Tensor Calculus For Physics Majors 003 | Two-Index Tensor Examples

[@andrewrezendes]

PLEASE DO NOT SKIP STEPS... Your current method is your unique strength as an educator. Also, let the view count and your personal desire dictate volume. Non-short answer: By starting with what is clear you BUILD UP the intuition of the general forms. This is a tactic that gets forgotten about somewhere in University courses. Until students come to a tutor and we have to use this "first principles" tactic, with examples, anyway. Simplest Example: Try asking students WHY anything to the zeroth power is one. Typical answer: "Cause Teacher said." On Volume of content: We can hit the play, pause buttons at whim. This isn't a credit based course where we have to be concerned about the volume of content on a unit exam. (Oh shit, maybe there is an exam...) Put as much volume as you feel adds good perspective. If anything, I think that heavier breakdowns are better. I would rather watch 5 videos to describe 5 topics, than one video that shows 5 examples of a topic. Thanks again bud.

[@footballpromos2148]

excuuuuuuuuse me,my man andrew has many other strong aspects as an educator :)

[@patrickcampbell8092]

These are very helpful. Thank you for showing the matrix expansions and "elementary" algebra that most books might skip over.

[@alefdias4468]

I like the step by step and the time you take to explain the physical meanings of the maths you do, no problem with longer videos to do it properly.

[@doge3707]

Wow this is amazing! I always wanted to learn about physics from the unabomber himself

[@AndrewDotsonvideos]

heckin roasted

[@ゾカリクゾ]

I am da true thug doge! >:(

[@heheheeh2781]

@@ゾカリクゾ gg ez owned git gud mountain dew doritos

[@isaacspivack26]

I like the depth you go into by showing all the matrices, it helps build intuition.

[@jm3415]

Definitely take your time and show all the steps please!

[@fardeenrafiq]

I'm a beginner but your videos help me a lot to get a glimpse of what it's like to study the advanced Physics. Thanks!!

[@stevewhitt9109]

I agree with Andrew Rezendes DO NOT SKIP STEPS! I have seen MANY MANY vids on Tensor Calculus, but I have gained more insight and intuition from Andrew Dotson than all the others put together. It is because he takes the time to make sure you understand everything and now I have. Steve Whitt, Iva, SC

[@AndrewDotsonvideos]

Thanks for the feedback!

[@Mohobofo]

Appreciate the videos bro. Appreciate the thoroughness. Most physicists just generalize and it is so abstract. The math is so intuitive for them. So thank you for explicitly explaining.

[@jflopezfernandez]

This series is amazing. I'm a math major trying to understand physics, and I hated when authors would use the implied summation because I had no idea how it worked until this video when it seems completely logical. Please don't skip any steps to try and shorten the videos; these videos are great because they're detailed, and after watching two and a half hours straight so far, I'm excited to keep going

[@akay37]

All i can say is thank you so much for this series.....

[@JohnDoe927]

Nobody: Skip steps! Professors: Sure nobody, I'll skip all the steps and leave them to the class!

[@ゾカリクゾ]

I'm no genius here, but I think having a bit of the theory behind tensors should go before more examples. I think these were a good introduction to tensors (though I don't know about this, don't take my opinion as completely valid)

[@DoTtAllRon]

I'd like to see the EM stress tensor as well! I've not quite caught up to the end of the series yet, so apologies if you get to it in a later video. Awesome work!

[@Mforader1792]

Yeah dont skip! Yo thanks again fam!

[@Mforader1792]

Rnd 2.....fight. lolwhat up!

[@Mforader1792]

Back lol bro youre getting mad airplay but its very much so sinking in !!! You da best dude!

[@franciscohamlin7544]

Shouldn't that energy integral at 14:54 have a factor 1/2 in front??

[@ゾカリクゾ]

10:49 "The proof is left as an excercise for the viewer" NO PLS

[@heavennoes]

Wait, how is the kinetic energy equal to integral of v^2dm, shouldn't it be v^2/2 dm

[@quarksgluons]

E&M stress tensor FTW

[@kobsterrock]

I know you're holding off on covering transformation rules, but I was curious... Doesn't the Einstein summation convention only work for combinations of contravariant and covariant components? also, The pace is perfect, E&M Stress Tensor please!

[@deeptochatterjee532]

I think so, but my Continuum mechanics professor did the same thing and just made it easier since we didn't know what contravariant and covariant meant.

[@macmos1]

yes, that is correct.

[@anshsrivastava1059]

The first tensor I encountered in undergrad physics was the quadrupole moment tensor, not the inertia tensor. ;-(

[@oldfire3107]

Obviously, I wanna see more examples in addition to those explained!

[@ゾカリクゾ]

It looks like the quality of the videos has increased. Nice!

[@aram9167]

When deriving the expression for the inertia tensor at the end, using bra-ket noation in the angular momentum would probably save you some time and make some things easier to see

[@CoreNexusGaming]

Please do both of the other tensors before moving on! i think it would be really interesting

[@ronaldoenderez8786]

I love your lectures on tensors and matrices, your beard kinda reminded me of James Maxwell, your the next Maxwell, I like your passion on physics, keep up the good work.😊

[@alfonsoguevara8661]

you should do the 2 tensors, btw thank for your through videos that have been helping me a lot in classical and quantum.

[@robinsonchukwu7295]

Wow... I can't believe I'm actually understanding this... How far I've come 😁😁

[@heavennoes]

good job.

[@duncanw9901]

How do you not have more subs smh also YEEEET more vids in this the better

[@tailslessons9634]

I know that we haven't gotten to contra/covariant tensors and vectors yet, but shouldn't the Electric Susceptibility tensor have lower indicies?

[@한두혁]

Hello! I am glad to see your Tensor calculus video:) However, for the electric susceptibility tensor, shouldn’t it be one upper index and one lower? (Comparing the rank of the tensor, between the left and the right of your equation, it doesn’t match.) But Im not sure about this and your comment would be helpful thankyou!

[@mcraden616]

I can't wait till these tensor videos are useful to me

[@NihalPushkar]

5:45 not necessary, u can only have diagonal terms and still it is not parallel to E

[@klong4128]

Good INERTIAL-tensor (mechanical engineering) and Physics-tensor(electrical engineering) introduction to TensorCalculus . Mathematical-Physics coming soon ?

[@zamiralice5498]

18:29 is not r * w = 0 because they're perpendicular?

[@raunaksarada]

pls make more videos on tensors

[@patrickcampbell8092]

Picky sidenote: does it make physical sense to integrate over mass?

[@AndrewDotsonvideos]

dm = rho dV. so you're really integrating over a volume element, with a density that might have dependence on something like r

[@patrickcampbell8092]

ah, yes, I see now where you mentioned it. dm becomes r^2sint dr dt dphi.

[@compphysgeek]

mass is additive, so it absolutely makes sense

[@angelmendez-rivera351]

You can integrate over any additive quantity.

[@abhinovenagarajan.s7237]

At 14:15 after evaluating the integral, you say this is the MoI of a small mass a distance R away. But the integral is done over a sphere of radius R and the final result you get is also that of the MoI or a solid sphere. So isn't that what you've calculated?

[@reubenler7784]

Freaking best explanation!

[@edonisalijaj8204]

Are u gonna cover whole tensors greater than 2?

[@juliecrawford9428]

Please do a vid on LorentzTrans.

[@ApplepieFTW]

Why was the second row, and not the second column used around 7:00? Shouldn't the entire y vector be put in the second column (consider for example the identity matrix)?

[@AndrewDotsonvideos]

Multiplying out the sussepitibilty matrix times the E vector is row times column. first row times E vector is attached to the x basis vector. Second row times E vector is attached to y basis vector and so on. What you're suggesting would be Column times column which is not a valid method of matrix multiplication.

[@devashishshah9021]

These videos are soooooo good!!!!

[@WaveSound123]

I want these two tensors as well. At least the EM stress tensor would be awesom to see. ( EM exam btw, please send help xD )

[@Onegod40-v4h]

Thanks Sir,for guidance through basics

[@eliaskristen4755]

Thank you sooo much this comes at the perfect time

[@ama7510]

sliding right through the dm's when integrating

[@antrikshrathore5151]

for the Inertia mass Tensor, shouldnt s = r/sin and not s = rsin?

[@Mforader1792]

Bro so I'm really getting this. The objective I need this the electromagnetic susceptibility tensor. That'd be epic to do a video on specifically. I think I have some value in see it done out. I can follow at this point point. I'm getting there with connecting mass and mechanics in both newtonian and vuccuo. Objective. Find the Lambda.

[@Mforader1792]

Transpoistionining and gravitational lensing have my attention in full.

[@Mforader1792]

Thanks for considering doc!

[@HuggumsMcgehee]

*Edit: Ok, I've worked the double sums out the long way, but I still don't fully understand what you mean when you said that we changed the basis. And looking at the final result I got from the double sums (you end up getting that r x ω = x^1*ω^1 + x^2*ω^2 + x^3*ω^3) I see how changing i to j works, but why is that even necessary? **Edit: I just figured it out. Changing from i to j allows you to factor the sum of ω^j out of the integral. Now that I see the final result however, what's the difference between all of the steps we took and just changing the letter i to a letter j? I'm confused about how you got "s = r*sin(theta)". If "s" is the distance from the origin to a given mass element, then what is "r" and what is theta? I'm also having trouble understanding why after about 21:00 you changed the "i" to a "j" and got rid of the delta. I do not have the strongest linear algebra background. By the way, this is BY FAR the best intro to tensors I've seen anywhere. No exaggeration. Thanks for posting.

[@samuelhawksworth1923]

I think it’s just more correct, even though i=j, they could be different which would render the kronecker d = 0, this equation for angular momentum applies only to where kronecker delta = 1, where i= j. The j represents all components, even though i does too, the specific components may be talking about separate components of either i and j, this means that in the moment where they are equal, the equation is correct. It’s just to be extra precise and I probably explained this terribly

[@caldersheagren]

Quadrupole tensor please!

[@yuminti3368]

So what is tensor???

[@manognadk7917]

In calculating the moment of inertia of the solid sphere, we would get the final and as (2/5)ms^2 right since we assumed the sphere's radius as s. Just a small clarification.

[@multimhine]

hmm around 13:20, was the θ part of the integral supposed to have the third power of sine? Still a great video btw 👍

[@deeptochatterjee532]

multiMhine • yeah because the dV has a sine² term

[@multimhine]

Deepto Chatterjee Ah sorry my bad. Thought it was a 2

[@ModCrafterBot]

how did he just know the integral of sine cubed?

[@alexanderquilty5705]

For spherical coordinates do you guys not use Row, Phi, Theta? (That’s what I was taught in Calc 3). It doesn’t make a difference just a change in notation but I was just curious.

[@angelmendez-rivera351]

Alexander Quilty In physics, we use r, θ, φ for spherical coordinates, and ρ, z, φ for cylindrical. In my opinion, the physics notation makes far more sense and is easier to explain intuitively.

[@fosheimdet]

What book is being used for this series?

[@jflopezfernandez]

Tensor Calculus for Physics: A Concise Guide by Dwight E. Neuenschwander

[@urosgrandovec3409]

how can you rotate around a point?? isnt all movement just rotation around some time dependent axis??

[@angelmendez-rivera351]

Uroš Grandovec No. If this were the case, then translational momentum would just be equivalent to angular momentum, and vice versa. The fact that they are not implies otherwise. Also, you can rotate around a point just fine in 2 dimensions.

[@drover7476]

class series, good level of difficulty to explain the topic. although andrew you write sigmas very questionably and im not sure I can take it anymore

[@speedspeed121]

When are you moving to NM?

[@UnforsakenXII]

Ah, you beat me to it. I never published anything but keep at it! : D

[@deeptochatterjee532]

Can you explain more the situation of an object rotating about a point? Not the math, just what you mean by that.

[@ゾカリクゾ]

Imagine you have a sphere in your hand and it's fixed in place. You can rotate it though (like a trackball). Now rotate it as crazily as you can. What's the axis of rotation? There isn't (necessarily). The only thing you can say about it is that every little rotation you make is around the center of the ball. That's what he means by rotating around a point.

[@deeptochatterjee532]

Francisco Russo so basically the only fixed point is the center of mass?

[@angelmendez-rivera351]

Deepto Chatterjee Yes.

[@usingcaio]

I dream a world where he does a series on group theory for physicists

[@AndrewDotsonvideos]

It’ll happen eventually

[@kingplunger1]

@@AndrewDotsonvideos And... ? ^^

[@raunaksarada]

you are a good explainer bro 🙄 keep it up

[@1987joey1987]

i love that stuff

[@housamkak646]

i still didnt know what a tensor is

[@macmos1]

really don't like the use of superscripts to denote indices :/ use subscripts...

[@AndrewDotsonvideos]

You have to get used to superscript indices. Tensor calc uses both.

[@macmos1]

Andrew Dotson I know... it is used for contraction, but you’re not using them that way.

[@angelmendez-rivera351]

Marco M It is not used for contraction. Contraction can be denoted without indeces. Superscript indeces are used for contravariant transformations.

[@miguelaphan58]

show them andrew...!!!!

[@2300NoFear]

P = NP

[@porit1023]

Do you even lift dude? jk. looking buff!

[@СпасСтоилов-с2ю]

You skipped a lot of steps and this video looks totally disconnected from the first two. You start building up the math from the ground and then suddenly in this video you jumped too much ahead.This video is not very useful.