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.

[ErickHrnndz]

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.

[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!

[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)=<u+v, u-v, u^2+v^2>

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=<x, y, z>

2:08:59 Leonardism

2:09:52 Divergence Theorem
2:17:47 Ex #7: Find the flux through vector field, F=<x+sin(z), 2y+cos(x), 3z+tan(y)> over the surface x^2+y^2+z^2=4
2:34:48 Ex #8: Flux of F=<xy^2, yz^2, zx^2> 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)=<cos(z), (x^2), 2y> when C: intersection of plane z=2-x and x^2+y^2=4

[ouss]

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.

[NaiThePiGuy]

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

[prim]

*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."

[_avenger]

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. :)

[aaryankumar]

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

[shaner]

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.

[tristinchapman]

Hello Professor Leonard, I just passed Calculus 3 for Engineers at Arizona State University as an online student and I owe it all to you. Thank you so much for providing such HIGH QUALITY education for all. I envy your students who had you in class. Thank you a million times, I will continue my dream of becoming an electrical engineer someday thanks to you.

[azwadrahman]

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

[bartsimpson]

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.

[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.

[ParthPatel-nh]

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 YouTube 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. <3

[seanmontague]

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!

[Andrew-qpbv]

@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

[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!

[AirwithAri]

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

[GUSTAVOCASTREJON-wi]

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. <3

[donovanrao]

Professor Leonard is literally the reason I love math so much! I returned to school to study EGN 2 years ago and never really liked math. Now I'm unimaginably inspired. Going into my calc 3 final next week with an A+! Thank you so much, please start making videos again!!!!