Vector Fields - Sketching 

You drew a swastika, but that's ok because you just gave a perfect explanation for drawing vectors right before my calc 3 exam on vector fields!

I’m here in 2022, thank you so much! This helped me a lot!!!☺️

If you understand this, you can almost understand everything in classical physics. Thank you very much. You are a Legend!!!

Couldn't learn how to plot vector fields in my class, but now I know exactly how to do them. Thanks so much!

jeez, this was so useful, after sweating over vector field theory for a couple of hours. thanks so much!

very useful stuff in many areas!! go vectors

Very time I type in a subject and I see my guy @patrickjmt name come up I get hyped. You know he does bits.

Thank you for making this video! Your method of making a values table was exactly what I needed to understand this! You taught me in 8 minutes what I've been trying to learn for 2 days now!

Thanks for nice explanation of the vector field plotting.

For some reason, the audio is being super soft for me so I turned on subtitles. Lol, look at 6:29. Anyways, thank you so much! This helped so much, I didn't even realize this video was made by you, your videos are always great!

Thank you! You've been helping me get through calculus since last year!

Thank u. U are helping me to study for my calculus exam which will happen in 1 week. Greetings from Brazil.

4:42 My professor did a drawing very similar to this when he did this in class, and I just see a swastika every time. I understand it's just because of the curl, so there's not really any changing it haha. But anyway, thanks for the video, I've got a test tomorrow morning :)

Thank you very much! You explained so clear that I understand how to draw vector field after watching your video only one time.

You might not be monitoring comments on this video any longer but I'll say this anyway: You and 3Blue1Brown Grant are the absolute best at pedagogy.

shouldn't the vector at (2,-2)` extend to the x-axis because it goes up 2 untis?

thanks mr. teacher; this lecture was quite helpful. thanks again...

I'm almost finished with Calculus 3 and I have Dif E next semester. I just wanted to say thank you for taking the time to make these videos. You have saved my butt for these courses. When I win the lottery I will be sure to send a nice chunk your way hehe

You got me through Algebra 2, and I thank you for that.

thank you so much, i was looking at the examples in my book, and i was just not understanding it. now it looks easy, you rock dude!!!

thanks you ,just wanted to say I really appreciate all the effort you put in making these videos . It really helped me and countless others . thanks

Thank you so much for posting this tutorial. I had a problem in plotting vectors for my Differential equation homework, but this tutorial solved my problem. This tutorial is better than my professor,,,,lol

Very Helpful, Thank You very much Sir.

Very helpful!

Does how pretty the picture look depend on how you pick your left side column points

Great vid patrick you should have made the equation F = yi -xj though.

vector fields are only used in more than 2 dimensions (2 free variables)?

HELPED ME ALOT!! Was getting confused with the exchanged x,y, i,j etc. NOw i totally get it.

Hello Patrick, THANK YOU so much for the work you are doing, I am studying at university in South Africa and your videos helped me pass math major for 1st year last year, I would have not made it without these videos. im doing chemical engineering which has scalar and vector fields, derictional derivatives, potential functions, vector integration, linear algebra, orthonomality and all that staff now and the videos are hard to find please help and let me know if they are on your site?

Amazing. You are such a legend! I had been worried for weeks about this stuff and it literally took 2mins to understand the concept. Keep it up!

Useful video thank you👍🏻

Brilliant! I got into this through programming but this helped me understand the maths and how algebra is exploring space :) Thanks dude

what F(x,y) gives a single dot with an arrow pointing out of it. I've seen those before. Would it be ? If so, how do you know which way the arrow points?

Very useful thank you

i love you patrick

Thanks man. You make it simple. Keep up the good work!

Wow, thanks! That was big help. I am glad I found your example.

Thank you so much 😭🙇‍♂️🙇‍♂️🙇❤

So the vector function you had, is that relative to the specific question or is it a standardised function for vector plots?

thank you so much Patrick! My math professor is absolutely useless, I learn everything from your videos

as always, you have made my life far easier. for that, i thank you good sir!

3-D vector fields example will be nice

@Hithall glad i could help you! : )

Thanks, very clear and well done preso

correct - excellent video but surprised others didn't spot the error.

Great job love the example. Thank you.

are those random points you chose to plug in?

Thanks ✨❣️

that was exactly what I needed, thanks!

Saved my life again!! Thanks!!

Wouldn't that last vector stretch to the x-axis? it goes 2 right and 2 up. 2 up from that position is the x-axis

Do you have a video for how to make slope fields for a differential equation?

I think in the end the wrong vector was sketched for the point (2, -2). It should have been or the point should have been (-2, 2)

@ManPuzzling no problem : )

Hi Patrick, I was wondering if you have a video on "the flow of a vector field"?

Thanks alot

Thanks Patrick!

On point, no pun intended.

Hey Pat, tnx for the Vid btw. was wondering if there's a way to identify a vector field by it's function without graphing it?

Thanks again for an awesome video!

What about for three dimension vector fields?

thanks bro. it helps me a lot.

thanks bro

@pr4life1016 That is exactly what I got also - so thanks for posting this comment. BTW: this is the first vector field I have seen drawn to scale. He picked his points judiciously so the vectors would not overlap and be confusing.Still it is a GREAT VIDEO.

again, just what I needed!

Good job man keep up the good work

thanks! Makes more sense now... But what if the equation is more complicated... i have something like (y)i + (6x^2 - 4x)j which gives me a weird set of arrows!

thanks, very helpful! I did have a question, what if the formula is i + j? I found this confusing as there is no indication of the x and y in that formula, unless we are to assume something, what should I be assuming?

fantastic maths thank you

our professor used this same function in class. we gave her shit because it looked like a swastika.

awesome

Great explanation. Thank-you!! :)

Very useful! Thanks a lot !

tnx JMT

very helpful, thank you!

This vector field is more commonly known as the swastika equation

this is great....

Can you solve F=

@1337zzyzx sure thing :)

Thank you!!!!! This just helped me so much! :D

This describes hurricane winds pretty much

Thanks :D and you should add a tag for slope fields for more views. :D

ok! :) good luck in the rest of your studies

4:37 Is this the final solution vector?

looool i saw that too!!!

4:30 - vector swastika

lol that happened to us in class and everyone cracked up!

What does it mean when students pays huge amounts of college fees for education and yet students are on RU-vid to gain free lectures?

there is nothing to say more thank u

what's up with the point (-2,2) lmao he wrote it as (2,-2)...

thanks

thanks man!

Nice video

not related, but it seems like most of people who make video about solving math problems are left handed !!!!

thank you sire

Most books assign i to x, j to y, and k to z.

I just jumped off a bridge.

thank uuuuuuuuu

Thank uuuuuuuuuuuuuuuuuuu

thank you ^^