at 11:30, where all of the unit vectors are in a box, the e_phi term should have a minus sign in front of the sin term. The derivation of the unit vector was completely correct, just when I re-wrote the expression I missed a sign. Sorry about that
As an engineering student of electronics major I was looking for this derivation in many sources but they don't exactly explain about derivations of unit vectors. So glad that I now know how to derive it. Thank you ❤
This video deserves soooo many more likes. I saw like 5 videos before this and couldn't understand a thing...but this man made it all easy. Thank u thank u ^^
For our first class this week, our professor emailed us to review spherical coordinates in advance, so I just watched all your Spherical Coordinates derivations as my review. Thanks for the clear and to the point derivations!
now I am in your place,our professor emailed us to review spherical coordinates in advance, so I just watched all Andrew's Spherical Coordinates derivations as my review
Hi Andrew, I am currently a non traditional physics student attending mechanics and I found this extremely useful. I think my Mechanics book 7th edition Fowler and Cassidy is normally up to par with reviewing calc 3 stuff but I was struggling to remember how systems move vectorially in a sphere. This derivation made much more sense to me. I was literally spinning my wheels trying to visualize it. Thanks so much!
These spherical coordinate vids are really good.🙂. Everybody needs to go through this stuff and this demonstration is nice and complete, and at a reasonable pace. As a teacher I am learning a lot about how to explain things.
I do t really know what a laplacian is, but the rest of these have made sense so far. It took me a second to get what you were doing at some points, but I guess that's because I've only been through two physics courses and am only about to take my first multivariable calc class.
Thank you so much for this explanation. I have to derive the toroidal coordinates for a homework assignment and this process is really helping me along.
Great video, but with one omission: During the calculation of the magnitude of the e vectors for phi and theta, you don't explain why there aren't any cross terms when squaring the trinomial before taking the square root. I believe the reason is that one doesn't exactly square the trinomial before taking the square root, but rather one takes the dot product of the trinomial with itself, before taking the square root. The dot product elimintes the cross terms, since the unit vectors are mutually orthogonal. Of course, this also explains what happens to, say, x-hat: The dot product of any unit vector with itself is exactly one, so it disappears.
Your final statement for the conversion for theta hat to cartesian, in the coefficient of y hat, has sin (phi)cos(phi), but should read sin(phi)cos(theta) , as you derived in the video.
I think this video is good. But there is a minor mistake in here, which is about the er and er hat. You didn't clarify whether er is a vector or a "unit vector". Things just went suddenly from er to er hat. Hope you can clarify that!
I don't know about Laplacian. Can I follow this course or should I learn laplacian first and then watch these videos. Until now, it is okay. Should I learn laplacian for next videos. Or Are you going to teach it in the future videos?
I'm building up a library of derivation videos that will provide the tools to derive the laplacian. Some knowledge of multivariable calculus would be helpful though.
loved the video! but why does the r unit vector requires only one step to get, and the other two (theta and phi unit vectors) requires two step? Thanks in advance!
How do you derive the cartesian unit vectors in terms of the spherical coordinates? I know you can just take the inverse of the transformation matrix, but is there another way? Pls help.
Your final solution at 11:30 is slightly wrong. The î term for the phi unit vector should be negative. Otherwise great derivation! I'm using yours instead of my books because it is so much more elegant.
Andrew Dotson Well, if you want to try it out, you just have to get the Cauchy Riemann conditions in polar form, take some second derivatives equating to zero, switch to the z-rho plane, and then it's pretty straightforward from there! I'll be putting out a video on it soon, if you want to check it out!
I'm not gonna say I was anticipating this upload But I did check for it on my lunch break (no I don't have a job I just call it that because in school that's what it for me - a break. In which I normally don't even eat lunch anyway 🤔)
Thanks, mate! But you made only ONE MISTAKE. After 11:25: the middle term of e-theta must be cos(theta; NOT phi).sin(phi).y. Just compare it with your result after 7:23. Someone has to do the dirty job of verifying things on CZcams ;-)
Watching this instead of studying for calc is the best decision I've made in my academic career
Trigonometric cancellations are among the most satisfying things to watch.
at 11:30, where all of the unit vectors are in a box, the e_phi term should have a minus sign in front of the sin term. The derivation of the unit vector was completely correct, just when I re-wrote the expression I missed a sign. Sorry about that
In my opinion the minus-sign is already there!
Such a beautiful explanation - exactly what i was looking for!
Biological Penguin glad it helped you!
You name😂😂😂 is hilarious
As an engineering student of electronics major I was looking for this derivation in many sources but they don't exactly explain about derivations of unit vectors. So glad that I now know how to derive it. Thank you ❤
your handwriting is actually satisfying
This video deserves soooo many more likes. I saw like 5 videos before this and couldn't understand a thing...but this man made it all easy. Thank u thank u ^^
You left out a minus sign in the x-hat term, for the e(phi) vector at the end of the video - ... otherwise :) ... GREAT video!
For our first class this week, our professor emailed us to review spherical coordinates in advance, so I just watched all your Spherical Coordinates derivations as my review. Thanks for the clear and to the point derivations!
now I am in your place,our professor emailed us to review spherical coordinates in advance, so I just watched all Andrew's Spherical Coordinates derivations as my review
Hi Andrew, I am currently a non traditional physics student attending mechanics and I found this extremely useful. I think my Mechanics book 7th edition Fowler and Cassidy is normally up to par with reviewing calc 3 stuff but I was struggling to remember how systems move vectorially in a sphere. This derivation made much more sense to me. I was literally spinning my wheels trying to visualize it. Thanks so much!
These spherical coordinate vids are really good.🙂. Everybody needs to go through this stuff and this demonstration is nice and complete, and at a reasonable pace. As a teacher I am learning a lot about how to explain things.
Watched more than 10 videos but got here what I was looking for
Thank you sooo muuuch, you saved my semester, I love youuu 💕
I do t really know what a laplacian is, but the rest of these have made sense so far. It took me a second to get what you were doing at some points, but I guess that's because I've only been through two physics courses and am only about to take my first multivariable calc class.
Thanks for your great explanations!! I'm all set to do my 'scary' homeworks which now don't look that scary!!
Thank you so much for this explanation. I have to derive the toroidal coordinates for a homework assignment and this process is really helping me along.
Awesome video with great explanation...
just a small correction
At 11:29 e_hat sub phi will be [- sin(phi) x_hat + cos(phi) y_hat]
Yes yes......anyways very nice video....cleared my concept
Watched more than 5 videos but got here what I was looking for
11:01
"That's not what e's look like"
Me when going through my old math sheets and not being able to tell what's "e" and what's theta
he says things look like hahaha so funny
Andrew's reaction at 10:38 is priceless! I love that xD
Thank you so much sir it is really helpful.
From India
Beautiful presentation...love it man
Just what I was looking for! Getting that degree one unit vector at a time :D
thank god you're not my teacher i wouldn't be able to focus I would just be lost in your beautiful eyes!
other than that great video thank you!!
In the summary at the end you forgot a minus at the e_phi vector
You're right, the derivation was correct though. Just re-writing it I missed the sign!
Very helpful derivation was looking for it everywhere but found here only. thanx
Thank you for simplifying this so much.
Andrew,this video was quite helpful and if possible do make a video on Non Inertial Systems
Some people make physics critical but some like u make it so dam simple as that, as it is
Whoop! I've finally started multivariate calc and have the need for this. 🤤🤤I'm so excited
Great video, but with one omission: During the calculation of the magnitude of the e vectors for phi and theta, you don't explain why there aren't any cross terms when squaring the trinomial before taking the square root. I believe the reason is that one doesn't exactly square the trinomial before taking the square root, but rather one takes the dot product of the trinomial with itself, before taking the square root. The dot product elimintes the cross terms, since the unit vectors are mutually orthogonal. Of course, this also explains what happens to, say, x-hat: The dot product of any unit vector with itself is exactly one, so it disappears.
this guy is just 'purrfect'
Wowwww so my whole life I've been deriving these geometrically (vector projections and the like) who knew there was an easier way lol I'm dead
It was really nice explanation 😊😊love it!!!
Very good vedio in which topic nicely explained.
Your final statement for the conversion for theta hat to cartesian, in the coefficient of y hat, has sin (phi)cos(phi),
but should read sin(phi)cos(theta) , as you derived in the video.
vey helpful...you have done a brilliant job!
Thanks for helping. Love from India
Great explanation thank you!!
I think this video is good. But there is a minor mistake in here, which is about the er and er hat. You didn't clarify whether er is a vector or a "unit vector". Things just went suddenly from er to er hat. Hope you can clarify that!
i guess last clip missed the minus sign with "sin" for e of phi
Excellent video on spherical coordinates thankqq sir
LINK TO OLD VID
I don't know about Laplacian. Can I follow this course or should I learn laplacian first and then watch these videos. Until now, it is okay. Should I learn laplacian for next videos.
Or
Are you going to teach it in the future videos?
I'm building up a library of derivation videos that will provide the tools to derive the laplacian. Some knowledge of multivariable calculus would be helpful though.
Andrew Dotson , aye, aye, captain. Good at it. Let's go...
Yeah
Great Sir
Thanks a lot
Thanks so much for this! Btw I think you missed a sign at 11:25
loved the video! but why does the r unit vector requires only one step to get, and the other two (theta and phi unit vectors) requires two step? Thanks in advance!
you are a god u saved me thank u
how did the partial derivative come in and how did you define e,sub,u. i don't get that part
How do you derive the cartesian unit vectors in terms of the spherical coordinates? I know you can just take the inverse of the transformation matrix, but is there another way? Pls help.
You save me a LOT!
at 11:25 y-hat component of e(theta) should be cos(theta)sin(phi). and x-hat component of e(phi) should be -sin(phi)
Your final solution at 11:30 is slightly wrong. The î term for the phi unit vector should be negative. Otherwise great derivation! I'm using yours instead of my books because it is so much more elegant.
Whoops, the derivation is correct, just the final boxing of all of them had a typo!
@@AndrewDotsonvideos Yup, yup.
Thanks for this video! ❤️
Great work man it helped a lot thanks
Extremely helpful!
This was very helpful, thank you
Thank you! Ily
Awesome video
Beautiful
Have you ever derived the Laplacian using Cauchy Riemann conditions? It's really fun if you haven't done it yet.
Can't say that I have!
Andrew Dotson Well, if you want to try it out, you just have to get the Cauchy Riemann conditions in polar form, take some second derivatives equating to zero, switch to the z-rho plane, and then it's pretty straightforward from there! I'll be putting out a video on it soon, if you want to check it out!
Andrew Dotson It's been uploaded! Here's a link if you want to check it out!
m.czcams.com/video/_TXtj2TOnBU/video.html
good explanation bro..it helped a lot
At about 5:00, what happened to r-hat when finding the derivative? I am not quite following how you just ignored it. Thanks
at 11:30 shouldn't there be a minus sign before sin(theta)X ?
And how can i change the unitary cartesian vectors in function of unitary spherical vectors?
I'm not gonna say I was anticipating this upload
But I did check for it on my lunch break
(no I don't have a job I just call it that because in school that's what it for me - a break. In which I normally don't even eat lunch anyway 🤔)
Great video!! But let me take a nap first... I’ll continue later.
At 4:00 , the expression we get for er(hat) and er in terms of x(hat) , y(hat)... are actually coming same ! Why is it so ?
Got the answer; because the er is already normalised
iam sad because this shows me how much iam suck at physics
what about derivatives of unit vectors in different coordinate systems?
Thank you indeed
The hot tr kinda contributed to my understanding 😅😅
thanks for the help dude!!!!
Bro, how could it be said that vector along direction of θ is the partial derivative of vector r with respect to θ?
Thanks a ton mate!
Y piece of the theta should be cos 0 sin phi.
Link the previous video.do you assist with project work.
Good video
That white board is triggering my ocd.
2:36
Where did this step come from ?
gratly expplained
THANK YOU
Nice! I want such a nice board (;
Still useful for engineering
Thanks, mate! But you made only ONE MISTAKE. After 11:25: the middle term of e-theta must be cos(theta; NOT phi).sin(phi).y. Just compare it with your result after 7:23. Someone has to do the dirty job of verifying things on CZcams ;-)
plz , Dr. Can you clean your board man!
100k🙂
Im doing engineering and i watched this video for my exam (illegal)
Can I take your photo
You messed up the "e sub theta hat" and "e sub phi hat" at the very end of the video.
❤
Plz make vedio about four vecter
jtm
ur whiteboard is grody asf sun. good vid tho
Clean your whiteboard please!
Thanks bro, but your hair scares me as if it has been troubled by the sheer complexity of your derivation.
stupid way