This video explains the spherical coordinates in the most concise yet crystal clear manner. Kudos! Your channel just gained a new subscriber.

Feels so weird to see a proper video after all the meme vids with Papa Flammy. Keep it up, Andrew!

Don't drink and derive Good one

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.

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 have no clue what’s happening in this video but his handwriting is unbelievably beautiful

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 !!

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

Amazing explanation! The best I have come across yet : )

Wow sir... This was the only perfect video available on KZfaq. Sir my deep request to u, please upload these types of calculus videos on derivations. Thank you sir 😍

you are an amazing teacher! helped me a bunch to visualize it better, thanks so much

Clear, consize, nice voice. Great video

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!

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!

best video I have ever seeeeeeeen. thank you so much !!!!!!

you saved my butt! i have a classical mechanics exam coming up but i'm weak at math so this is so helpful!!!

Tnx Andrew to probably explain this fact.....you are a good teacher......

its really good and easy to understand, thanks mate :) and yeah dont drink and drive lol

Superb... Very well explained... Thnx bro

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 so much your videos always explain so well and have helped me so much awh brilliant! :)

Really nice exposition other than the equation for r right at the beginning.

That was pretty easy and cool, thanks buddy though, you nailed it

Thankyou for such a better explanation

that's so magical !!

Thank you. The video solved my question.

Thanks Andrew, Great Video!

JazakAllah Thanks 👍

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.)

thank you so much sir 🙏 i have been looking for this derivation all today

Thankyou so much for this video, Sir! It was reallyy very helpful!

took my uni teacher 2 hours ... you just explained it in 5 minutes and way more better

Thank you so much!!!! I’ve never understood this 😭😭

Pretty cool, it's really helpful!

Excellent

Excellent....

I salute you 👍, I am Indian, you are an excellent teacher..🙏🙏🙏🙏

The best ❤️🙏

can you also make a vid about the derivation of the acceleration formlas, including taking the derivatives of the unit vectors plz?

Well done bro very clear explanatiom thanks a lot

شكرا لك من اعماق قلبي فلسطينية تدرس الرياضيات ارجو من الله ان يوفقك 💞💞

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!

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.

Thanks Andrew :)

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.

this is what ı want thank you so much for your explanations and proofs

Great playlist! thank you :-)

Best Explanation...

Really Helpful thankyou

Thank you sir!

Bro casually makes life better😅

Thank youuuuuuuuuuuuuu for this video.

Great job

Very helpful. Thankz

Brooo thank you so muchh 😭😭😭

Nice video!

Damn, that whiteboard has gone through quite some strugles😂

Damn that‘s trivial but how do you write that pretty?

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.

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)

Thanks dude.

you did great

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

Very nice

This is really dumb and unrelated, but I like how spiky your hair is 😂🙌🏽✨

Thanks. This was helpful

papa flammy says what's up

Thanks for the explanation.I understood the thing that my professor was trying to explain for a week now.

finally one i can understand

2:38 Orthogonal vectors or orthonormal vectors? Orthogonal is generalization of orthonormal.

You saved my life

arigatou gosaimasu 🙏

awesome

Reminds me a little bit of calculus 3... which reminds me of headaches and tears LOL

Wow we are juggling the same stuff in our physics classe

this was great!!

Helpful... thank you..

excellent

please make a video about tensor.

Thank you bso much

Nice !!

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

I still regularly write letters backward too,

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

Also this is how we learn it in my maths degree haha

very good

Omg this makes sense now

I think, r = sqrt(x^2 + y^2 + z^2), not just x squared and y squared.

Wow I understand it now coooooolll haha

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. 😉

Yo, first :Ρ Edit: I wasn't, awesome video though

r is not equal to √x^2+y^2+z^2 if i am not wrong

Does X'=y?

You'd think after all the years mathmaticians and physicists would agree on something.

u r handsome, hilsen Ittqa & Sylvia.

your board needs some expo spray!!!

thanks