Surface And Flux Integrals, Parametric Surf., Divergence/Stoke's Theorem: Calculus 3 Lecture 15.6_9

Surface And Flux Integrals, Parametric Surf., Divergence/Stoke's Theorem: Calculus 3 Lecture 15.6_9: How to Parameterize a Surface, How to perform Surface Integrals, How to do Surface Integrals of Vector Fields (Flux Integrals), The application of The Divergence Theorem, and the application of Stoke's Theorem.

[@ErickHrnndz7]

I could have taken the time to write you a personal email, but I ultimately came to the conclusion that it be best for the public to read this. Professor Leonard. You are the definition of a hero. I have yet to find another individual in higher education as passionate and dedicated as you. I hope you understand that all credit I received in my Calculus courses, is due to your hard work and selfless service. It is, in deed, sad that this is the end, nevertheless I foresee myself still referring to your videos in my future as an engineer. Be aware of how great your teaching is going to impact the world, as me along many of my colleagues in engineering constantly recommend your videos. The world needs individuals as yourself to create better paths in mathematics. Huge thanks from myself and all the Aggie engineering family.

[@ProfessorLeonard]

I truly, humbly, and gratefully appreciate your words... Thank you very much!

[@Folinic]

WHOOP! Glad to see other Aggie engineers enjoying Prof. Leonard's videos.

[@Garebare1]

Bro Aggie engineering here!!! A-A-A-A-A

[@Peter_1986]

Let me put it this way: I have a teacher at my university who is really great in every way - but professor Leonard is BETTER.

[@uncleroq]

straight up

[@vektyr]

18:15 Ex #1: ∫∫ (x+2y+z) dS when S: y+z=4 inside x^2+y^2=1 37:30 Parametric Surfaces 41:10 Ex #2: x=sqrt(y^2+z^2) 46:57 Ex #3: x^2+y^2=z^2 55:23 Surface Integrals 1:00:10 Ex #4: Find S.A. of x^2+y^2=z^2 1:19:18 Ex #5: ∫∫ (x-y)/sqrt(2z+1) dS when S: r(u,v)= 1:34:06 Flux 1:52:55 Ex #6: Find Flux of F across surface bound by z=1-x^2-y^2 and x^2+y^2=1 where flow is described by F= 2:08:59 Leonardism 2:09:52 Divergence Theorem 2:17:47 Ex #7: Find the flux through vector field, F= over the surface x^2+y^2+z^2=4 2:34:48 Ex #8: Flux of F= across surface x^2+y^2=4, z=0, and z=5 2:51:41 Stokes Theorem 3:06:08 Pregnant Leonard 3:08:30 Ex #9: Closed Surface ∫ F•dr, F(x,y,z)= when C: intersection of plane z=2-x and x^2+y^2=4

[@mazphamm]

Vektyr thanks so much

[@adhir.8348]

holy shit, thank you! professor, you should include this in the description!!

[@leonardo006]

you're amazing, thank you. right before finals lol

[@Jono.]

I had to skip right to Pregnant Leonard when I read this

[@chicapercebe]

A HERO

[@prim16]

*The transcription of his speech:* "It's the beginning of the end. The tears they shall flow, the comfort it shall come... the wonderful journey we've taken is now sadly coming to an end. I know you'll miss me, but you need to move on. The grass is not always greener, yet still, we must try to make the journey. Unless you all want to fail and come back here, and just take it again and again. You can do that, but we always try for forward progress. This is not a line integral on a conservative vector field that creates a complete # curve. We want work to be done. We want Green's Theorem to apply. Your education has come full-circle in a non-conservative way."

[@Ethan-gb3zh]

you forgot the "boom" *mic drop*

[@savannahenriquez3988]

I love that you posted his speech from the beginning because after the end of the video it all makes sense:D Prof. Leonard is a master in his craft.

[@aarrjunumrikar5345]

Oh god thank you.... I loved the first part but didn't get much! 😂😂I just saved it... D savage speech!!😂😂

[@ericsills6484]

3-1/2 hours and this is 2-1/2 of it :-D

[@kerry_jcs]

What the "flux" are you talking about? 😁

[@azwadrahman4796]

This isn't just a Professor. This is mozart, this is picasso, this is Calculus taught in the most beautiful way possible.

[@kesjerdna]

Yes, @Professor Leonard. You're the best math teacher I know...

[@MikoPellas]

Beautiful words right here^^^^^

[@boshooda1941]

alright buddy, why don't ya take er easy there. It's just explained really well in a way that makes sense. Prof. Leonard worked really hard on these lectures to make them make sense.

[@allknowledge7146]

Chill out lol

[@charmainemwamuka1732]

Wrong, this is Tchaikovsky.

[@miguel_______]

Before 2023 ends, I really wanted to take a time and write you some words of gratitude Professor Leonard. When I started taking Calculus in college I had a really bad time; I didn't understand, I had bad grades, and stressed up to the top. But it was not until you appeared like an angel that things started to get better. With your incredible skills to teach, your patience, and last but not least, your sense of humor, I finally started to master Calculus. My grades got up and ended passing Calculus 3 with an A, which is something I never thought to achieve. A subject that once was a nightmare for me, became a subject to which I developed affection and interest. On behalf of all students, I want to thank you for your job as a teacher and your voluntary decision to share it with the rest of the world. Although it is free, once I start working I am sure I'm going to be back and make the donation you deserve. With this being said, I'm afraid that my long journey of Calculus with Professor Leonard ends up here, being eternally grateful. See you Professor!

[@ouss991]

hi professor i just wanted to say you're the reason i started enjoying math again , and your lectures played a huge part in helping me get into medical school to fulfill my dream of becoming a doctor, and i thought you should know that what you're doing changed my life for ever after i've given up on my dream. so thanks alot and i hope you see this comment.

[@ProfessorLeonard]

That just made my day. Best of luck and you have my best wishes!!

[@Robot404_]

+ous991 Is that Calum von Moger in your profile picture?

[@ouss991]

no, it's just me hahaha but i no longer look like this

[@Robot404_]

ouss991 oh damn nice.

[@i.i]

same here thank you Professor

[@VectorSpace33]

Shout-out to everyone that has made it this far through the whole playlist. Good job!

[@_avenger9709]

I don't think I've ever seen a professor work so hard to ensure that his/her students actually understand what the hell they are doing as much as this man. So many professors will just give you the formulas and breeze past the concepts especially in many math and science courses. This is not to say that they don't know their stuff, but rather sometimes it seems like alot of professors don't do enough coverage of concepts. Professor Leonard's teaching is by far the best I have ever seen. Clear, concise, intuitive; his lectures have everything a top quality lecture needs to have. Thank you Professor Leonard for sharing these videos with the world. :)

[@ProfessorLeonard]

Thank you very much for taking the time to write this... made my Day!!!

[@_avenger9709]

You are very welcome sir! :)

[@Peter_1986]

_ avenger9709 A lot of professors don't actually care about the students, they just stand and half-heartedly cover a bunch of material and then they are like "okay, job done here, now I can go back to my research". It's extremely obvious almost immediately when a teacher has that attitude. They are those "serious", formal and apathetic types who just stand there and mumble almost to themselves throughout the entire lecture and never interact with the students. Basically the complete opposite of Professor Leonard in every way.

[@triparadox.c]

@@Peter_1986 I honestly think that professor shouldn't really teach if they want to do research. They have enough money from research, no? Please let those who have passion in teaching to actually "teach".

[@NaiThePiGuy]

This is the best mathematics teaching I've ever seen. Profs should watch this and take notes

[@NaiThePiGuy]

Like, I'm actually just watching for enjoyment - I'm not even in school anymore

[@SuperMapleaddict]

Same here! I love the way he teaches and interacts with the students. It honestly feels more like I am watching a TV series, than watching a lecture, while also retaining so much information that he has been teaching! It's wonderful.

[@Feynaro]

I'm waiting for videos like this to replace lectures; professors can exist to have office hours and answer questions like they do and they have more time for research. No need for thousands of professors to separately teach the same things that one person can do very well.

[@leninpaul3459]

well said Ian! my prof should learn his ways cause my prof's lectures suck and his exams are hard AF.

[@alexandermackenzie3456]

Yeah, like mine -- who got fired -- for not teaching.

[@shaner3333333333]

My calc professor went on a trip for the last week of class before finals without telling us. Thank you, Professor Leonard, for not going to Costa Rica before making this video.

[@triparadox.c]

LMAO XD

[@joeyGalileoHotto]

T E N U R E

[@tshepisomotsoko9536]

that's wild

[@aaryankumar2586]

Have my last calculus exam in 8 days. Just finished this, it has been a long journey, indeed. Thank You, Professor.

[@stevenjames5874]

Same boat! Good luck if you go onto Diff Eq m80

[@jcnotnot8120]

“That’s my job as a teacher, to make sure you get it” What a great outlook on running a class.

[@AirwithAri]

Professor Leonard deserves a Noble Peace Prize for keeping us all sane and for making calculus a beautiful thing.

[@Itsjustj82]

indeed!👍👍

[@PhonicRex376]

The beauty you are seeing is easy examples and him not covering things properly. But I agree, Calculus is beautiful if you do it right.

[@astrotaco_bps]

I GOT AN A IN CALCULUS 3 GOD BLESS YOUR HEART.

[@revl6151]

loser

[@ArcherGabs]

@@revl6151 You are the loser here I guess

[@huanglinwan7075]

@@ArcherGabs I agree with u

[@Jeremy_Fisher]

@@revl6151 Wow, I can tell who failed Calc 3 here. Better luck next time.

[@Peter_1986]

@@revl6151 I don't know about you, but I would call someone who aces a Calculus 3 course and thus unlocks a lot of job opportunities in the future a _winner._

[@MrStrakatus]

I've never failed or even came close to failing a math course until Calc3. Had 40% on my midterms and needed 60% on my finals to scrape by with a D. I binge watched all of the second part of Calc3 on your channel in 3 days and I got 93% on my finals! Thanks Prof Leonard, you've saved me having to repeat Calc3, it really means a lot to me.

[@bartsimpson4668]

Out of all the math teachers I have ever had, it is safe to say that Professor Leonard is the MAXIMUM (using Lagrange Multipliers of course). Every. Single. Topic that confused me was in some way addressed and explained beautifully. You explained everything in a PLANE and a SIMPLE manner. Thank you so much! I hope you make linear algebra videos in the near future. I’d be STOKED if you RESURFACED for those videos.

[@rushunnhfernandes]

Hey hey😂😂... Nice puns... I'm really waiting for that linear algebra course or even differential geometry

[@Andrew-qp7bv]

@3:06:27 that's crazy! That's an insane amount of dedication to helping people you probably will never even see. You've helped hundreds of thousand of people (if not millions) do better in calculus, me included. From the bottom of my heart Professor, thank you

[@abdulmohaimin9729]

Words can't possibly describe the level of how grateful and utterly thankful I am for this entire journey through calculus 3 that you, sir, have provided for free the the public, and have helped countless students like me see the beauty that lies within mathematics. I just can't thank you enough for every single lecture that you gave, it literally saved us. I wish that this message finds you in the best of your health and of your loved ones and I wish you read this one day. Thanks again sir for everything. God bless you.

[@quiquitohernandez7977]

Stokes Theorem 2:51:35

[@rocketman3459]

cheers

[@chrisjfox8715]

Doesnt that Stokes Theorem problem he did need another surface to keep the cylinder from going to + or - infinity? Otherwise it's not a closed surface, is it?

[@SI29222]

@@chrisjfox8715 No because a closed surface is only required for divergence theorem, not stokes, which requires only a closed curve.

[@seanmontague6479]

As this is the last video in the calculus sequence, I want to thank you for putting out such amazing content. I have found it to be an invaluable resource during the calc sequence and it has motivated me to continue delving into math and peeling back the layers. Thanks for making these publicly available!

[@ProfessorLeonard]

You're very welcome!! I'm very happy you found them so useful :)

[@user-nh3sr3fr4o]

Dear Professor Leonard, I hope this message finds you well. As I reflect on my journey from Calculus 1 through to the completion of Calculus 3, I feel compelled to express my profound gratitude for your exceptional guidance and mentorship. Your teaching has deepened my understanding of mathematics and significantly shaped my academic and personal growth. From the first day of Calculus 1 to the final class of Calculus 3, your passion for teaching and commitment to your student's success have been evident. Your ability to make complex concepts accessible and engaging has greatly enhanced my learning experience and instilled a deeper appreciation for the subject. As I move forward, I carry with me the knowledge gained and the invaluable life lessons imparted by you. I wish you nothing but the best in all your future endeavors and want you to know that you have my utmost respect and gratitude. Thank you once again for being such an influential figure in my life.

[@lugia8888]

Yeah right. If you actually need this material you will find out how much of this he doesn't go through correctly.

[@YourRoyalHenry]

ending this class feels like I have finished an actual college course from professor Leonard. also very sad to think that we have never met a teacher who is as dedicated, as amazingly interactive with the class. WORKS HARD TO PUT IN MATH PUNS xDD the journey of calc 1,2,3 with you has been entertaining, informative, and truly beautiful. THANK YOU PROFESSOR LEONARD!

[@divyanshumishra953]

Same here. I finished today..!!

[@Jewfit]

This man got me an A in calc 1, 2 & 3! Thank you Professor Leonard!

[@pablodavidlp9760]

When I started Calculus III I wasn't sure if I was going to pass my class because I failed my first exam. My situation was similar to the one that Noel Robles had. It took me hours to finish my homework and I was frustrated because I didn't understand the material. Nevertheless, I found your videos just in time because at the end I managed to get A in calculus III, something that seemed impossible when I first started (wish I had found these videos when I was taking calculus I, my life would have been a lot easier). Hence, I just wanted to thank you for posting these videos, you have no idea how helpful they were to me.

[@ProfessorLeonard]

You are very Welcome!!

[@molokomokubedi631]

I was in the same situation, I got mediocre marks for calc 1 and calc 2 before finding out about prof Leonard. I started getting top marks in Calc 3 when I start watching his videos. Certainly, there is no better lecturer/teacher than Professor Leonard. BIG THANKS from South Africa!

[@nathantonning]

These lectures have been one of the best resources that I have ever come across. Professor Leonard, you outperform the MIT professors in your teaching abilities. I want to come and thank you personally if I am ever in the Merced area. Keep up the good work!

[@AIPlayerrrr]

Nathan Tonning I go to mit, it’s much harder than this. But Leonard did a good job tho

[@TheMasterOfWishes]

@@AIPlayerrrr weird flex but ok

[@AIPlayerrrr]

wishywish how is this a flex? Btw I just graduated. So technically I don’t go to mit any more.

[@mathewschau9361]

@@AIPlayerrrr The original comment compared the teaching abilities of Professor Leonard to the teaching abilities of MIT professors based on, presumably, KZbin videos. He simply spoke his opinion on a subject that he felt had adequate pertinence and personal experience to accept as "correct". You're reply had little relevence to the original message and seemed woefully ill-put. You simply stated that MIT courses were more difficult which have no relation to the actual message of the first comment. Basically, this established one of two things: you either do not understand English or you simply wanted to mention you went to MIT. Obviously, you went to MIT so you're not dumb so this is a "flex". By putting a silly little comment you reveal your crippling insecurity that you unhealthily cope with by posting your achievement on the internet. You shamelessly grope for attention even against complete strangers on the internet. Continuing this trend, it is very likely you will reply with all your other achievement and how great you and your life is. Please do not do this. Any further discussion will only exemplify my point. Don't take this personally. Your comment just happened to be the straw that broke the camel's back

[@AIPlayerrrr]

Mathew Schau ok thanks for ur opinion. But it’s irrelevant.

[@nehaljhirmaria11]

Hi Professor Leonard, you are definitely the best teacher on KZbin. Lots of people have said you this that you are doing a great self-less job . And I am grateful to you for these lectures, I understood everything so well . This is sad that Calculus comes to an end here but it was a beautiful journey. Hope you read this!

[@ProfessorLeonard]

Thanks very much!!!

[@user-py3fz2bu9f]

It is 1/21/2024 at 5:44 PM as I'm typing this. I started this course on 7/24/2023, and I had to take a break starting from early September until mid-December because I got busy with my semester. I picked it back up again after the semester ended, and I have just finished this lecture. My amazing teacher in high school who taught me Honors Pre-Calculus and AP Calculus BC used to assign us your videos during the quarantine 3 years ago while she was taking care of her mother in a different state since she had gotten sick from COVID. I got a 5 on my AP Calculus BC exam, and I'd like to partly thank you for that, because your lectures helped me while my teacher was taking care of her mother. As a result, I haven't had to take Calculus I nor Calculus II in college. I really loved your lectures back then, and I could tell that your style of teaching had influenced hers too, which I think is part of the reason why she was so great. I'm currently a Computer Science major and I have not had the chance to take Calculus III at my university yet, but I see references made to it everywhere, so I decided to take matters into my own hands and taught myself using this course. I just want to thank you, from the bottom of my heart, for putting these quality lectures on KZbin FOR FREE! I understand Calculus III quite well now, although some more practice problems could definitely help, so I will do those in my own time. As for the concepts, I really appreciate how you explain them and it truly helps me understand it on an intuitive level. You make math so fun and engaging to learn. I've had many teachers in the past who create such a desolate and bleak atmosphere in their math classes. But when I took classes with my Pre-Calc and Calc BC teacher in high school, and when I watch your lectures, I feel excited to learn more. I went from hating math to loving it thanks to you two. When I graduate and get a job, I wish to donate to you for all the help that you've been in my academic career. Once again, Professor Leonard, thank you so much.

[@dhakshan]

"That is what my job is as a teacher. Make sure you get it, that you understand it" This single line is enough to prove his worth

[@john9486]

I just finished my Calculus III final exam, without your informative and well organized videos there is no way I would have been able to do as well as I did. My online class officially consisted of reading the textbook, watching five minute videos my professor posted, and then doing a five problem assignment. Without your wonderful videos I would have fallen behind incredibly quickly, instead I am set to get and A in the class. I want to thank you for creating these videos and making them free to watch. It truly is wonderful to see that anyone can gain a high quality math education just by watching KZbin. Thank you again and I’ll see you in Diff. EQ!

[@HighestRank]

Free my ass! It's full of fourteen minute ads

[@GioCode-bs5gk]

@@HighestRank You do know that adblock exists ?

[@zazmeister5889]

I fell asleep watching youtube and woke up to this. Pretty nice video overall, might have learned something about Stoke's Theorem in my sleep, so that's kinda awesome.

[@NikhilArunRavenwood]

The 27 dislikes are from the math teachers that are in awe of how amazing you are. I struggled to learn from my professor and so I began my search for a better resource online. I was at first shocked by the length of your videos, but after watching one, I realized how in-depth you go into the topic and how useful every second of the video is. You truly are an amazing professor and I wish you the best of luck in your future endeavours.

[@jacolaw8900]

Thank you professor. Without you, I could not have gotten all "A+"s in Calc 1-3. You are the best math professor in the universe.

[@bigbobo3572]

I don't know him and he doesn't know me, but he has my utmost respect and thanks. He is a gift to all math students. Thank you, Professor Leonard. You have no idea how much you helped, no idea at all.

[@zachariahkovac2048]

Just finished. Thank you so much for continuing to help students learn calculus through these videos. I am a chemistry major with ADHD, and I thought that Calc 3 was going to be the end of it. While I still struggle with focusing on the tests. I finally got a passing score on my exam. I am genuinely excited to learn more math. I found your videos last semester, and it really helped me; I feel behind. This semester, that did not happen. For the first time ever, I am ahead of the class and genuinely understand what I am doing. This teaching style is so helpful. STEM is hard, but not impossible!

[@TIHUXSDW]

I am surrounded by sorrow. This amazing journey has come to its end. I have been watching your videos since calculus one, and this is the last episode of the show..... I will be facing challenges without your caress hand tomorrow. I will be brave, and I will triumph the battles! Thank you, professor Leonard, for bring us so far!

[@v1v2go]

Hey Professor, I just wanted to take the time to thank you for all your videos. I study engineering at a major engineering university in Bavaria and always struggled with higher mathematics (as we call it over here). So much in fact that I came dangerously close to getting kicked out for failing higher math 2 (differential calc, integral calc, and analysis combined) three times. I took to studying your videos and actively working on the problems you present. Your aptitude for explaining incredibly complex abstract mathematical models and principles in an understandable and logical way is incredibly impressive. My mathematics professors, who's titles are longer than the rest of their names, seem to have zero ability to speak outside the boundaries of mathematical jargon, leaving many student like myself scratching their heads and failing exams. In the end I passed my exam and am well on my way to finishing my bachelors degree, something I may well not have accomplished without your help. So danke schön and keep up the good work. I will certainly keep recommending your videos to students over here. Greetings from Germany -Max p.s. Some Numerical Mathematics and Statistical Adjustment Computation videos would be brilliant ;)

[@MrSilviugordes]

We did this in highschool. IT class.

[@kocejamk]

I just want to drop in and say how helpful this video series has been. I was doing horribly in the first few units of my current multivariable calculus class, and I thought that I was going on a downhill slope towards just not understanding the class at all and barely passing. I stumbled upon your videos miraculously when I missed my class on 3D local minima and maxima, and I've been hooked ever since! I nearly failed my first exam, but after finding your videos, I recently got a near perfect score on my second exam! I'm currently studying for the final and finishing up the rest of this video series, but as others have done already, I have to credit almost all of my success in this class and learning/understanding multivariable calculus to you! Thank you so much that you have done for me and all of your students/people watching these videos, you really really make a difference in students' lives!

[@bowlofmilk222]

Im a college student, majoring in environmental engineering, and wrapping up my last calculus class. I've watched your videos throughout all 3 calculus courses and have excelled in each class, all thanks to you. The intro of this video actually made me shed a tear (pitiful, I know). You have not just kept me afloat in these classes, but with your enthusiasm, I have grown to genuinely enjoy my time in these difficult, higher level math classes. I have my last midterm for calc 3 tomorrow, and my final next week. It really feels like the end of an era, and strangely enough, i'll really miss these videos. You have no idea who I am, but you have changed my learning experience completely, and i'll be forever grateful. i'll let you know when I become a successful environmental engineer. who knows, maybe ill save the earth:)

[@Padthai_Shrimp]

Thank you Leonard!!! You Guided me through calc 1, calc 2, and calc 3. I was a high school drop out, I never could pass algebra 2. And thanks to you, I've aced all my Calc courses. Its nice to reflect back and see how far I've come, with hard work and a good professor(You!), math is not impossible. Thank you for putting these resources online. I am forever grateful and I'll promise to pay forward your deeds.

[@QsHsNation1]

My calculus 3 course was going a bit too slow for my taste, so over the course of about 3 weeks, i sat down and spent about 5-7 hours a day watching your lectures, taking down all the notes possible and working all the examples, and I have finally concluded this long and compact journey with big ole' stack of about 150-200 pages of calculus and now understand calculus better than I ever have before. There's no way I could thank you for this video series. You've become an inspiration to how I want to teach others one day.

[@mollycon4589]

Thank you for helping me finish my semester strong with this transition from lecture to online classes. Not only have you helped me pass my class, but you also make sure to give thorough explanations so that anyone watching fully understands the concept, including myself. While I wish I would have found you sooner, I am glad I ever found you at all. Forever recommending you to anyone struggling in math. Best wishes during these hard times (and during all times)

[@abdulahiibrahim552]

It’s been a long journey from algebra to calc 3 , i remeber the first day i had calc 1 lecture i felt like i’ll not able to handle this and am not those who were made to be an engineer, but luckily i found your videos a time when i was most needed, i was watching your videos from intermediate algebra to calc 3 and i felt like am falling love in math coz everything start to make sense. i start doing well in my classes feeling like am one of the students who get the highest grades in each calc class that i took and that’s because of you just you no-one else. I can’t just say thank you beacyse i feel like its not enough i’ll support your channel and recommend my friends and i hope i’ll meet you one day to say you thanks in person while am infront of you i wish you a good life full of joy and happiness. thanks againg professor Leonard !

[@thezeneris]

As a forty-something who is back in school during the pandemic, your videos have been a life preserver. I am the type of student who needs to really understand the subject, and you have been the teacher I needed. I will miss you as I go into Linear Algebra. Thank you for the wonderful lessons.

[@luisaugustobianchessipasso6971]

Hello professor, I just wanted to thank you from the bottom of my heart for this long and great opportunity of learning calculus with frankly one of the best teachers I've ever encountered. My passion for mathematics only grew by each lesson I've watched on these 3 playlists. Professor Leonard, I'll dearly remember you and your lectures for the rest of my life.

[@8100834]

Why do I only find this guy the evening before my test!?

[@zeeshanpasta8440]

Just finished the series after watching you throughout high school, now a sophomore in Mechanical Engineering. I am so thankful that you decide to share your knowledge to the world for free, as a lot of people would've charged money for this. Thank you so much for an amazing semester, can't wait to continue your videos in Differential Equations!

[@TheSpasmer]

I'm 50 years old and will now graduate college. Just finished the entire series of videos. Feels so good I had to go back to patreon and increase my monthly donations. Thank you Mr leonard.

[@didom.1228]

I will miss you so much for Differential Equations!

[@TheFinalStanza94]

0:36 "I know.. i know you'll miss me". This guy actually is the Jesus of math

[@user-mt7if9ru3w]

I am 55 years retired man plus I am a high school graduate since 38 years. After retirement I stated online learning to pass time and get more information. I chose this channel to study calculus and I feel I can get the degree easily if I want to. Thanks a lot

[@airthrowDBT]

I fell asleep on youtube and this is where I ended up, hello smart people, big fan

[@spencergellner5471]

you are what i hope to become as a teacher when I graduate.

[@dustinmcgladrey4821]

So I didn't pass Math 11. Still watching this video. You're the kind of math teacher I wish I had!

[@gillturnbull1885]

Just wanted to let you know that 4 and a half years on, you're still changing lives! How do you do the magic of making this all seem so doable!? Massive thanks.

[@rstar1237]

what a journey it has been, I have now completed calc 3 thanks to professor Leonard 🙌🏻😭

[@blogspoto]

The end got me to tear up a bit, thanks to Professor's Leonard implication i felt like a part of the journey,a part of the never ending beauty of mathematics presented by the most passionate mathematician.Thank you for everything you've done for me,sir,you got me literally in love with math and you have shown me the beauty of it and you have given me the motivation to study/work harder on this and learn as much of it as i can,and i would definitely love to see more from you,whatever that may be.

[@SpencerRemy]

My Calc 3 class has been a nightmare this semester and your videos have been a huge help to me. Thank you for making them and for making this stuff a little easier to understand.

[@mw2blazer]

This great man spent months creating this calculus class even though he could have just easily spent those months doing something else and just teach the class through a textbook. It really shows that you are a man that cares for others. God Bless You!

[@jithinsreekumar8943]

I have never been so sad when a class ended.Such a great teacher,made every second of these lectures so interesting and all my concepts are now crystal clear than ever.Thanks a lot from the bottom of my heart Professor for sharing these lectueres. May God bless you.

[@Slurpee_12]

Hi Professor Leonard, I just wanted to let you know that I am truly grateful for you Calc 2 and Calc 3 series (I hadn't discovered you for Calc 1). Truly, without you, I would have done much worse in these classes. My previous Calc 3 exam, I got my highest grade on a university exam since I've enrolled. Your teaching is phenomenal, and I cannot thank you enough. It appears that you're in the beginning stages of preparing a Differential Equations lecture, but it seems that I am going to miss it. We'll be parting ways for now, but I can truly say that I will remember you for the remainder of my life. I wish you the best of luck, and thank you for all of the hard work that you've done for me and for everyone else!

[@RossRocks07]

You are the most amazing Prof I have ever seen. You teach better than all of my teachers combined.

[@paladin1147]

Professor Leonard, you are my hero. Your teaching is impeccable; you are a teacher with a heart of gold. I cannot describe how grateful I am for you. I have been on this journey for two years now, you have been a big part of my life for the past two years. I am sure you already know this but so man people are so grateful for breaking the subject down piece by piece and leaving no troops behind. I will be a patron to show my support and spread word about you. Everybody who takes Calculus deserves a chance to know you exist. Thank you so much.

[@niklasj9191]

Thank you Leonard, you have truly changed my view on math. I have gone from hating and not understanding math to truly understand the different concepts, and being able to finish an engineering degree because of it. You are a great teacher, and i wish the very best to you!

[@aaronkyei-asare3084]

Ay bruh, on mommies you da GOAT b. I finessed my calc 3 class with your lectures. Go tf off bruh. Keep doing you. Stay great. You my real professor. Love you.

[@KiNgS4EvAful]

PLEASE DO DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA

[@Peter_1986]

He has posted an insane amount of material for Differential Equations recently - look it up if you have missed it. :D

[@huanglinwan7075]

@@Peter_1986 does he post the videos of linear algebra?

[@Peter_1986]

@@huanglinwan7075 He has said that he will start working on those videos in the not too distant future, but that he is currently busy with a couple other courses. You can hear more information about that in his video "Professor Leonard's Important Announcement 2019".

[@huanglinwan7075]

@@Peter_1986 oh ok got it .Thank you ! >_

[@Peter_1986]

@@huanglinwan7075 If you are looking for some introductory Linear Algebra material then I can recommend "Linear Algebra And Its Applications" by David C. Lay. That book is easy to read, and very intuitive, and it immediately starts with showing how you can use matrices to easily solve systems of linear equations. There is also an optional section early in the book that even shows how matrices can be used to balance chemical equations, which I found really useful when I studied chemistry.

[@thespaceagent3991]

idc if i am going to get any likes on this comment or what grade i am going to get this semester for my exam, but one thing i can certainly say for sure is this man singlehandedly brought me through calculus and i wished i started watching his videos way before my college journey started. I just hope you see this message, profesor leonard, and i just want to say thank you for everything you have done for my journey in college math. Legend, and stay buff as always~

[@Chrome47]

You're the fluxing man!! These videos have been a huge help this semester!! Just wanted to say thank you for your excellent content and have a great summer.

[@emilyse147]

Your videos are amazing!!!! You should do differential equations and linear algebra!!!!!!

[@walrusboy91]

But.... I'll never get to hear these again........ "honestly all I heard was .... but I'm imagining you said....." "head nod if you're ok with that one?" "show of hands if you're alright with that one?"

[@wardotard]

You memba'? You memba'!

[@NataliaBMeza]

I just want to say, the world needs more passionate teachers who take their jobs as seriously as you do professor Leonard. Your focus on making connections instead of crossing an item out of the list and your genuine love for communicating and helping people UNDERSTAND is what makes you a real teacher. Thank you so much for sharing all of this content and your genuine love for calculus with the world.

[@gabrialpetersen914]

I just want to say thank you from the bottom of my heart for everything that you do for us. As many others have said you are our hero and the best math professor I have ever seen. I will always remember you as the man who taught me math. You make your videos entertaining, intuitive and I really enjoy watching your lectures, you have me hooked from start to finish. If I had grown up with a father figure in my life I would've wanted him to be just like you. You are my role model and you have changed my life. Again, THANK YOU and we love you professor Leonard.

[@thebigVLOG]

Thank you for the journey P. Leonard, your name is amongst the Gods now.

[@gottafeelalive]

thank you very much professor !!! have a great summer =D

[@derpderpinson7449]

I know everyone's commenting something like this so it's not that original but still... It's because of you that I've had any kind of success in my math classes in these first couple of years in college, and I'm genuinely going to miss coming to your videos for help. I've seen no one in my life with your teaching ability and I hope you continue to aid students like you have me and the rest of us for years to come. Thank you Professor Superman.

[@zorxey3189]

Thank you so much for all of these playlists. I watched the entirety of Calc 1, 2, and now 3, and I am so grateful for all the effort you put into your work. I never would have understood calc this well without you.

[@KennethPutt]

Flux @ 1:35:50, Divergence @ 2:10:01, Stokes @ 2:51:35.

[@sharadsaxena1588]

World best teacher.......

[@henrikrynauw244]

4 years later and Professor Leonard is still carrying us through calculus, thanks a lot ! I will keep on referring your quality videos to anyone in need as was done for me. :)

[@bonzpi]

We have reached Journey's end. white shores and beyond, a far green country, under a swift sunrise. It's not so bad. so do all who live to see such times, but that isn't for them to decide. All they have to decide is what to do with the time that is given. This task has been entrusted to u professor leonard, no one else can complete it. And i lived happily ever after

[@andrewknotts21]

i fell asleep and woke up to a Calculus 3 Lecture.

[@qilqil8914]

Hope you woke up to the monologue

[@1willFALL]

best monologue from 0:00 - 1:13. them puns though.

[@funmaster5249]

I will forever remember the time you've put into making these videos. I hope someday I get to shake your hand and thank you in person.

[@khanster]

I've been watching this playlist in concurrent with my cal-3 class and you've been vital. If I ever become successful, I never forget a debt. Thank you Prof Leonard.

[@johnsullivan1606]

I'm actually a little sad I've reached the end. This was so entertaining. "Head nod if you're ok with the idea..." "Is it hard?" "Not really"

[@gmr4life]

do you do differential equations? or are planning to?

[@aaronrashid2075]

He has loads now (sorry if it’s late)

[@RinaNewhouse]

I wish I knew how valuable your resources were at the beginning of my multivariable calculus class. Rather than jamming through hundreds of problems, not to pick up anything, and feeling frustrated, you describe your concepts cleanly, clearly, and beautifully. The series of three-hour videos, ironically, has saved me time.

[@HalfHotHalfCold]

Leonard, it's been a long road and it is crazy to think that it is over! Your influence will never be forgotten and I know you will continue to help students achieve the grades they deserve. Thanks for everything.

[@jkp-qe4ty]

Professor Leonard, what school are you working at??? I really envy those students who are listening your lecture directly!!

[@adhir.8348]

merced

[@danielolivera2618]

when will you teach linear and differential eq?

[@michaelempeigne3519]

linear differential equations are easy to solve. The idea is to find a function y which satisfies the differential equation. Recall : d[ u ( x )* y] / dx = u ( x ) * dy / dx + y * du / dx ( eq. 1 ) Now for a differential equation such as : dy / dx + P ( x ) * y = Q ( x ) ( eq. 2 ) and multiplying this equation by u ( x ) : u ( x ) * dy / dx + u ( x ) * P ( x ) * y = u ( x ) * Q ( x ) (eq. 3 ) the only difference between the top line ( eq. 1 ) and ( eq. 3 ) is what is multiplying y, therefore : du / dx = u ( x) * P ( x ) du / u = P ( x ) dx ln u = int [ P ( x ) dx ] u ( x ) = e^[ int P ( x ) dx ] after that it is easy to simplify and solve for.

[@restitutororbis964]

Daniel Olivera I heard khan academy is pretty sweet.

[@MathTutorVideos]

@@michaelempeigne3519 That's no. No. That's one type of very simple ordinary different equation of first order. It only works for a very specific case. That's equivalent to saying "Integration? That's easy. The only thing you need to know is increase the power on your polynominal by 1 and divide by the new number. Next add a c as a constant of integration. That's it. Calculus 2 is easy." (one case/technique out of about 20 you need to know) There's about 20-30 types of differential equations of different orders, etc you need to learn to solve in a DE course.

[@benjaminh2612]

Thank you, Professor Leonard! I started watching your videos May of 2016 for my summer calculus course, and now I'm at the end. You taught me more than how to use calculus, but also how to break general problems down into steps. I've used your method to study for more than just my math classes. Thank you for sharing your talents, and also the humor! God bless you!

[@omarmagdi2732]

Someone must build him a goddamn STATUE! ...He's prolly the best Professor, he is witty, funny, straightforward, never leave you perplexed nor bored...Thx god destining me to come across Leonard.

[@joselrnzrodriguez]

can you make videos of differntial equations?

[@TheMrEM4N]

+Jose Lorenzo Rodriguez He has them up if you look under his old Calc 1 content

[@mourneris]

I definitely agree with you. We need Differential Equations content. I'm talking about like Ordinary DEs. Like, homogenous and non-homogenous. Laplace Transforms. Etc.

[@jfresh2054]

+Mourneris are you talking about calc 1 differential equations? the basics? or are you taking about differential equations class, which you take after calc 3?

[@joselrnzrodriguez]

+Puppylove Abbie after calc 3.

[@mourneris]

Puppylove Abbie The one that is the cousin of Calculus 3. At my university you can take DE after Calculus 2. It's MAP 2302.

[@DahGoldenLegacy]

"Head nod that youre okay with that one"

[@Jeremy_Fisher]

* Nods furiously in front of computer *

[@pulsie]

I don't know how many hours I've spent watching these videos... all I know is I've enjoyed every second. Thanks for being such a great instructor Prof Leonard, because of you Calc 3 has been my favourite course this semester and perhaps even throughout all of university. I hope to find my calling in life someday as you clearly have.

[@Zhim94]

3 months, 8 - 10 hrs a day to create this class... wow. You are the best, and as soon as my exams are over, I will donate to you!

[@Zhim94]

Thanks to you, I passed! Thanks professor!!

[@benkane197]

what if they dont give you a function of z ? What if they give you a sphere only? What if they give you something like x + 2y +3z = 1 What is your g(x) ??

[@benkane197]

someones gotta explain this to me

[@dooby5953]

Solve for Z and there is your function of Z. If they give you a sphere do the same thing solve for Z. x^2+y^2+z^2=1 solve for z which would give you the square root of x^2-y^2+1. The question must define if its in the positive or negative side, so you don't remove half of your sphere when you take a square root.

[@vitaminwasher]

Linear Algebra or Discrete Math anytime soon? :D

[@kesjerdna]

Yes. And then Combinatorical Optimization and Algorithms and Data Structures.

[@thedailyepochs338]

@@kesjerdna honestly this will be so helpful

[@chrisrabe655]

As many before have stated. I can't thank this professor enough for his work and dedication in these videos. Discovered his video series near the start of Calc 2 and followed the videos from then on until the end of Calc 3. I can honestly say both my professors I had for actual lecture, while they meant well, were not as clear and concise as Prof. L. Thank you for all that you do and enjoy building your house you have been working on the last year sir!

[@realifeTonyStark]

Having my last calculus exam in 5 days, i honestly feel like i know you personally now. South African loves you Prof. the Picasso of teaching

[@brendandaddino500]

Bruh you need to be at UC Merced. Professors need your help communicating better to their students.

[@ArturoRamirez-pp1kp]

Brendan Daddino amen brother

[@dude3650]

So true. I would go to every single one of his lectures.