx-v=1 or dv/dx+2v=-2 or dv/dx=-2v-2. This is a simple separable equation dv/(-2v-2)=dx. Now integrate both sides: (-1/2)ln(|v+1|)=x+c. This implies that ln(|v+1|)=-2x+C. Finally, apply the exponential and solve for v to get v=-1+Ae^{-2x}.
@akashdeepsingh51505 жыл бұрын
Dear Sir!! you are the one of the best professor I have ever seen. if u are on social media like Instagram or facebook then please let us know that so that we will start follow you on other platforms too.
@canman50605 жыл бұрын
Bernoulli is a name appeared very often in Fluid Mechanics.
@kayleew8215 жыл бұрын
you are the best thing to happen to our universe
@The1RandomFool2 жыл бұрын
As an alternative way to derive the substitution, you can divide both sides of the equation by y^n. Then the indicated substitution becomes easier to see.
@agamsingh27195 жыл бұрын
god, I freaking love you
@jarvisty36404 жыл бұрын
This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.
@harrymonfort2834 Жыл бұрын
give this guy a raise
@anthonymason8652 Жыл бұрын
Leonard, you're the best.
@vl...64263 жыл бұрын
you made math look easy and cool for me, thank you for that.
@matthewwolcott5984 Жыл бұрын
2 hours recording this math video in his free time. Professor Leonard is a badass!
@seaque.5 жыл бұрын
these videos saved my life...
@justinnelson38493 жыл бұрын
if every math teacher watched professor leonard the world would be a much better place
@ayeshaali39903 жыл бұрын
im gonna remember him in my prayers may god bless you
@soledadagca3 жыл бұрын
i love you professor leonard greetings from ecuador!
@Danny-ql2it2 жыл бұрын
The first example was also a separable equation, -2 goes to the right side, you factor it out to get -2(1+v). Then just divide by 1+v and integrate
@shahzad12062 жыл бұрын
Thank you so much sir ,,could'nt be more easier than this,,thanks alot,,❤❤❤love from Pakistan
@celinewest12505 жыл бұрын
This video saved my life, thank you so much!!
@VndNvwYvvSvv3 жыл бұрын
It's good to practice the theory for linears, but like Bernoulli always gives a result, you can shortcut the linear to y = 1/rho • ∫ rho F(x) dx, or in this case v= and back-substitute. Just be careful to apply 1/rho (or 1/mu) to the entire integral including C.
@abdhq22994 ай бұрын
I just wanted to mention that at 54:33, where you get the Linear differential equation, it turns out you can also solve it by using seperable equations. You can bring 6xv to the right side and factor 6x out...
@saurabhkujur63312 жыл бұрын
Thank you professor Leonard
@prabuddikachathuranga80293 жыл бұрын
පට්ට...supiri..Thanks sir..respect ..
@sam-kx3ty4 жыл бұрын
you're unique and I feel you should one day be a professor at Carleton University or MIT .
@dinithisahanika78232 жыл бұрын
thank you very much sir. love from sri lanka ❤
@marcuswesley4394 Жыл бұрын
This guy is a math rock be star. Where was he when I took Cal 1,2,3, and Diif EQ?
@Peter_19862 жыл бұрын
This type of equation randomly showed up during the solution steps for one of the example problems in my Applied Mathematics course about perturbation theory, and I had forgotten about it.
@tasnimhuka Жыл бұрын
I was so lost in class but this video helped me alot thanks
@maxanstine11395 жыл бұрын
My friend recommended this channel to me. It is really helping me study for my first DiffEQ exam. I did notice a POSSIBLE ERROR at 24:20 bottom right-hand corner. V=Ce^(-2x) -1 does not = Ce^(-2x) +1 Great video. Please keep making videos! This is crazy helpful!
@ahmedrabia73093 жыл бұрын
Thank you pro.Leonard
@rainasajid66784 жыл бұрын
You are the best, Sir. Loads of respect from Pakistan!
@jarvisty36404 жыл бұрын
This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.
@rainasajid66784 жыл бұрын
@@jarvisty3640 subscribed :)
@jarvisty36404 жыл бұрын
@@rainasajid6678 I found that video lecture so nice. There are a lot in the channel and I think is is just new.
@theoendre64845 жыл бұрын
Thanks professor for this fantastic lecture.
@callmegiorgioorsmth50042 жыл бұрын
Thank you professor ! This helped me so much!
@nikolozperadze48872 жыл бұрын
MasterClass!!!
@johnkupa88854 жыл бұрын
prof Leonard LIVING legend himself
@nathaliadiego65183 жыл бұрын
you are a life saverrrrrr
@ezu8501 Жыл бұрын
love you prof leonard
@maxwellcunningham89082 жыл бұрын
Just learned homogenous and Bernoulli equations a couple hours before my exam today using your videos, and I felt like I actually knew what I was doing on the exam. Thanks for being a great teacher!!
@mikem92705 жыл бұрын
Got a diff eq final tomorrow but I'll be fine... probably... maybe...
@ProfessorLeonard5 жыл бұрын
Trust yourself. You'll be fine
@mikem92705 жыл бұрын
@@ProfessorLeonard Thank you, I will :)
@carson84175 жыл бұрын
@@ProfessorLeonard your videos + Slader.com have saved me and are allowing me to pursue a career that I never thought I would be able to because of the math requirements.
@aaron.glidden3 жыл бұрын
Two years late, but I also have a diff eq final tomorrow
@seabasschukwu69884 ай бұрын
@@aaron.glidden3yrs late but I don’t have diff eq final tmro
@joshua.wolfe13 жыл бұрын
Super helpful! Thanks so much for your detail!
@abasslinelow8 ай бұрын
This man is far more handsome than a math professor has any right to be. (Also, he's really, really good at teaching.)
@Mark-di6cz5 жыл бұрын
Thank you so much for the lectures. Do you think it would be easier to get the equation in standard form, then multiply through by the reciprocal of the y^n on the right side. Then substitute, that way you don't have to solve for y in the v=y term. Just take dv/dx and substitute on the left side dy/dx term.
@belissegiovanni10 күн бұрын
THANK YOU
@mrm.m59005 жыл бұрын
Thank you Prof,, you are the best,, thank you very much
@zaga325 жыл бұрын
Just a suggestion why not divide everything by y^n then just substitute your v=y^(1-n) and dv/dx = (1-n)y^(-n) * dy/DC. That way you avoid having to do the multiplication and simplifying at the end. Maybe that can help :).
@ivankaraivanov61522 жыл бұрын
Thanks for the video. However, I want to point out that at 8:47 you wrote y^2 = v^-1 => y = v^(-1/2). Correct me if I am wrong, but I think you should have written y = (+,-)v^(-1/2) instead. So I am not sure if you are allowed to make the following substitutions as you did.
@abdallababikir91542 жыл бұрын
the plus minus gets absorbed by C
@jamesgu17555 жыл бұрын
1st! Salute to Prof Leonard!
@barryhughes97645 жыл бұрын
I'll second that! The master at work...incomparable.
@abdur-raghmaanmatthews54085 жыл бұрын
awesome work on explaining this
@jarvisty36404 жыл бұрын
This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.
@angelicafoster44885 жыл бұрын
Hello is there a Differential Equations book that you would recommend?? Which one do you use when you teach?
@5caioc5 жыл бұрын
Awesome teacher!! Thanks for all the help!! =)
@SrJumbo5 жыл бұрын
Much love Professor!
@nagozerafrank1582 жыл бұрын
sir thanks but which method are you using after obtaining the integrating factor when you are about to reach the step of substituting back V
@ElifArslan-l9g3 жыл бұрын
thank you so much
@robertbrandywine5 жыл бұрын
The thing I can't "see" is why *minus* n? 1-n can be restated as +1-n or -n+1. If we just wanted a difference of 1 we could have used n+1 (or 1+n). Is it because when you differentiate a function of x^n you always get nx^n-1?
@mohammadnematullah22965 жыл бұрын
Umdah! Thanks alot Mr. Leonard
@deadchannelasdf5 жыл бұрын
Do you have a video for Euler's Method? Also thank you for all the help. Saved my buns in Calc 3
@domon78903 жыл бұрын
You are a freaking champ dude, I wish schools and textbooks taught like this. This was very clear and it helps a lot that you explain the logic behind the method.
@abdulmomun55925 жыл бұрын
He’s back.
@ProfessorLeonard5 жыл бұрын
Yep! I took a break for Thanksgiving and I'm going to take another for Christmas Break, but I will certainly be filming again in the Spring and until this project is complete. Enjoy!
@abdulmomun55925 жыл бұрын
Professor Leonard You are a living legend. Respect and Love, I have learned a lot from you Sir and still learning and will definitely donate in the near future cox I maybe getting a job :D.
@seabasschukwu69884 ай бұрын
@@abdulmomun5592did you ever donate
@fooliemon4 жыл бұрын
At about 43minutes, why do you leave the Cx^4, instead of absorbing the x^4 into the C?
@MrMishra8145 жыл бұрын
Learning calc through you for electromagnetics. Do you have any idea how many videos this series might have?
@Nhlplayingrn4 жыл бұрын
You're the GOAT!
@petrmasek45062 жыл бұрын
The first equation can be done by variable separation right?
@shashanksangireddy38782 жыл бұрын
if nobody got me, i know that Professor Leonard got me. Amen