Trust me If I had a teacher like you, I would't miss a single class. Your way of teaching makes maths fun and not just some problem solving methods and calculations on a notebook. Thank you sir.
I especially appreciate how the concept gradually unfold and the time and derivative respect time get in to play. A great interpretation about line integral.
I'm trying not to cry while in the library I've been trying to understand this for so long and in a couple of minutes... there it is! Oh my god thank you so much
Thank you so much Dr. Bazett, because of the visualization and intuitive description I actually understand what the line integral represents, at first I didn’t even know what I was trying to actually calculate!
I would just like to say THANK YOU for making the conceptual explanation walk hand in hand with the visuals. That was something I had hoped to cover more when taking calc 3 and it helped so, so, much.
@@DrTrefor I was gonna say the same thing. Your visual aids are intuitive, and I wish watched this 2 years ago when I was in Calc 4. This is top notch!
This made my day! All of my friends were struggling with this and l was so scared but luckily yours is the first video l stumbled upon and now l have a crystal clear concept of this!
Man this is so cool. I was searching for some videos to learn about this topic in spanish but there are only people telling you the formula of the integral and making the calculus straight up, but I really wanted to understand the concept before digging into the exercises and this helped me so much. Thank you a lot!
The way you present the material makes so intuitive and easy to approach. This by far the best explanation for line integrals i have seen out there . Automatic subscribe from me, you got me hooked . Thanks Doc !
Wow! Great video. I've been refreshing some Calculus III material since it's been about a year since I've taken the course and your videos are really helping :)
Thank you so much sir, you explain everything to the root and even give examples! Great for us students who aren't fortunate enough to have a teacher with an explaination style that fits us.
man u r a lifesaver, I have studied this topic in college for about a month and did not understand a word, but this video has made this concept way easier, thnx a lot man
Really appreciate the content you created! I learnt calc back in undergrad, but I forgot so much. Your videos helped me to pick up and extended original knowledge base. Thanks!
The best visuals and explanations I have seen so far. Immensely helpful for Calc 3 (II) refresher I am taking currently with edX. You were meaning when "k goes to infinity" instead of "n going to infinity"--but all of us understood!
Snow analogy is so good. I surprised that Trefor didn't connected blue curve and circle with half-transparent barrier and then didn't said "This is snow height about what I was talking!"
This video really helped me visualize what I was calculating when I was doing the calculations. Thanks a lot your explanation was very thorough and helpful!!
12:00 hey guys just a tip, this can be also written as the integral of f(g(t),h(t)) . |dr/dt| . dt or the integral with respect to t of the function parametrized, times magnitude of the derivative of vector function with respect to t
Nice video, as always! 1) It would be even nice to point out that, the pythagorean thing can be written simply as | r'(t) | , and that | r'(t)|.dt denotes the infinitesimal arc length. 2) I hope you also add in coming up section , the line integrals of a vector field.
Good point. And of course it's the same thing, but some texts also write it as |v(t)|. Anyways, I"m launching a whole series on vector calc so line integrals in vector fields are definitely coming:)
@@DrTrefor Is it also possible show that line integrals are independent of the parametrization, using visualization ? Please include in the series if possible :)
Wow. Just wow. I got A for every single undergraduate maths course but still impressed so much by your visualization. I plan to study a master degree in mathematics next year, so I have a question that I hope you don’t mind to answer. My question is: “Is it possible to visualize maths at graduate level like what we can do with calculus, probability density function and linear algebra? “ Thank you very much for your lectures. And by the way, if you want to commercialize your courses in higher maths, I would be a loyal customer. I would be happy to pay $500/course(I think it’s reasonable price, compare to online courses in Actuary).There are so few intuitive yet still rigorous maths course online. MOOC are just too easy, and recorded lectures from universities are just too dry and lack of visualization.
Dr Trefor, u r simply the best. Do you have a textbook? U make mathematics an interesting series to watch 😜! I always look forward to ur videos. Thank you for making life a bit easier.
I'm actually working on some this semester. Soon I'll be release my differential equation playlist (it's coming after vector calc) and that one IS going to have a custom, free, open source textbook. After I do that, I kind of want to go back and make maybe not textbooks but more like workbooks for some of these courses.
I am a college student from China.Honestly speaking,there are lots of Calculus videos in Chinese webs,but no one can rival yours.Thanks a lot.
Trust me If I had a teacher like you, I would't miss a single class. Your way of teaching makes maths fun and not just some problem solving methods and calculations on a notebook. Thank you sir.
I am from the United States and trust me, you guys always say “I am from India” immediately. Why? What does it have to do with anything?
@@hydropage2855 you are right. I don't know why do we do it. But may be to let content creaters know a little about their global viewership.
You are a fantastic teacher, the fact that you are able to make it so simple shows how much you understand. (it applies for the other videos as well)
Yeah, it shows he understands both the topic and the way his students learn. Rare combination
I especially appreciate how the concept gradually unfold and the time and derivative respect time get in to play. A great interpretation about line integral.
No one destroys calcukus lecturers in uni so well as Dr. Trefor. This is on high level.
Greetings from India !
Really appreciate the teachings which are making my understanding of the subject a lot better.
Glad they are helping!
This is legit the best math channel on UA-cam.
Thank you!
I'm trying not to cry while in the library
I've been trying to understand this for so long and in a couple of minutes... there it is! Oh my god thank you so much
Can’t imagine that people before learn these stuff without ur help, definitely tough for them.
seriously thank you for formatting this in a way that makes it easy to understand what’s actually going on behind these integrals
I love how enthusiastic this man is! It's almost contagious
You're an absolute hero, this makes so much sense, I wish regular teachers were as helpful as you are
Thank you so much Dr. Bazett, because of the visualization and intuitive description I actually understand what the line integral represents, at first I didn’t even know what I was trying to actually calculate!
this channel is one of the best channels i have ever seen about calculus
Thank you!
Best explanation that I've seen of this idea. Great work!
You have no idea how helpful this video has been. Thank you so much for the stuff that you do.
YOU ARE A GENIUS! I am going to remember the snow bank example for life.
I would just like to say THANK YOU for making the conceptual explanation walk hand in hand with the visuals. That was something I had hoped to cover more when taking calc 3 and it helped so, so, much.
Super underrated channel! Definitely will recommend. I would go more into why I love this channel but I have to study for a Calc 3 midterm!
Much appreciated!
So grateful to have someone who teaches the concepts in such a great manner 🙏✨✨
Man, it is so difficult to imagine what is line integral but after this video it's very clear . Thank you 👍
Sir you are definitely helping me pass Cal3. Thank you so much for making these well-explained and visualized series!
only 99.3K subs ! there should be 10M subs for the quality of teaching you are providing.
So close!
What a beautiful introduction to a rather tricky concept. Your choice of example makes the concept far more clear than any textbook could.
Super impressed by the vids in this series. Really well explained and visualized!
Much appreciated!
@@DrTrefor I was gonna say the same thing. Your visual aids are intuitive, and I wish watched this 2 years ago when I was in Calc 4. This is top notch!
This made my day! All of my friends were struggling with this and l was so scared but luckily yours is the first video l stumbled upon and now l have a crystal clear concept of this!
This channel deserves at least 5 million subscribers. This channel is painfully underrated 😔😔
I hope it gets there ha!
I owe you my life professor, you just saved my semester, thank you.
You're really saving my class. THank you ^_^
I always love intuitive introductions!
Glad they are helping!
Man this is so cool. I was searching for some videos to learn about this topic in spanish but there are only people telling you the formula of the integral and making the calculus straight up, but I really wanted to understand the concept before digging into the exercises and this helped me so much. Thank you a lot!
Oh Brother Trefor you have done it again - many thanks! Another superb compliment to Lectures 19 & 20 MIT 18.02 Multivariable Calculus.
Another banger. Your teaching style is so good.
Very helpful
Love from INDIA🇮🇳🇮🇳🇮🇳❤️❤️❤️
The way you present the material makes so intuitive and easy to approach. This by far the best explanation for line integrals i have seen out there . Automatic subscribe from me, you got me hooked . Thanks Doc !
This stuff makes a lot more sense when muliple youtube professors explain it to me and draw me some pictures. Thanks for relating it to arclength.
Wow! Great video. I've been refreshing some Calculus III material since it's been about a year since I've taken the course and your videos are really helping :)
Great to hear!
Such a great tutorial! Thank you for explaining things soooo clearly.
You made me feel the subject.
One of the most informative UA-cam vids ever.
Thank you so much sir, you explain everything to the root and even give examples! Great for us students who aren't fortunate enough to have a teacher with an explaination style that fits us.
man u r a lifesaver, I have studied this topic in college for about a month and did not understand a word, but this video has made this concept way easier, thnx a lot man
@Christin Kunjumon That's why I don't attend college lectures...Khan Academy and This channel are more than enough
I didn't realise how much I didn't understand until I watch this. Thank you
This videos are awesome! Greetings from Chile
Really appreciate the content you created! I learnt calc back in undergrad, but I forgot so much. Your videos helped me to pick up and extended original knowledge base. Thanks!
Greetings from Pakistan!
These visualizations really help to make sense out of these equations.
Appreciate your work.
How did i not find this channel man i loved every second of it instant subscribe
Your explanation made the concept way easier to understand. Thanks a lot
Oh my goodness! You are the coolest! I can't wait to be smart enough to get into this! Totally fascinating they way you sell it! Thanks!
The best visuals and explanations I have seen so far. Immensely helpful for Calc 3 (II) refresher I am taking currently with edX. You were meaning when "k goes to infinity" instead of "n going to infinity"--but all of us understood!
Thanks!
Thank you so much, I really appreciate that!
love from bangladesh sir, your videos helped a lot to understand the topics deeply. keep doing the good work.
I have to commend you for your graphical representations, they are much appreciated
Great series! Your enthusiasm really makes this better
Thank you so much!
WOW ,great got a simplistic understanding in detail to such an important topic,THANKS
Snow analogy is so good. I surprised that Trefor didn't connected blue curve and circle with half-transparent barrier and then didn't said "This is snow height about what I was talking!"
I m really wasting my time and money in college .
U r an irreplaceable gem sir
Educational & instructive ... Excellent presentation!
Thank you. You saved my time. You explained well in less time.
Glad it helped!
absolutely fantastic explanation!!
Glad it helped!
Prepping for the GRE and didn't get a good grasp of calc 3 thanks for these vids dude
You ideas to explain line integral was awesome and i like it
Glad you liked it!
@@DrTrefor I send this to all my friend in my college
This video really helped me visualize what I was calculating when I was doing the calculations. Thanks a lot your explanation was very thorough and helpful!!
12:00 hey guys just a tip, this can be also written as the integral of f(g(t),h(t)) . |dr/dt| . dt
or the integral with respect to t of the function parametrized, times magnitude of the derivative of vector function with respect to t
Great explanation! It helped me a lot. Saludos desde Argentina!
Glad you liked it!
The way ur teaching is awesome sir 😊
it's nice to know you're now a doctor. Props!
Haha been one for five years, but finally got around to changing the channel name:D
This video made me feel smart
Thank you very much for your time and effort.
Nice video, as always!
1) It would be even nice to point out that, the pythagorean thing can be written simply as | r'(t) | , and that | r'(t)|.dt denotes the infinitesimal arc length.
2) I hope you also add in coming up section , the line integrals of a vector field.
Good point. And of course it's the same thing, but some texts also write it as |v(t)|. Anyways, I"m launching a whole series on vector calc so line integrals in vector fields are definitely coming:)
@@DrTrefor Is it also possible show that line integrals are independent of the parametrization, using visualization ? Please include in the series if possible :)
A very good introduction of the line integral. Thanks.
Glad it was helpful!
Amazing seriously outstanding
Keep it up :)
Wow. Just wow. I got A for every single undergraduate maths course but still impressed so much by your visualization. I plan to study a master degree in mathematics next year, so I have a question that I hope you don’t mind to answer. My question is: “Is it possible to visualize maths at graduate level like what we can do with calculus, probability density function and linear algebra? “
Thank you very much for your lectures. And by the way, if you want to commercialize your courses in higher maths, I would be a loyal customer. I would be happy to pay $500/course(I think it’s reasonable price, compare to online courses in Actuary).There are so few intuitive yet still rigorous maths course online. MOOC are just too easy, and recorded lectures from universities are just too dry and lack of visualization.
Not even concept, but yes trying to visualize and have clear mental pictures is super important all the way through grad school
Excellent video
Loving your classes. Thank you thank you 🙏❤
Understood and practical 👏🏻
Amazing video, and very well explained. Thank you!
😍😍😍😍amazingly explained as always..
love from india 😊
Thank you!!
THANK YOU SO SO SO MUCH! your videos, explanation and everything is perfect for me! instant subscription :D You are great at explaining things.
Thanks for the sub!
Dr Trefor, u r simply the best. Do you have a textbook? U make mathematics an interesting series to watch 😜! I always look forward to ur videos. Thank you for making life a bit easier.
I'm actually working on some this semester. Soon I'll be release my differential equation playlist (it's coming after vector calc) and that one IS going to have a custom, free, open source textbook. After I do that, I kind of want to go back and make maybe not textbooks but more like workbooks for some of these courses.
@@DrTrefor I am sorry to ask this but will these youtube videos and text book remain free for next 1-2 years?
@@rin-or3no pretty sure they're gonna be free lol
@@DrTrefor Great Idea. I think a workbook would be very helpful .it would be a great way to test ourselves
you taught so good, keep doing it.
I appreciate that!
Awesome awesome awesome. So concrete and so specific
Extremely underrated.
Thanks a lot sir 🙏, respect from🇮🇳
Finally i understand line integral
Thank you so much sir for making us clear our concept and visualization helps us alot in understanding the concept of line integral
Man : Hey Trefor, Why not get more views on your video?
Trefor : Because I don't make videos for view.
Thankyou so much for the amazing explanation:)
You're very welcome!
Thanks sensai, you helped me again
First class explanation
it is awesome to learn visually and your explanation is great 👍
Thank you! 😃
This is so beautiful. Thank you.
I always like your stuff and teaching skills sir
omg this video is incredible!
Awesome explanation sir!
I'm from Brazil, I am doing a physics major at UNB ( universidade de Brasília ). Thank you for your videos 👍
cool! Good luck in your degree:)
I loved this derivation, simple, consise, and beutiful
Thank you sooooooooo much sir LOVE from INDIA❤️🇮🇳
Why do math books not explain things as easily as the professor in the video? In 10 minutes of this video, I saved myself hours of pain.
EXCELLENT 💫✨