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
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!
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 :)
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
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 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 !
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.
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!
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
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!
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!!
Geometry we can visualize this whole derivation as just pulling the curve C into a straight line, computing it’s arc-length, finding what the “pulled-tight” version of the curve above C is, laying it out on the x axis and then just performing a regular integral on that curve on an interval equal to the arc-length of C
Oh yes, I've been looking forward to the vector calculus playlist. I have a question, Dr. Trefor; do you plan on going any higher in terms of math? Abstract Algebra, Real Analysis, Topology?
Topology is the most likely of those (I'm an algebraic topologist) and I think CZcams needs a really good series on that. I could do analysis or algebra, but I actually think the standard introductions have lots of resources for those already and I don't know if my particular blend of animations would add that much on top. Instead, for higher level content I'll probably do more one-of videos or mini series on cool topics, a bit like 3blue1brown does a some point.
Is that Riemann sum correct at 9:06? I was expecting 'n' to be the upper bound on the sigma.
oh great catch, yes of course!
@@DrTrefor lol
you actually understand what this means jeez bravo
@@chconstans4630 so you didn't understand that?
@@chconstans4630 it makes sense tho
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.
Greetings from India !
Really appreciate the teachings which are making my understanding of the subject a lot better.
Glad they are helping!
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.
No one destroys calcukus lecturers in uni so well as Dr. Trefor. This is on high level.
Can’t imagine that people before learn these stuff without ur help, definitely tough for them.
only 99.3K subs ! there should be 10M subs for the quality of teaching you are providing.
So close!
This is legit the best math channel on CZcams.
Thank you!
You're an absolute hero, this makes so much sense, I wish regular teachers were as helpful as you are
this channel is one of the best channels i have ever seen about calculus
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
YOU ARE A GENIUS! I am going to remember the snow bank example for life.
This channel deserves at least 5 million subscribers. This channel is painfully underrated 😔😔
I hope it gets there ha!
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!
seriously thank you for formatting this in a way that makes it easy to understand what’s actually going on behind these integrals
So grateful to have someone who teaches the concepts in such a great manner 🙏✨✨
I love how enthusiastic this man is! It's almost contagious
Man, it is so difficult to imagine what is line integral but after this video it's very clear . Thank you 👍
You made me feel the subject.
What a beautiful introduction to a rather tricky concept. Your choice of example makes the concept far more clear than any textbook could.
Sir you are definitely helping me pass Cal3. Thank you so much for making these well-explained and visualized series!
You have no idea how helpful this video has been. Thank you so much for the stuff that you do.
Very helpful
Love from INDIA🇮🇳🇮🇳🇮🇳❤️❤️❤️
You're really saving my class. THank you ^_^
I always love intuitive introductions!
Glad they are helping!
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.
This videos are awesome! Greetings from Chile
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.
I owe you my life professor, you just saved my semester, thank you.
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!
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!
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
One of the most informative CZcams vids ever.
absolutely fantastic explanation!!
Glad it helped!
Oh Brother Trefor you have done it again - many thanks! Another superb compliment to Lectures 19 & 20 MIT 18.02 Multivariable Calculus.
I didn't realise how much I didn't understand until I watch this. Thank you
Another banger. Your teaching style is so good.
Such a great tutorial! Thank you for explaining things soooo clearly.
I m really wasting my time and money in college .
U r an irreplaceable gem sir
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.
Greetings from Pakistan!
These visualizations really help to make sense out of these equations.
Appreciate your work.
I have to commend you for your graphical representations, they are much appreciated
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 !
Excellent video
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 :)
Prepping for the GRE and didn't get a good grasp of calc 3 thanks for these vids dude
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
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
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!
Your explanation made the concept way easier to understand. Thanks a lot
this man is a goddamn war hero
- engineering/compsci/physics/chem/math students, 2021
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
Thanks a lot sir 🙏, respect from🇮🇳
love from bangladesh sir, your videos helped a lot to understand the topics deeply. keep doing the good work.
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!
Thank you. You saved my time. You explained well in less time.
Glad it helped!
Thank you very much for your time and effort.
First class explanation
Extremely underrated.
How did i not find this channel man i loved every second of it instant subscribe
A very good introduction of the line integral. Thanks.
Glad it was helpful!
This video made me feel smart
Educational & instructive ... Excellent presentation!
The way ur teaching is awesome sir 😊
Great series! Your enthusiasm really makes this better
Thank you so much!
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
Awesome awesome awesome. So concrete and so specific
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:)
Man : Hey Trefor, Why not get more views on your video?
Trefor : Because I don't make videos for view.
Great explanation! It helped me a lot. Saludos desde Argentina!
Glad you liked it!
WOW ,great got a simplistic understanding in detail to such an important topic,THANKS
Finally i understand line integral
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
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!
I loved this derivation, simple, consise, and beutiful
you taught so good, keep doing it.
I appreciate that!
Loving your classes. Thank you thank you 🙏❤
Belissimo!
Thankyou so much for the amazing explanation:)
You're very welcome!
😍😍😍😍amazingly explained as always..
love from india 😊
Thank you!!
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!!
Thank you so much it is really well explained
Thank you sir, you helped us too much.
Thanks sensai, you helped me again
Amazing seriously outstanding
Keep it up :)
Understood and practical 👏🏻
omg this video is incredible!
Thank you sooooooooo much sir LOVE from INDIA❤️🇮🇳
thanks a lot this concept is going to useful for students who are preparing for jee advanced exam
Amazing explanation
EXCELLENT 💫✨
Geometry we can visualize this whole derivation as just pulling the curve C into a straight line, computing it’s arc-length, finding what the “pulled-tight” version of the curve above C is, laying it out on the x axis and then just performing a regular integral on that curve on an interval equal to the arc-length of C
Oh yes, I've been looking forward to the vector calculus playlist. I have a question, Dr. Trefor; do you plan on going any higher in terms of math? Abstract Algebra, Real Analysis, Topology?
Topology is the most likely of those (I'm an algebraic topologist) and I think CZcams needs a really good series on that. I could do analysis or algebra, but I actually think the standard introductions have lots of resources for those already and I don't know if my particular blend of animations would add that much on top. Instead, for higher level content I'll probably do more one-of videos or mini series on cool topics, a bit like 3blue1brown does a some point.
Thank you so much sir for making us clear our concept and visualization helps us alot in understanding the concept of line integral
Superb Explanation
You are a genius
Respect 🙏
Very helpfull, thank you!
This is so beautiful. Thank you.