Finding the scalar potential function for a conservative vector field // Vector Calculus

The fundamental theorem of line integrals told us that if we knew a vector field was conservative, and thus able to be written as the gradient of a scalar potential function, we could evaluate any line integral almost trivially by just evaluating that potential function at the endpoints. But how do we FIND the scalar potential function? This video introduces that method. First we test that our vector field really is conservative using the test we saw previously. But after we know the method applies, we apply a trick involving alternating integration and differentiation to get a handle on the constants that come up, and ultimately get the scalar potential function. Finally we see an example were we use the potential function for a specific line integral.

0:00 Goals
1:00 Test for Conservative
2:50 Find Potential Function
9:43 Compute Line Integral

MY VECTOR CALCULUS PLAYLIST:

OTHER COURSE PLAYLISTS:

OTHER PLAYLISTS:
► Learning Math Series
►Cool Math Series:

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

SOCIALS:

[euva]

I clicked "like", not for the sake of the big Youtube algorithm in the dark sky, but because you are good teacher.

[yologreatdose]

Omg your an absolute legend Dr.Trefor. I have spent hours trying to understand each 1.5 h lecture only to realize this man here just took a 1.5 h lecture to 12 min and made it 5 times easily to understand. I salute you for you time and effort to make student life to learn much more enjoyable.

[NeelShah]

When I first saw line integrals I was really scared of it. After watching your videos on vector calculus series seems like a piece of cake now. One of the best teacher ever. Thanks a lot for all your hardwork.

[gosiagniadek]

I swear to God your videos explain in 15min things which I was trying to understand for the last 7 weeks of lectures. Thanks for your work

[bite_ketansharma]

I spent two days in frustration trying to understand this, and you taught it to me in twelve minutes, thank you.

[ericktapia]

This man is the goat! I practically passed my semester by watching @Dr. Trefor Bazett videos (specially the playlist of multivariable calculus and linear algebra). I have a lot of respect for this man; the time and work it takes to record and animate videos like this is not short nor easy.

[markpadley]

Absolutely superb explanation - I am returning to this area of study after many years. How I could have done with YouTube and Dr Bazett back in the 1980's! It would have saved me hours and loads of stress! Now it is my turn to communicate aspects of this subject to engineers and computer scientists - After a gap of some 30 years, I have caught up in just a few hours what I was expecting to take a few weeks of study - great resource Trefor- thanks

[KushagraMishra-ps]

Thank you for explaining this in an easy language, I literally wasted 1-2 hrs in study material while you explained it in 10 mins!

[ΓιώργοςΤ-ετ]

I have a habit.I click like before i see the whole video, because i know that it's gonna be a perfect one!Thank you!

[scrappybuilds]

Thank you, Dr. Bazett! Currently taking Calc V and this series of videos has helped a lot with my broader conceptual understanding.

[rohitchowdhury]

Love and respect from INDIA.
Thank you sir.

[akbeh]

Very awesome video. It made calculus concept clearer that I ve been studying since 1, 2 years

[simonwax]

This really helped me see the process after much confusion thanks.

[mohitshakya]

Your lectures are just amazing and quite helpful, thankyou so much for your lectures ...

[tanayasharma]

i knew i would learn things quicker here, so skipped the online college lecture and came here to learn it the easy way instead of wasting 1 hour in the class

[AdolfKambinda-fp]

If you just do all three integrals and find their union you gonna end up at the same place. Great video by the way

[Inner_Sphere_s]

Thank you so much for this sir
U did a great job
Now it is too easy to understand potential function.💕

[micolcresto-dina]

going through examples like this is great! would be cool maybe to see more of these. Maybe like a playlist on doing difficult questions from each topic and going through them slowly...

[oliverbrewster]

This series is so helpful! Thanks so much

[poojagurjar]

Namaste sir ji 🙏🏻
Why it is necessary that 'C' is a function of (y, z) . it may be a single constant