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.
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.
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 :)
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
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'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
@@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!
Dear Professor Trefor, which book of calculus you are using for your video contents? Your videos are really great for learners.. Please make motivational videos on real analysis, topology and functional analysis to cover the basics..
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 :)
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 RU-vid 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.
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!
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.
Do you plan on making more videos that explain textbook content? Because vids you make are very helpful at generelizing content without watering it down.
Vector calc playlist is actually mostly complete. In my actual course though, I do give my students lots more examples but I'm a believer in active learning so I want studenst trying lots of practice problems
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!
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.
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
Why can't we unwrap the circle to an intervall of 2pi? It should be easier, as it's based on a circle...I know it'd be difficult to break the 3d with 2 variables function into a 2d one variable...however it should be easier to make an integral on a 2d plane rather than in a 3d plane...am I wrong?
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.
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!
Hello Dr. Trefor thanks for your youtube channel. It's inspiring me a lot. Could you tell me what program do u use to visualize 3D graph and shaded it with colors? thanks!
