I like theta much more for the angle between the projection of the vector onto x,y plane and the positive x axis because it is what we are used to for all of the math before Calculus III before introducing the z axis (when dealing with the (x,y) plane). It is easier to remember for me, but that's mostly a matter of personal preference.
honestly, you're an amazing teacher andrew! will be doing my undergrad y1 for physics this coming month, excited to dive deep into the world of physics
Why the hell physicists have to disagree with mathematicians? 😆 I'm a physics student and I agree with the mathematician's version cause that's what we learn in polar coordinate before getting into spherical version.
I was reading through the second edition of "Introduction to Electrodynamics" by Griffiths, and found the conversions (p. 45), but couldn't really understand them, as no derivation was shown; however now that i watched your video its crystal clear. Thanks! Sometimes when you don't understand something (e.g. a derivation, or a result) the best thing to do, is try it out yourself.. (but couldn't since i was travelling in a bus).. Danke!
The notation used in this video is the dominant one (not just in physics but also in engineering) while the notation used in most North American calculus texts is almost never used beyond Calc III. That means anyone planning to take advanced math courses should be following this video, regardless of field of specialization.
I love how passive aggressive he is when talking about whether to use the convention of mathematicians or physicists but proceeds to use the physics convention lmao
Wow sir... This was the only perfect video available on TH-cam. Sir my deep request to u, please upload these types of calculus videos on derivations. Thank you sir 😍
DUDE, I'm new the channel so just saying hi! but seriously, I'm currently taking E&M and my grade on the first exam was a 72 and I scared shitless.. ill be watching out for your videos to help me out!
Ill definitely look into to it thank you! Ive come to the conclusion that its a rinse and repeat process. I just have to come to terms with the fact that I'm going to fail miserably a million times and one before I finally crack the code to success in my journey through physics. I look forward to it. P.S. keep up the great work!
Something I had a realllly hard time with in E&Mwas reminding myself that this is all trying to describe something that's real. I had to work towards not just looking at it as one math problem after another, and start asking myself what I would expect the solutions to look like and if they made sense physically. Asymptotic behavior goes a long way!
Andrew Dotson exactly what my Professor informed me. He said stop looking at these problems algebraically but more from a geometric perspective. That it’s important to justify the answer.
Thanks. Very helpful. Until now, I’ve always thought of x=r sin theta times cos theta as meaning ...r sin theta tell you the degree to which cos theta is maximized. As if r sin theta is like a potentiometer working on cos theta. If r sin theta is zero then cos theta is minimized. If r sin theta is 1 then cos theta is a full sin theta.
You're putting out a lot of content; hope you're enjoying it as much as the rest of us.Also, can we just make messy hair a staple characteristic of mathematicians? (I'm down.)
Why is there disagreement between whether or not the angle is phi or theta? What does it matter? It's just a variable name right? I could call my coordinates pizza, dog, chocolate instead of x,y,z
The theta swapping makes perfect sense once you realize physicists work sitting down and looking forward while mathematicians work standing up and looking down, you know, on the physicists. 😉
A disagreement over something that trivial? I feel like theta should be the one on the xy plane but it doesn't really matter. Which side do you think Newton would've taken :P
It's annoying. You really can just switch theta and phi, but it just gets confusing when reading a calc book, and then doing something like E&M where it's switched. Newton totally would have called one theta_1 and the other theta_2 lol
46 and pi Haha I was joking, physics and math are both awesome! Technically the polar angle (the one that appears "flat" in this video, on in between x and y) is traditionally denoted , θ (theta), just think of polar graphs in two dimensions, where you only use r and , θ. So that is the general argument for using , θ as the polar angle, although using it as the azimuthal angle (the angle that is between z and the r) instead of φ (phi). Again it's just convention, although the reason mathematicians use θ for the polar angle is because of its use in the polar coordinate system.
This video explains the spherical coordinates in the most concise yet crystal clear manner. Kudos! Your channel just gained a new subscriber.
bork
Feels so weird to see a proper video after all the meme vids with Papa Flammy. Keep it up, Andrew!
I like theta much more for the angle between the projection of the vector onto x,y plane and the positive x axis because it is what we are used to for all of the math before Calculus III before introducing the z axis (when dealing with the (x,y) plane). It is easier to remember for me, but that's mostly a matter of personal preference.
thanks a lot man, been a long time since I learned this in my first year in college, needed a refresher
Don't drink and derive
Good one
When u drink u go to do..... But when Andrew drinks he study and do wonderful things so shut up
This is the best explanation of spherical coordinates I have ever seen!! I am a Physics student and this was very helpful, thank you very much !!
i have no clue what’s happening in this video but his handwriting is unbelievably beautiful
honestly, you're an amazing teacher andrew! will be doing my undergrad y1 for physics this coming month, excited to dive deep into the world of physics
How is it going?
Why the hell physicists have to disagree with mathematicians? 😆
I'm a physics student and I agree with the mathematician's version cause that's what we learn in polar coordinate before getting into spherical version.
totally agree haha
Concise and helpful! (from a physics major) Thanks! It's so easy to derive, I don't know why I was never shown this in school!
wow after all these years i finally understand!
That was awesome, bro!!❤️
I was reading through the second edition of "Introduction to Electrodynamics" by Griffiths, and found the conversions (p. 45), but couldn't really understand them, as no derivation was shown; however now that i watched your video its crystal clear. Thanks!
Sometimes when you don't understand something (e.g. a derivation, or a result) the best thing to do, is try it out yourself.. (but couldn't since i was travelling in a bus)..
Danke!
agreed
Amazing explanation! The best I have come across yet : )
Clear, consize, nice voice. Great video
Tnx Andrew to probably explain this fact.....you are a good teacher......
you are an amazing teacher! helped me a bunch to visualize it better, thanks so much
The notation used in this video is the dominant one (not just in physics but also in engineering) while the notation used in most North American calculus texts is almost never used beyond Calc III. That means anyone planning to take advanced math courses should be following this video, regardless of field of specialization.
best video I have ever seeeeeeeen. thank you so much !!!!!!
2:38 Orthogonal vectors or orthonormal vectors?
Orthogonal is generalization of orthonormal.
Don't be oversmart...
Superb... Very well explained... Thnx bro
I love how passive aggressive he is when talking about whether to use the convention of mathematicians or physicists but proceeds to use the physics convention lmao
Wow sir... This was the only perfect video available on TH-cam.
Sir my deep request to u, please upload these types of calculus videos on derivations.
Thank you sir 😍
took my uni teacher 2 hours ... you just explained it in 5 minutes and way more better
شكرا لك من اعماق قلبي
فلسطينية تدرس الرياضيات ارجو من الله ان يوفقك 💞💞
its really good and easy to understand, thanks mate :) and yeah dont drink and drive lol
DUDE, I'm new the channel so just saying hi! but seriously, I'm currently taking E&M and my grade on the first exam was a 72 and I scared shitless.. ill be watching out for your videos to help me out!
Stick with it! there's great resources online for E&M, especially griffiths worked solutions.
Ill definitely look into to it thank you! Ive come to the conclusion that its a rinse and repeat process. I just have to come to terms with the fact that I'm going to fail miserably a million times and one before I finally crack the code to success in my journey through physics. I look forward to it.
P.S. keep up the great work!
Something I had a realllly hard time with in E&Mwas reminding myself that this is all trying to describe something that's real. I had to work towards not just looking at it as one math problem after another, and start asking myself what I would expect the solutions to look like and if they made sense physically. Asymptotic behavior goes a long way!
Andrew Dotson exactly what my
Professor informed me. He said stop looking at these problems algebraically but more from a geometric perspective. That it’s important to justify the answer.
_"I'm currently taking E&M and my grade on the first exam was a 72 ..."_
In my E&M course, I don't think anyone got better than 40 on the first test.
Thank you so so much your videos always explain so well and have helped me so much awh brilliant! :)
Thankyou for such a better explanation
thank you so much sir 🙏
i have been looking for this derivation all today
you saved my butt! i have a classical mechanics exam coming up but i'm weak at math so this is so helpful!!!
Thanks. Very helpful. Until now, I’ve always thought of x=r sin theta times cos theta as meaning ...r sin theta tell you the degree to which cos theta is maximized. As if r sin theta is like a potentiometer working on cos theta. If r sin theta is zero then cos theta is minimized. If r sin theta is 1 then cos theta is a full sin theta.
It isn’t r*sintheta*costheta, it is r*sintheta*cosphi
Thank you so much. It made perfect sense.
JazakAllah
Thanks 👍
Thankyou so much for this video, Sir! It was reallyy very helpful!
Really nice exposition other than the equation for r right at the beginning.
Thank you. The video solved my question.
Damn that‘s trivial but how do you write that pretty?
Well I love watching your videos and I love that I can actually understand the math in this one with my measly calculus 1 background lol
Thank you so much!!!! I’ve never understood this 😭😭
this is what ı want thank you so much for your explanations and proofs
Thanks Andrew, Great Video!
That's a great one there.
Damn, that whiteboard has gone through quite some strugles😂
Pretty cool, it's really helpful!
Great video! I"d do one thing differently: I'd describe this as conversion of spherical to cartesian coordinates, not the reverse as you twice did.
Really Helpful thankyou
Bro casually makes life better😅
I salute you 👍, I am Indian, you are an excellent teacher..🙏🙏🙏🙏
That was pretty easy and cool, thanks buddy though, you nailed it
Thanks for the explanation.I understood the thing that my professor was trying to explain for a week now.
You're putting out a lot of content; hope you're enjoying it as much as the rest of us.Also, can we just make messy hair a staple characteristic of mathematicians? (I'm down.)
It feels good to do it! Glad you like it!
Well done bro very clear explanatiom thanks a lot
Thanks Andrew :)
Excellent
Excellent....
Thank u soo much it was very easy to understand nd u r cute😊
imo the inclination angle should start on the xy plane, and not the z axis. (pi/2 - theta for physicists and pi/2 - phi for mathematicians)
Well done 👍
that's so magical !!
Great playlist! thank you :-)
The best ❤️🙏
can you also make a vid about the derivation of the acceleration formlas, including taking the derivatives of the unit vectors plz?
You'd think after all the years mathmaticians and physicists would agree on something.
Why is there disagreement between whether or not the angle is phi or theta? What does it matter? It's just a variable name right? I could call my coordinates pizza, dog, chocolate instead of x,y,z
Best Explanation...
Very helpful. Thankz
arigatou gosaimasu 🙏
Great job
Thank youuuuuuuuuuuuuu for this video.
papa flammy says what's up
This is really dumb and unrelated, but I like how spiky your hair is 😂🙌🏽✨
Thanks. This was helpful
Thank you sir!
Does X'=y?
Brooo thank you so muchh 😭😭😭
Reminds me a little bit of calculus 3... which reminds me of headaches and tears LOL
Thanks dude.
you did great
this was great!!
Nice video!
please make a video about tensor.
Also this is how we learn it in my maths degree haha
I think, r = sqrt(x^2 + y^2 + z^2), not just x squared and y squared.
1:02
You saved my life
finally one i can understand
The theta swapping makes perfect sense once you realize physicists work sitting down and looking forward while mathematicians work standing up and looking down, you know, on the physicists. 😉
r is not equal to √x^2+y^2+z^2 if i am not wrong
I still regularly write letters backward too,
Very nice
Wow we are juggling the same stuff in our physics classe
excellent
A disagreement over something that trivial? I feel like theta should be the one on the xy plane but it doesn't really matter. Which side do you think Newton would've taken :P
It's annoying. You really can just switch theta and phi, but it just gets confusing when reading a calc book, and then doing something like E&M where it's switched. Newton totally would have called one theta_1 and the other theta_2 lol
Helpful... thank you..
May you tell why Physicists and Mathematicians disagree on the notation?
It's just a convention thing.
Andrew Dotson Yeah I first learned it the physics way and thought that it was the only convention. I've never seen it how mathematicians write it.
Because physicists are wrong.
Spencer Taylor Yeah I've since met a mathematician, and he says the same thing.
46 and pi Haha I was joking, physics and math are both awesome! Technically the polar angle (the one that appears "flat" in this video, on in between x and y) is traditionally denoted , θ (theta), just think of polar graphs in two dimensions, where you only use r and , θ. So that is the general argument for using , θ as the polar angle, although using it as the azimuthal angle (the angle that is between z and the r) instead of φ (phi). Again it's just convention, although the reason mathematicians use θ for the polar angle is because of its use in the polar coordinate system.
awesome
Lol am I drunk? Isn't this from spherical to Cartesian as opposed to the opposite?
your board needs some expo spray!!!
thanks!
Wow I understand it now coooooolll haha