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A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)

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In the final video of my vector calculus playlist (congrats to everyone for making it to the end!!!) I want to do a bit of an overview of the major theorems we have seen in this course - Stokes' Theorem, Divergence Theorem, Green's Theorem - all are part of a unified framework. Loosely, integrating a differential operator such as the curl or divergence along a region equates to a quantity computed just along the boundary. Exactly what quantity (flux vs circulation, say) changes depending on the set-up, but they all obey this principle. Indeed, this principle really goes back to the fundamental theorem of calculus II, which was also the root for the fundamental theorem of line integrals we saw earlier in the course.
Anyways, a HUGE thank you to everyone for following along, and I wish you best of luck in any exams!
MY VECTOR CALCULUS PLAYLIST:
►VECTOR CALCULUS (Calc IV) • Calculus IV: Vector Ca...
OTHER COURSE PLAYLISTS:
►DISCRETE MATH: • Discrete Math (Full Co...
►LINEAR ALGEBRA: • Linear Algebra (Full C...
►CALCULUS I: • Calculus I (Limits, De...
► CALCULUS II: • Calculus II (Integrati...
►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivar...
►DIFFERENTIAL EQUATIONS: • How to solve ODEs with...
OTHER PLAYLISTS:
► Learning Math Series
• 5 Tips To Make Math Pr...
►Cool Math Series:
• Cool Math Series
BECOME A MEMBER:
►Join: / @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: www.amazon.com...
SOCIALS:
►Twitter (math based): / treforbazett
►Instagram (photography based): / treforphotography

Опубликовано:

17 дек 2020

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Комментарии : 300

@j.o.5957 3 года назад

You know why I love this? Because with this, anyone in the entire world, no matter their background or income, can learn university level math. For free. Your videos outshine all the math classes my university to the point where it's no comparison. Gonna be a huge advertiser of yours going forwards.

@standowner6979 3 года назад

Only if the person speaks English

@Michael748159263 2 года назад

@@standowner6979 Gotta learn English too then xd

@davidcastillo4938 Год назад

Thank you so much Dr for helping me throughout my calc iii course. I got a 93% on my final and can finally get some rest this winter break. Hope this helps!

@DrTrefor 11 месяцев назад

I totally missed this 8 months ago, so a delayed thank you!!

@noonesperfect 3 года назад

One of the great playlist on YT for sure, thanks for all efforts. Kudos

@DrTrefor 3 года назад

Wow, thanks!

@naveennaidu9064 2 года назад

@@DrTrefor Prof u've done all this for free, We can't just thank you, ur effort deserves alot alot of respect!

@khawar0o7 Месяц назад

Thanks a lot, Dr. Bazett. I have a Masters in Mechanical Engineering, but our professors never really took the time to give a conceptual understanding of vector calculus. Your videos are a lifesaver.

@DrTrefor 19 дней назад

Thank you for sharing, that's awesome!

@ManojKumar-cj7oj 3 года назад

this whole series is incomplete without this last video finally I understood the essence of vector calculus thank you very much, Dr. Trefor

@francisc.coria_ 2 года назад

Just ended the playlist and I can only think that 'THANK YOU' isn't enough to say. You're such a great professor and made all this process of learning calculus amazing. Hope you receive all you have given to us! Thank you, Dr. Trefor Bazett! *Argentinian hug* 🇦🇷

@DrTrefor 2 года назад

Amazing, well done!

@anujmishra6834 3 года назад

Every thing is round it ends where it starts. so beautifully covered professor , loved it . respect

@abhinav_mzn 3 года назад

Need this type of content on yt.

@ErfanAzad-od3th 2 месяца назад

Dr Bazett you are a beacon of hope for every student of mathematics. You are a true teacher. You are capable of teaching complicated subjects in an intuitive and interesting manner. I want to sincerely thank you for everything you have taught me. I’m looking forwards to your future videos.

@user-jm6gp2qc8x 3 года назад

Finishing this series, Now I'm feeling nostalgic

@DrTrefor 3 года назад

Congrats on making it to the end!

@user-jm6gp2qc8x 3 года назад

@Kathe Schweinberg I've seen these messages in many places

@garmands 3 года назад

So I have reached this video at last. When the pandemic hit and universities switched to online education, it was game over for the universities. RU-vid content creators had been perfecting their game for years and there is absolutely no way universities can compete with this. The reality is, I can go watch a grainy doodle video on the portal of my university, or I can come here and watch an absolutely stunning playlist about the same thing that is just so much more thought through and visually immersive. And it is free. So a massive 'thank you' is in order. The way you present topics should be shown as an example to professors on how to present complex concepts in an understandable manner.

@DrTrefor 3 года назад

Congrats on making it to the end, and thank you so much for your kind words:)

@allison5169 2 года назад

2 playlists in one day has been a success. Thank you so much

@DrTrefor 2 года назад

Wow!

@NuclearPhysix 3 года назад

Your graphical representations are so clear and cleverly selected. Makes it easier for me to visualize what you are explaining. Thank you so much

@DrTrefor 3 года назад

Thank you, and you’re most welcome!

@raghuramabl6729 2 года назад

Thank You for this wonderful playlist. Initially, I saw two-three videos in between but did not get the concept, so decided to watch the full playlist it took me around 6:30 hr which really helped me to boost up my knowledge. Once again thank you. You are one of the wonderful teachers on youtube💕❤🙌👌

@avinashsivaraman9682 3 года назад

Thank you so much for helping me through vector calculus. Surface and line integrals didn’t make sense to me at all before I watched your videos

@DrTrefor 3 года назад

So glad they helped! Congrats on making it to the end:)

@hritizgogoi3739 2 года назад

Professor Bazett. Take a bow. You are one of the best things that happened in RU-vid

@elatior Год назад

The visuals and the way you presented make the ideas come together so clearly and helped with my understanding of vector calculus. Thank you so much for making these videos!

@pouriapmd6077 Месяц назад

I just finished watching this playlist, just wanted to thank you for your efforts. your teaching is fantastic, not even comparable to my class at university.

@mitsosyt7853 Год назад

I am in my final year of high school right now studying stuff to get in med school and I have a large interest in advanced math. I can say that this playlist helped me understand all the topics of vector calculus perfectly. Thank you for this, you did an amazing job! :D

@moinshaikh1963 2 года назад

Sir you have made an excellent playlist! I'm not just talking about topics you covered in videos, detailed description of each video, the segregation of sub topics in every video and the order in which you covered those topics.

@JimMorikuni 2 месяца назад

Thank you Dr. Trefor for such a wonderful playlist. As an engineer, I learned the equations of vector calculus many years ago but never really understood what they meant (the geometric interpretation). Your enthusiasm and your gift of teaching helped me understand them in a much more intuitive way.

@djredrover 2 года назад

a year after I graduating uni, I finally intuitively understand vector calc thanks to you, sir. During Uni, I saw all this stuff as symbol puzzles and never intuitively. Thank you thank you.

@DrTrefor 2 года назад

Glad to hear that!!

@therunkumar 3 года назад

Your content is as wonderful as the content of guys like 3Blue1Brown and Zach Star. Your enthusiasm is wonderful and I hope I get to see more of your videos in my recommendation feed.

@DrTrefor 3 года назад

Thank you for such a lovely comparison!

@therunkumar 3 года назад

@@DrTrefor I don't know what to say really. I'm aspiring to become a physicist in the near future and I'm hoping to get a better intuition about the basics of linear algebra and calculus from your playlists. Thanks a lot for your service.

@adamsusel3801 3 года назад

I needed this last week before my final! But fr though, this playlist has been incredibly helpful

@DrTrefor 3 года назад

haha shoot well hope it went well regardless:D

@charlieconsidine848 5 месяцев назад

Thank you so much for this course. This intuitive series gave me a much better understanding of the equations in my math class and an appreciation for the laws I learned in physics. You do an excellent job conveying difficult material to us

@carlmcgrath484 Год назад

Got my Vector Calculus exam next month. This will be my third time sitting it. Your videos have helped my understanding so much, just finished the playlist. Thankyou Dr Bazett!!!

@carlmcgrath484 11 месяцев назад

Update. I passed! Trefor you are the best i love you! I have my maths degree now whooop

@lochlynreed2253 3 года назад

Your ability to simplify and communicate convoluted ideas is absolutely phenomenal! what a natural educator

@DrTrefor 3 года назад

Thanks so much!

@jgregory6077 3 года назад

Dr. Bazett, thank you so much for this series on vector calculus. You have made this potentially complicated subject into one that can be easily understood, an outcome I attribute to your exceptional intellect, your passion for helping others learn, your talent for communicating effectively online, and your dedication of time and energy to making this all work out all right so that one leaves with a sense of wonder, enjoyment, and enlightenment.

@DrTrefor 3 года назад

Thank you and congrats making it to the end!

@husseinmhammad54 3 года назад

Waited for this😍

@ashvanth_iitb Год назад

completed this playlist in 1 day, a day before my endsems 💀 hope I do well thanks a lot prof, u taught very well

@kiddjmadd 3 года назад

I just finished the whole playlist, what a journey! It must be great for students to have access such high quality content, but us practicing engineers get a lot out of it as well. I deal mostly with lumped parameter analysis, but after completing these videos, the CFD and FEA distributed parameter concepts will be much more intuitive. Thanks so much!

@DrTrefor 3 года назад

Hey congrats on making it to the end, that’s awesome!! Glad to hear about the applications in engineering:)

@augustobiazonperboni7076 2 года назад

Good afertnoon dr. Buzett, I have just finished this playlist and I would like to thank you for all these amazing videos. It’s really impressive how you can expose the theory so clearly and at the same time so fast. Your videos are so helpful for a lot of people. Thank you again for your exceptional job. Best wishes.

@DrTrefor 2 года назад

Congrats on making it through, that’s awesome!

@colbyscott8545 2 года назад

Hi Dr. Trefor, I want to thank you dearly for this playlist. My calculus 3 final exam was based entirely off of the final chapter of the course, which was all vector calculus. I realized my professor's teaching style wasn't helping me understand vector calculus once I realized I still didn't really understand what a line integral was even a couple weeks after we were introduced to it. I searched in the RU-vid search bar, "visualizing line integrals" and that's how I found your channel. When you mentioned this playlist I decided to check it out and realized it was exactly what we were learning! I find your teaching style seems to match perfectly with how I learn - your visualizations are immaculate and I think they were the key to my understanding. Thanks to you, I earned a 94% on my final exam and, for the first time, secured an A as my final grade in a calculus class! I thank you from the bottom of my heart for allowing me to not only understand but also finally enjoy calculus 3. I quite like the Eat Sleep Math Repeat hoodie on the website, what are the dimensions of the medium and large sizes? I tend to flop between the two. Thank you so much!

@DrTrefor 2 года назад

Glad you enjoyed!! I actually just ordered that hoodie myself in the "Large" and I should be getting the first samples very soon. From what I can tell from the distribution folks these fit pretty standard, but I always like going slightly large as will shrink a little bit washes.

@nikhils216 3 месяца назад

Awesome Playlist. Thank A Lot Prof. Trefor. Your beautiful explanations and picturisation made this Topic very simple and interesting. Thank you so much for making this wonderful content. Best Playlist on YT.

@CaseyHarris-wr3ok Год назад

Just finished the series, I am so overwhelmed with gratitude that I am motivated to make my first youtube comment ever. You are a real one, I love your work and your passion for every topic you discuss, I can't wait to watch your series for future math classes. I am for sure going to buy some merch on the website. I love you and THANK YOU!!!!!!!!!!!!!!!!

@DrTrefor Год назад

So glad you enjoyed it!

@keiyiulai3629 2 года назад

I seldom leave comments under videos but I feel like I MUST do this for the end of this legendary playlist. A big thank you to you for making these videos. They literally save me :D

@DrTrefor 2 года назад

Thank you! Congrats on making it to the end:)

@HardeepSingh-qp3pe 3 года назад

I have seen every video more than three times,,,, amazinggggg

@DrTrefor 3 года назад

So glad they have been helping!

@rxwop3698 3 года назад

Thank you so much, the intuition in this series was unparalleled.

@gabriellarson6507 3 года назад

youre the reason I passed my calc class, THANK YOU TREFOR :)

@DrTrefor 3 года назад

Congrats, that’s awesome!

@ifyjossy98 3 года назад

I could not take my eye offs the playlist until it ended. It is a great one, it made me understand the topic far better now.

@DrTrefor 3 года назад

Congrats on making it to the end!

@dae8105 2 года назад

Give this man a medal

@amanpandey1316 2 года назад

Thankyou very much for this playlist... Perfectly explained.. easy language.. covered almost every topic... As a physics student this is very helpfull for me.. before studying electromagnetism one should go through this playlist once ..

@ayanavroy8269 3 года назад

Thank you for this course! I remember having to watch your videos for a Univ. of Cincinnati Discrete Math course, and found your way of teaching to be really engaging. And now, this playlist has been equally as helpful. I remember taking Multi in school and just mugging up all of the vector calculus formulas, now their actual meaning makes so much more sense. Hope that you can make more courses like this in the future!

@DrTrefor 3 года назад

Cool! Glad they helped, I miss my old UC days:)

@Superdoodle1000 3 месяца назад

Thank you so much. Your course teaches vector calc in the same language as my school and follows the book exactly. This was a huge help and I appreciate it

@anthonyheak3479 9 месяцев назад

Your videos are great! You speak loud and clear, so it was easy to understand you.

@rifatahamed7052 2 года назад

What an amazing series! The videos are very useful in learning the core concepts of this field. Thank you for the effort that you have put to make the learning more enjoyable!

@DrTrefor 2 года назад

Glad you enjoyed it!

@rifatahamed7052 2 года назад

@@DrTrefor Big time! Keep up the good work.

@aleg7340 3 года назад

You're timing has been perfect, I have this exam next February ahah; I just wanted to say that you're amazing, a true blessing; you, 3blue1brown, professor Dave and all the other RU-vid channel of this kind are the future of education; passion is what makes a great teacher and it's clear that you have plenty of it (by the way, the final insight on the differential operator was Incredible, and of course my prof didn't explained it to me ahaha, thanks a lot really)

@DrTrefor 3 года назад

THank you! And good luck in your exam in feb:)

@richardneifeld7797 3 года назад

my son was taking BC Calc in HS which includes vector Calc, so I decided to a take a refresher course, and yours was outstanding! I feel like I now know vector calculus at an intuitive level that I did not have back in the days of college and grad school. Thank you!

@victorsalasgomez5097 2 года назад

Exam is in 6 hours, I am confident thanks to your passion for teaching. Bravo maestro!

@DrTrefor 2 года назад

Good luck!

@lubnaabbas7329 Год назад

big thank you!!!!!!!!!!!! This playlist has made my life som much easier!

@emrekt22 3 месяца назад

Thank you Dr. Bazett for helping me pass this course with ease

@MelodiCat753 2 года назад

This video made me cry. It's so beautiful!!!

@simonwax7575 2 года назад

Thanks for your help from Australia hoping I get through next weeks exam!

@dawarjdeka9613 9 месяцев назад

so digested the full playlist ,,and ready for my end semester exam tomorrow. thanks a lot dr Trefor..lots of love from India

@user-md4rq8td3t 8 месяцев назад

Quality and intuitive video collection you have. 🙏🙏

@naveennaidu9064 2 года назад

I've learnt this course so fast!!! The best thing is, Prof u've made it so so simple and precise!!! I had never thought of them explained so simple . A real teacher indeed, hats off, ur CONTRIBUTION is helping all students across the world!! Global teacher, may God bless u and ur family. This really really helped me alot, I'm an engineering student , aspiring for GATE @INDIA , u've helped me build such strong base in calculus, I'm gonna rock on engineering subjects now , Lots of love from INDIA 😍😍😍😍😍😍😍

@swaroopdewal4626 3 года назад

You are an awesome teacher. You just visualise vector calculus. Finally i ends this, before this i was struggling so much.

@DrTrefor 3 года назад

Congrats on making it to the end!

@swaroopdewal4626 3 года назад

Thank you so much !!

@owaiswaheed1652 Год назад

I appreciate your teaching style and really like the way you are inducing interest in Students. Keep up the good work!!!

@hikmatullahpakhtoon3694 3 года назад

finally finished an amazing playlist. Thank you so much Dr trefor. Lots of love from north west Pakistan.

@bendavis2234 Год назад

After watching all of your vids since Calc 3, your vids have been a great supplement to my studies! I think that the shortness and clarity of your vids is what makes it so effective. Compared to hour long lectures at school, I've learned just as much from your 10-minute videos. There's a surprising amount of information that gets lost during the lecture that is easily picked up in your vids, despite their brevity. Thanks a lot!

@kirankumarpanda7551 Год назад

best ever playlist for vector calculus

@jadfadel9681 3 года назад

Thank you very much! This playlist helped me prepare for my exams. Exams aside though, these things are very interesting to learn and understand even if you're not enrolled in a university. When things become graded, the student's goal shifts to learning enough to pass the course rather than understand the material and try to innovate with it.

@DrTrefor 3 года назад

Glad it helped!

@gauravjoshi2320 3 года назад

Completed the entire course...❤️ Loved it! Love you from Uttarakhand State, India🇮🇳

@DrTrefor 3 года назад

Congrats on making it to the end!

@luizsantos1700 3 года назад

I haven't watched your channel for a while and you have done a lot of things 😍. Congrats and thank you for your great work! I'll watch the Calc IV playlist to help in my Electromagnetism course. I'll like and share all for sure! Please keep doing these wonderful videos.

@DrTrefor 3 года назад

Thank you and enjoy!

@markampatsidis8853 2 года назад

Εxcellent work!!! "Unifying Principle": the "heart" of ANY explanation.

@Sloanpierce222 3 года назад

My understanding of calculus has increased more in the last 3 days then it has in the last 3 months of school, thank you

@omanshsharma292 3 года назад

I was having problem with physics calculus, just skimmed through your calculus series and it seems so clear now.... I just can't thank you enough

@DrTrefor 3 года назад

You are most welcome!

@khansarubab3257 3 года назад

ru-vid.com/show-UCLiSQM08GcX38D8KmIi7izQ You can get videos with full concepts on this channel too.

@darkphoenix_007 Год назад

Completed the entire playlist in 2 days. That's how interesting & fun to understand this was. Take a bow Dr. Trefor

@structuralanalysis6885 3 года назад

700+ likes and ZERO dislikes ! Man, you are just brilliant !

@RAJANGUPTA-ce8lg 3 года назад

today i ended with all the video of vector calculus ................a lot of Indian ,a lot of Iitian wacthing you ..............one thing i expect from u sir .....please provide the ppt of all the topic u covered daily in description ......thank u soo much ........luv u sir .............

@DrTrefor 3 года назад

Congrats on making it o the end!!

@RAJANGUPTA-ce8lg 3 года назад

@@DrTrefor Thank u sir ..........your visuliszation really help me understand math......sir please cover PDE vedio lecture .............a group of engineering student waiting for this

@admiralhyperspace0015 3 года назад

MashAllah, great bro. You explained it so crisply. I found this explanation in griffith E and M and you really outdid yourself by generalizing at the end. Really, really appreciate your work. And keep it up. You are helping alot of us. Thanks.

@DrTrefor 3 года назад

Thank you so much!

@mdsyfullahfahim7384 3 года назад

This is the best math course I've gone through in my whole life. I now can feel every bit of that. Thanks a lot for such content. Wishing you a great life.

@DrTrefor 3 года назад

Congrats on making it to the end!

@nikhilsingh5233 3 года назад

we need more professor like you, sir.

@DrTrefor 3 года назад

Thank you!

@joshuaisemperor 3 года назад

Many thanks for creating these kind of videos!

@DrTrefor 3 года назад

My pleasure!

@user-sd6qe6kz5y 2 года назад

Completed the full series today. Thank you so much for the outstanding videos!

@DrTrefor 2 года назад

Congrats on making it to the end!!

@aldotovar9231 3 года назад

I'm so glad I've found your channel. Thank you for all of this!

@DrTrefor 3 года назад

You are so welcome!

@SGNxBall3r 10 месяцев назад

Made it to the end! Great series!

@DrTrefor 10 месяцев назад

amazing! Congrats:)

@leon_noel1687 2 года назад

This is the best video. I don't need the details first. Give me the picture then I want to learn the details next. Thx.

@samborisuk9687 3 года назад

This playlist has been amazing and fundamental for my studying. Thanks so much!!!

@DrTrefor 3 года назад

You're very welcome!

@jkgan4952 Год назад

This playlist was gold from start to finish! THANK YOU SO MUCHHH :)

@sachinu1986 3 года назад

Very well structured videos with a gist of all important concepts

@wetwingnut 3 года назад

This filled in a lot of blanks for me. TY

@yongmrchen Год назад

finished watching all the videos from calculus 1-4 today.

@DrTrefor Год назад

Wow congrats!!!

@dagadabhanu Год назад

It was fun to learn with you. Got some great detailed insights. Appreciate your efforts Dr. Trefor

@gsejal1039 3 года назад

I'm very happy to have found your channel. Helped me understand things in a very easier way. Great work sir!!

@DrTrefor 3 года назад

Glad to hear that!

@romanayon8483 Год назад

Thank you, Sir,though a 'thank' is not enough how much it helps me to understand vector calculus

@nicholasdjedjos7988 Год назад

Thank you so much for posting this series!

@mnada72 3 года назад

Thank you so much for this top quality course. I enjoyed the learning experience and benefited a lot. I think these marvelous playlists deserve from me a second pass on them to get the max out of them.I am moving on and would like you to suggest the next to start with , line algebra or discrete math. Thank you.

@surendrasingh-nm3op 2 года назад

Really good. Wish you all success and happiness, Sir.

@boidaemon8733 Год назад

I had previously watched the entire course on vector and multivariable calculus by Grant over on Khan academy, but i left very unfullfilled, it felt really overwhelming, and even though i learned alot of the key concepts, all of the pieces just weren't fitting for me. But with this playlist you have really stepped up to the plate and made everything super clear. I particularly enjoy how you make connections between all of the theorems. And show the computations, Well done, i feel that i have a much better grasp of the subject now.

@Ehsanfarzin-iu9rh 7 дней назад

Thank you so much, Dr. Bazett, for your incredible and in-depth teaching. I truly appreciate it! 🙏 Could you please recommend a textbook that aligns with this course?

@SajjadAhmad-wv8mw 2 года назад

"Equations are just the boring part of mathematics. I attempt to see things in term of geometry." Stephen Hawking This is what I'm always looking for, since I haven't been through all of these videos but watched most of them that helped me a lot in understanding calculas III. Thank you, @Dr. Trefor Bazett