potential function of a conservative vector field (KristaKingMath)

► My Vectors course: www.kristaking...
In this video we'll learn how to find the potential function of a conservative vector field.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@bman8540]

Just in time for my calculus 3 test in 30 minutes. Thank you! Your videos have helped me since calculus 1!!

[@kristakingmath]

I hope the test went well!

[@KirinIchiban]

Did the test go well?

[@bman8540]

@@KirinIchiban I got my engineering degree and have been a working professional 5 years this month :D

[@oggoatx2175]

@@bman8540 so dope !

[@Aj-oz3ek]

Currently 2 AM studying for a test about this and line integrals! Thanks for the videos!

[@kristakingmath]

You're welcome, Alex! Good luck on the test, I hope it goes great!! :D

[@brianzar1943]

You should be named "The Queen of Math". Thanks for those wonderful explanations.

[@kristakingmath]

+Brayen Zar You're welcome, I'm glad they're helping!

[@nipunasudha]

How can you be so clear & understandable? These are awesome!

[@kristakingmath]

+nipunasudha Thank you so much!

[@alienpuppy]

Thank you so much. Finally learned how to find the potential function after having watched 1000 videos

[@kristakingmath]

You're welcome, so glad it helped!

[@lizchatham5940]

Of all of my Calc III lectures, this is the one I missed. As soon as I saw the condensed explanations my calculus books, I came straight to your channel. Thank you again for a wonderful explanation! So clear and concise.

[@kristakingmath]

Love that! I'm glad I could help fill in the gaps. :D

[@GIFPES]

Amazing class! Despite the fact that I was understanding "scary crow" instead of scalar curl...ehehe....but please do not take it too seriously, I am not a native english speaker. One of the best classes I have ever taken on this subject!

[@ryanhillard7821]

Comment leaver here, this was extremely helpful, the way my calc 3 professor explained this idea was very confusing and full of "matching". While your explanation was clear and concise and helped me understand the theory and steps behind the problem. Anyways, thank you for posting this video.

[@kristakingmath]

Thank you so much for letting me know, I’m so so glad it helped!! ❤️❤️

[@mariasimon7622]

Thank you so much ❤️, greetings from a Namibian math major student. My gosh you make life easier 😂😅. Thank you once again 😊.

[@kristakingmath]

You are so welcome, Maria, I'm glad I'm able to help! Best of luck with completing your math degree, keep up the good work! :D

[@charlesasare3488]

You're the best. I wish part of tuition will be pay to you.

[@muwongeevanspaul9640]

Thanks so much Krista, I have fully understood. Please may the good Lord bless u so much. Really, so much , so much.

[@kristakingmath]

Thank you! I'm so glad everything made sense! :)

[@peteranderlan8858]

thank u very much! Greetings from an austrian engineering student! :)

[@kristakingmath]

Hi Peter! I'm so glad it could help. Thanks for the comment. :)

[@beachwave5705]

there is a much easier way to do this, but i only found out from a youtube comment in some other video from like 8 years ago integrate each portion of the vector field respectively so like for the (ye^x + siny) component integrate with respect to x and then for the other portion with respect to y if you get repeated numbers just use one of them add all your numbers together and add a + C

[@beachwave5705]

heres the comment: For anyone wondering, there's a much easier way to do this. Simply integrate each component of the vector field F by dx, dy, dz respectively, and the potential function is a combination of each unique term (i.e. if there are two terms that are the same, don't add them, just use one of them in the potential function).

[@PrepaidClaw]

Funny enough I came to this video to figure out the specifics of that exact comment, thanks for using the example from the video as reference!

[@beachwave5705]

@@PrepaidClaw tbh i completely forgot everything from calc 3😭 i just took my algebra final today tho so shit im still fresh on that

[@beachwave5705]

@@PrepaidClaw but it’s weird how when you’re on such a niche side of youtube you find relevant comments on different videos

[@chiragvaghela07]

Ma'am you saved the day! Thanks a lot.👍

[@ronniebyrd4618]

I one day too hope to be Math Jedi

[@Bartekkru100]

Where is @Ronnie Byrd? Is he safe? Is he alright?

[@ronniebyrd4618]

@Brent nope

[@ronniebyrd4618]

@@Bartekkru100 yeah man. Stoked about the election and looking forward to 202. Gonna be some real fireworks to top 2020! How are you holding up?

[@Bartekkru100]

@@ronniebyrd4618 Not American, but happy with the outcome anyway.

[@joshlehman2657]

great video. thank you very much. your videos really help. however, as a stickler on notation F is a vector please use instead of (, , ,) to show it is a vector

[@ensea_TV]

@Iphone 3G is showing that it is a vector while (,,) shows that it is a point

[@merthatayhocaoglu1668]

you are the best in math , Thanks my teacher ... !!

[@kristakingmath]

Well thank you very much, I'm glad you're enjoying the videos!

[@merthatayhocaoglu1668]

Thanks really İ Like it too much

[@TheCaner135]

YEAAAAAAAAAAAAH Finally some good fucking channel that explains this topic well, thanks a fuckton

[@hayathayatullah3787]

You made it as a sample as flowing water

[@nelschnyder]

how would we solve this if a third point was involved? ex: F(x,y,z)

[@hasan3545]

does the curl method for find if F is conservative always work? or does it only work for 2d vectors?

[@trazz99]

So what happens if say g'(y) = y^3 ?

[@iliaskarimi5751]

thank you sooooo much!!!

[@mowneekhachaudary]

thanks krista!!

[@ThilebanTheEngineer]

5:11 undefined if ln 0 or less than 1? you meant less than 0?

[@karimkhan1312]

excellent

[@backyardmachinist]

How do you find f(x,y,z)?

[@JimmyxMurphy]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

[@nithushan7763]

Should the potential function always have a constant?

[@maryammasanuri486]

why we dont need to integrate e^x which is equal to 1/x e^x?

[@kristakingmath]

The integral of e^x is still just e^x. There's no 1/x when you integrate.

[@justinabata6257]

Good food = Good brain

[@DASmallWorlds]

Late to the party, but isn't this suspiciously similar to solving an exact differential equation? I ask because I'm taking MV calc and differential equations/inf. series at the same time haha

[@mark4035]

ty :)

[@kristakingmath]

You're welcome, Mark! :D

[@namehere630]

Thank you! Have you left KZbin? :(

[@kristakingmath]

You're welcome, Name! I haven't left, I've just been busy with other projects. :)

[@stevenkurtscholz]

F is a vector not a coordinate point

[@CstriderNNS]

you talk to Quick you don't give us time to think about what you're saying

[@cesarc6044]

Pause button, rewind bonehead