Finding a Potential for a Conservative Vector Field
HTML-код
- Опубликовано: 14 окт 2024
- 🔍 Unlock the Secrets of Conservative Vector Fields! 🔍
In this video, we explore the fascinating topic of finding the scalar potential for a conservative vector field. Understanding this concept is essential for anyone studying vector calculus or physics.
What You’ll Learn:
Defining Conservative Vector Fields: Recall for a vector field 𝐹 to be conservative we have a scalar potential function 𝑓 so that the following is satisfied: ∇𝑓 = 𝐹
Step-by-Step Process: Follow along as I demonstrate the method for finding the scalar potential 𝑓 We’ll integrate the partial derivatives of the vector field and make important observations along the way.
Why Watch This Video?
Clear Explanations: I break down complex concepts into easy-to-understand segments, perfect for both beginners and advanced students.
Boost Your Skills: Enhance your mathematical toolkit and confidence in tackling calculus problems involving vector fields.
👍 Join Our Learning Community!
LIKE this video if you find it helpful!
SHARE it with classmates or friends who are studying calculus!
SUBSCRIBE for more insightful tutorials on calculus, vector fields, and mathematical concepts!
#ConservativeVectorField #ScalarPotential #VectorCalculus #Mathematics #MathTutorial #EducationalContent #LearningCalculus #ProblemSolving #Physics #Engineering #Integration #PartialDerivatives #CalculusConcepts
![Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs [Divergence, Gradient, and Curl]](http://i.ytimg.com/vi/lKXW7DRyyro/mqdefault.jpg)
Hi all! Wanna help a RUclips education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
😁 You’re a legend!
Honestly RUclips might be one of the greatest educational tools ever created. I have learned almost everything from my calc III and physics class from RUclipsrs willing to spend their own time to share their knowledge on the subjects. Thanks so much!
What is a good RUclipsr for physics???
Doc Schuster is pretty good!
Hey I'm taking the same classes as you, im in fye taking physics and Calc 3 at purdue
I hear that soothing, slightly droning voice, and I know everything is going to be OK, because Patrick will do what my overpaid professor should have done.
Damn straight.
Amen Brother lol
@Theodore Myles Shut up bot
Google should change their logo to honour Patrick for a day. It should say, 'Patrick- saving asses of STEM field majors since 2007.'
Here in 2021, yES
Saint Patricks day
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).
But this way works too, just more work!
are you sure? I want to believe
@@lonkbadonk3195 it totally works and has saved me ample time!
Thanks mate! For once I didn't follow patrick's video so you helped me out so much in less than a minute!
I derived something similar but you just put all the pieces together for me, thank you so much
it doesnt work for every of the equation though I tried
Patrick is by far the best maths tutor and he knows it :p
just doin' the best i can!
I feel like I need to invite Patrick to my graduation. I basically learned calc II and III from him!
In 2024, you're still being watched, yet you continue to engage with others. What an incredible Professor.
I have been having problems with these types of problems all day and you helped me so much. I truly appreciate your videos. Thank you a million times and thank you for inspiring me to teach just like you do in the future. Millions of thanks.
A generation of degree students that owe their career to PatrickJMT lol
4 years later another generation owing the same debts appears.
On my will will be written: Send Civil Engineering degree to PatrickJMT.
literallyyyy
1000%
several generations man. Almost 15 years of this guy saving our asses
I have no idea why i pay £9000 a year to go to university on the UK. I learn so much more from these videos than I do from university. Wish i could send Patrick the money instead! :') Thankyou Patrick!!
i also wish you could send me the money too ;)
maybe i can print out some certificate from the school of patrickjmt for you if you do...
im sure she's probably graduated after five years.....
Lol, $9000 a year. That's a community college in the US.
Excellent. If it weren't for you I would be screwed. College instructors do not know how to break it down to us here at Virginia State University. They move too fast and expect you to grasp it on your own time. Well they are right, I spend my personal time trying to figure these things out. Watching you on youtube has allowed me to keep up.
IMO: Professors take doctorate level courses in which they learn to prove mathematics and explain the theoretical side. When they teach college classes they tend to get caught up and focus too much on theory which is almost never applicable to us students (at least at the undegrad level) (unless of course the professors have theory questions on tests then yes) But for the most part this is why I preferred my high school teachers and youtube lectures, because they taught me calculus and physics without all the crazy theory that takes up too much class time. It's great to know for trivia but theory should only take a small fraction of the total class time to be able to go over questions.
Thanks Patrick , your explanation is brief and simple .. I advice all the students if they skipped the classes , they should watch your video to understand . Good job
I just want to say that math texts in college are terrible.
+MisterBinx yes, they usually are
+MisterBinx I agree. My university of harvard at urbana sampahgne has terrible txtbooks
Agreed. They over-complicate things and give you formulas that you don't need.
Thomas Calculus Any-th Edition is pretty terrible. I used it for calculus 2 and prayed I wouldnt use it cal 3... lo and behold, here I am.
@@DuckyBalboa same lmao
I've watched your videos for over a year now. I just want to let you know that I acknowlege and respect your ability to write left handed on a white board and rarely smudge. As a fellow lefty, you inspire me.
Patrick saving lives! Thanks
Lmao you're here?? I have to say I wasn't expecting to see you... XD
Calc 4 midterm in 6 ours and these are FINALLY making sense. Thank you Patrick!!!
Ah thank you! I have my calc 3 final in about 8 hours and I still hadn't figured this out. Helped a ton!
same here ......
@@pagoeagle_4198 You aren't in CME100 by any chance are you?
Hey thanks a lot for your videos, I have a complex analysis midterm tomorrow and your uploads are a great way to review the computational aspects of it.
how did it go?
@@Playground639 got a B 🤷♂️
Someone should nominate you for a nobel peace prize for saving math grades everywhere (so serious)
There's a hole in my backyard, and sometimes I like to get naked and paint myself orange, sit in it and pretend I'm a carrot.
Thank you so much for this video!!! My professor has a really thick asian accent and I can never understand what he is trying to say. When he went over this lesson I had no idea what he was talking about, but you made your video really clear. Thank you again!!!
Exam in 10hrs, had completely forgot how to do this. Your video brought it all rushing back. Thanks
Thank you for your help patrickJMT! You're my hero.
Wow, you explained this concept so clearly and simply! I wish my professor would go through examples like this in lecture. Thank you so much for posting this!
I've been confused about the h(y,z) for weeks at 3:45, now it makes sense where it comes from! Thanks! Wish my university professor explained it that way...
Thanks man, I had alot of issues with these for no reason, they are easy now because of your teaching.
Wow why couldn't my professor have just explained it like that, that just made soooo much sense thanks a ton!!
glad i could help you :)
Putting your math tutor ad in patrickjmt video is probably the worst ad placement I have ever seen...
I know. "Pay for what you are already getting for free!'
wow... for someone who took this class years ago this really helps me remember it better
you are a god..3 semesters of calculus i would have failed royally if it hadn't been for your videos...god bless you man
on another note, these videos have helped me since calc 1, thanks patrick
Thank you so much I’m in calculus right now and this sections lecture was a bit confusing. This video helped a lot.
Patrick, you saved my love for math! REALLY! While I know that my current professor is a smart guy, he's not really good at simple explanations. I could not wrap my head around this concept. And now... It feels so natural to think about it! You truly are a GEM! I'm watching EACH of your videos before I try working book problems. I feel better about my upcoming final exam.
patrickJMT you are my life-saver!!! Thank you so much!!!!
Studying for a test tomorrow and this is quite helpful. Thanks.
You are the only reason I am passing calc at uni. Honestly man I would be so screwed without you.
Even after a whole decade after uploading, Patrick still saves a poor mechanical engineering students will to put effort into math. Me and my passing grade will be forever thankful.
Hey Patrick i would like to thank you very much!
I am a student from Brasil of Control & Automation Engineering.
Thank you so much for your videos it helps me a lot.
That is it.
Thank you so much for a clear, thorough, well-paced explanation!! I wish you were my Calc teacher.
Been redoing webassigns for an hour. you really saved me a lot of time. Thank you x
hey dude..... are you still there!! fella thats a great teaching!! the best teacher ive ever seen in my entire life!! may u live long!!
T minus 15 minutes before class. Patrick JMT to the rescue. Thanks brah
Yeah, Patrick I am not even kidding I spent 2 lectures being lost because my professor is terrible at explaining things, and with 1.5 watches of this video I was able to do my homework in 30 min flat. THANK YOU SO MUCH
This was super helpful I greatly appreciate it I'm studying for finals right now and this had me stumped thank you so much.
In a self-taught online calc 3 class... thank you so much!!! Much better than their convoluted proofs...
Thank you so much! I've been looking for so long for an explanation and this explanation was wonderful
Thanks heaps mate, this helped me out a lot in a time of need! Happy travels
Thanks a lot Patrick, you're the best!
i was soooo confused, but this helped alot!!! i appreciate all of your vids. thanks so much!!!
Thank you! Very helpful. I now understand something I didn't understand from the lectures.
I would pay handsomely to have you as my personal tutor! Thankyou for helping me through my uni math assignment :D
Oh my gosh ! Thank you so much ! There is no german videos or helpfull threads. I tried to understand this for like 4 hours. I hope i got it now, You are my hero! Thank you!
haha ^
Thanks a lot for helping me get some of the more confusing aspects of my calc 3 final! And thanks for breaking up the monotony of studying by inadvertently drawing a dingus at 2:19.
Finals preparation! Thanks, patrickJMT!
that was a perfect explanation, thank you so much
My math book skipped a lot of the steps on how or why they did things. Thanks for making it clear! 🙂
she has the phd in mathematics, not me. she is one who does research and publishes, not me. she is the one writing a book on math and art, not me! :)
i have an exam in an hour hope this helps
+Timmy Burch k
ba-dum-tss!
excellent explanation. Much better than my calculus teacher did. I understood everything perfectly. Thank you.
@patrickJMT That's true, I'm a Physics major and we're going into complex analysis, that stuff is pretty crazy!
Really digging the HD Patrick!!! It's actually easier to pay attention when the video is clear, believe it or not haha
Thank you patrick, your really a God send:)
I know this is a really old video but thank you so much for making this!
You have done it again!. Thank you JMT :)
wow was soooo confused about this until i watched this and now its like how did i not know how to do this! ( i mean that in the most flattering way possible lol). ur awesome! pretty much passed my math unit cus of you! :)
I couldn't understand my book, it skips so many steps. Thanks, you made it so simple
im gunna email my math prof and be all like, "you see, It isn't that hard to explain, so why in the hell can't you do it?"
I now understand potential functions!!! .. i re watched this video like 6 time to understand what i was doing wrong(everything)...
great job on the videos man you just explain thinks way better than my proffessor and judging from all the comments it looks like im not alone
You are awesome! srsly, I learn more from your short videos than my 2 hour lecture. Keep it up! I'm def going to show people this :)
@lxiam spread the word - id appreciate it.
shouldnt the answer be negative according to the definition of a scalar potential?
Great video!
Not surprised I’m the oddball out as I am a high school student watching a Calc video...
I was curious, trying to inspire myself knowing the math I do now is nothing compared to this. 😂
Very eloquently explained. Thank you.
Thanks so much! The clearest explanation of this I have found yet! :)
@RafamSales glad i could help you :)
Can you please upload Stokes theorem
Your videos are always helpful to me i am your follower .good job.
Thanks Patrick! Very helpful!
You're a legend! My book was way too confusing
patrickJMT>>Stewart Multivariable Calculus: 6th Edition
This actually makes sense now. Thanks! Keep up the great work!
i sat down for THREE hours trying to make sense of the lecture notes that i got from my math professor and i couldn't do it. I watch your ten minute video and BAM, it all makes sense! I've watched some of your videos and it makes sense EVERY time. whatever you do, keep making videos, because you don't know how many people you are helping! thank you so much!
the possibility of it being a function of x was ruled out when he did the first integration of 2x + yz. When he integrated 2x + yz, the arbitrary constant/function couldn't be a function of x, it could only be a function of y and z.
That was an awesome explanation man. Appreciate that!
Tnx , your helping everyone alot!
The double integral over D of confusion = PatrickJMT. Simple really.
Thank you so much! This video is super helpful! Couldn't have done my homework without it =)
Just what I was looking for. Great explanation! Thanks a lot :)
You're an angel! I can't thank you enough, Sir!
Thank you Patrick, this makes complete sense now!
Thank you sooooooo much for your wisdom!!
Great job! good verbal + written explanations
perfect! glad it helped :)
Oh my god, so potentials were actually this "easy"... I guess all that matters is how you explain :) Thanks a lot, I understood much more from this than reading in the course book!
this video was tremendously helpful! thank you!
Thanks man! Really helped me understand how to do this!
i am more surprised to find a video of 720p quality which was recorded over 12 years ago.
hi patrick, I don't need to say how helpful you are to us! I have a question. I find the potential by taking an integral for each component and set them equal because they need to give me the f eventually.I get the answers right so far but I'm wondering if that technique has any disadvantages or might fail me someday?? it shouldn't but I wanna make sure
Just saved me with this concept. Thanks homie