Your handwriting's really nice :D It's spelled "demands", not "demends". I think you could've unpacked the Levi-Civita notation for the cross-product explicitly so it would be clearer for other people. At around 39:10, Φ should not be 90 + θ but rather 90 - θ, since Φ decreases when θ increases. It works out though, because cos(90 - θ) = sin(θ), which you mistakenly put as cos(90 + θ) = sin(θ). With the second coordinate system, the way you handled Φ geometrically had some flaws as well, but the components turned out to have the right terms. But I'm just splitting hairs here. Great job on this video, and I'm looking forward to the next ones!
@@AndrewDotsonvideos I just realised that cos(90+x) = -sin(x), so shouldn't F_x' = |mg|sin(x)+|f| since the the -|mg| would cancel out the negative with -sin(x)
Okay so far the feedback suggests I need to speak louder when facing the whiteboard, and I was a little hand-waivey with the inclined plane problem (which I recognized while editing the video). I'll be sure to be more careful with my arguments geometrically in the future. I'll also include a reference in the beginning of each video to explicitly state what will be covered so you don't have to watch the whole video to find out. Was debating fitting the whole section on vectors into this one video. Glad I didn't!
Andrew Dotson I'm almost a bit surprised how good this actually is! One more small thing you could consider to make it flawless is to put the audio through some "filtration" program to get rid of the static background noise. Looking forward to watching the rest, especially now that I just finished my exams!
BLAIR M Schirmer Well, you are an arrogant one, for sure. You apparently do not understand the concept of "context." This video is not intended as an introductory course nor for beginners, nor is it designed for people who have no idea of what a tensor. He has other videos designed for that type of audience. This is not his incompetence, this your damn incompetence for not knowing how to search videos on a channel. It's incredible how people in 2018 were still not aware of how to competently use UA-cam.
BLAIR M Schirmer Also, he DID mention the definition of a tensor very early on in a video, and then talked about it would be absolutely unhelpful to start talking about it immediately. So, looks like you have a bad case of not paying attention, or of being a dishonest prick.
0:00 Important Introduction ___________________________________________ The elements 4:53 Products of vectors and their intuition 6:29 Derivatives in vectors 7:35 the Gradient, Curl and Divergence ___________________________________________ What we do with them 9:20 we begin with coordinates 12:40 representation of a vector r in this coordinate idea 14:24 Basis 18:30 Dot product for the introduction of new concepts: Metric, Kronecker Delta ___________________________________________ Applying this products and ideas 20:28 Dot product between two general vectors 24:21 Cross product between two general vectors ___________________________________________ Quick note if you're not careful with angles 29:36 Comparison Dot product for x component and y component ___________________________________________ Physics problem 33:16 Block on plane intro 35:24 2nd Newton Law for the problem and the first way (non block-local x & y) 42:38 2nd way, we rotate our view so we are inclined with the plane (block-local)
This was a refreshing take on how to interpret dot, cross products and the gradient. I've never been quite as good at applied maths as at pure, so I relish this video and the chance to improve my understanding. Looking forward to learning tensors, I've never seen them before!
As a hobby student who came here through your meme reviews, this is absolutely the most helpful tutorial for tensors on UA-cam. All the other tutorials assume you already know the foundations, but as a hobby student my foundations are full of holes, so it's nice to see things like the Kronecker delta defined by a logical progression than with a bunch of words that don't mean anything to somebody who doesn't have a good foundation to start from.
AWESOME VIDEO! HYPED FOR THIS SERIES! *One suggestion*: Even though I know very little, You should've introduced Einstein Summation in the video first, that would've made your notation a lot less cluttered...
I was honestly very confused about our first few lessons in mathematical physics because there were so many new terms/symbols introduced (unlike regular math classes) like the Kronecker delta and Levi-Civita, so my fundamentals before tensor analysis is really fragile. This video really helped me review our past lessons, and I can say I have a much better understanding now on matrices and coordinate transformations. Thank you for being a very good teacher. Your explanations are very clear. Xx
Congrats for the great videos man!! I found a couple of minor errors at min 38. i) The relationship between phi and theta the way you are expressing them should be: phi = 90 - theta. ii) This error then cancels with a second one here: cos(90+theta) = sin (theta) !! With the correct phi / theta relationship, you can use instead: cos( 90 - theta) = sin (theta)
Andrew. Yeah it's me again lol Just wanted to make a suggestion for the series If videos are long (like this one), it might help to write the list of topics to be covered in the video and write clear titles when you are talking about them. Also, I don't know your exact plans, but I would do these videos once a week; you give some time for your viewers to see the latest video on the series and most importantly, to let the ideas sink in (I feel how tough these topics can be for people with no actual university-level education in physics, such as many viewers here). Anyway, great video :)
Thanks for the feedback! I think a list of topics at the beginning would be helpful. I wouldn't be able to make them more frequent than once a week if I tried. I think once a week or once every other week will be how it ends up playing out. Especially once we actually get to the more subtle math.
The fact that actual math and physics is actually being taught surprised me, since most (if not all) videos I have seen from this channel are meme/joke videos!
Good tensor-concept applied to static engineering vector (physics transformation vector) as an introduction to real-tensor (Einstein notation) such that layman easily understand from familiar realm understanding the complicated-unknown-tensor realm .Good example of illustration .
Isn't he still correct since the block is sliding in the negative direction? I think he just skipped a step, otherwise the equation would show that friction + the x component of the normal force is equal to the force, and therefor the acceleration experienced by the block, which is obviously not true. Sorry if I missed something.
I think he made a bouble mistake and got it right. Phi is not equal to 90°+theta, instead it should be 90°- theta. So eventually he got it right. I'm currently at 39:11
just wanted to see if there are any comments regarding the whole \phi = 90 deg + \theta and \phi = - 90 deg - \theta and is cos(90 + \theta) = - sin(\theta) or +sin(\theta) caused any confusion and there were some comments were it caused confusion how you dealt with the angles. The whole confusion could have been avoided if you had identified the opposite angle as \theta instead of introducing a new angle \phi. you want to make your life easier that's why you change coordinate systems because equations might have a simpler form in different coordinate systems. you don't want to introduce difficulties by a poor choice of angles ;) .. other than that, great series, keep it up!
I loved your explanation so far, despite only making it a couple minutes in. While some of the notation looked a bit foreign from your explanation I started to understand what the underlying concepts were. Thanks for these great videos! :D
I feel shame being a graduate student and still having a hard time grasping the nature of tensors, hope you will bring me some different perspectives since group theory and representation in quantum mechanics is just other words for nigthmare to me right now! Love from Paris and be safe
I really like how you explain setting up problems. Could you do more videos on setting up problems? My mind is drawing blanks staring at my practice problems in this classical mechanics textbook.
In the second example with the rotated (prime) reference frame, I got confused by the fact that you labeled your x-component as negative in the triangle and your y-component as positive which you changed later. If you use your angles properly, which you mostly did, then you don't need to place the negative sign in front of the components. They'll come out positive or negative based on their angles with respect to the relevant unit vector. I had to think about the issue with the sign of cosine as you did it in the problem. You're correct in saying that it's an even function, so if I flip the sign of the argument, the sign of the result will remain the same, however, because the angle between the unit vector i-hat and the gravitational force vector is oblique the resulting cosine will be negative. If you flip the sign of the argument, the cosine will remain negative. That was really throwing me for a minute and it's a very easy mistake for anyone to make. Honestly, still having a hard time thinking about how you introduce that to a student without introducing the sign in there in a potentially confusing way. You would've had to write "cos(90º+θ) = -sin(θ)." I also think it might be helpful to actually draw the unit vector and force vector of interest tail-to-tail. That way you can see what angle you're dealing with better.
DUUUUDE this is pure gold. I just have a minor issue: could you use barred letters when changing to another coordinate system? the primes look the number one (1). Thanks bro.
I think you should have written the Levi-Civita symbol with lower indeces, and the component of the cross product also with a low index, a contravariant symbol. Or, alternatively, kept the upper index on the cross product, but written the Levi-Civita symbol with mixed indeces. This would have been especially useful, since it would have allowed you to seemlessly transition into explaining the Einstein summation convention in later videos in the series. Also, you should have emphasized in the explanation of the transformation of coordinates that φ = 90° - θ, since it would have driven home the point that sin(θ) = cos(φ). There is more to be said, but you already acknowledged it in your edits and comments, so it is all good.
Hey Andrew, the video is awesome. I had been waiting for it. One small thing though is that the sound is quite feeble... a more sensitive mic or talking a bit louder might help.
DocAlex That's not entirely true. I've used plenty of physics textbooks that use i, j, k. My professors also used that notation, and it even gets used in papers.
Hard to discern if you've never heard of it at 11:50, it is the Kronecker delta: en.wikipedia.org/wiki/Kronecker_delta (also in the video description, I see it now)
just a small remark since you said that a hat almost always denotes a unit vector and you left out the hat when referring to non-unit vectors. the e - notation for vectors, i.e. e_x, e_y, e_z, comes from the word Einheitsvektor, meaning unit vector.
At the beginning of the video when you wrote the tensor transformation equation, I had difficulty determining the difference between which symbol is a prime symbol ( ' ), a number one, or the letter i.
Hey, Andrew! Nice stuff. But I got stuck with one point concerning a unit vector's length. You said at around 18:50 like let's consider basis vectors but with a length not equal to one. What does it mean to a basis vector to have a length different from the unit one? I thought that we measure lengths relative to basis vectors, lengths of which are conveniently thought of as the unit ones. Then relative to what do we actually measure the length of a basis vector?
What's important here is that the basis vectors are not of equal magnitude. Sure you could call the magnitude of one basis vector "1" for convenience but the other basis vector(s) would not also equal one. So relative to any arbitrary magnitude both basis vectors can not simultaneously equal 1 for any units of measurement you could choose.
First time I have ever seen the levi-civita symbol in super script. I suppose it doesn't make much a difference but that was my one issue in the video not already mentioned in the comments.
Hey, i have a question i really like your videos and am interested in math, in what order should i learn math, like in highschool it is basic algebra, trigonometry, taking derivatives, doing integrals ect. how would you approach university level math, diffirential equations ect.
Calc I, Calc II, Calc III, Differential Equations / Linear Algebra, Partial Differential Equations. And maybe throw complex variables in there somewhere if you're feeling froggy
They should call it the kronecker sameness. Because calling it the kronecker delta makes you think it would be true (1) when there is a difference between the inputs.
Hello Andrew did u make a video about derivation of the energy-momentum tensor of electromagnetic field,if not plz can u make one,and thnk u alot ur videos really help me.
Hey can I ask what about Physics motivates you to major in it? I'm currently in high school and I want to decide whether I should major in Physics or Engineering. Some insight would be very much appreciated
he has a video on that very topic. It is called So you want to be a physics major (ua-cam.com/video/Y9RnTpIl8TY/v-deo.html). You should also watch this other great video I found on the topic (ua-cam.com/video/Kk8q500rYo4/v-deo.html), I warmly recommend it. I'm also a high school student, so if you want to talk about it, I'd be happy to. If you are interested I can send you my contact information...
i would just like to know if the directional derivative tells us how much the function is changing in the direction of the normal vector? the gradient itself tells us the direction in which it is changing the most.
Your excess of knowledge is sometimes your biggest problem in explaining things. Stay with the subject! Having knowledge isn't a guarantee that you can transfer that knowledge ;-) But I like anyone who tries to share his knowledge with others. What I don't like, might be usefull for someone else.
Your handwriting's really nice :D
It's spelled "demands", not "demends".
I think you could've unpacked the Levi-Civita notation for the cross-product explicitly so it would be clearer for other people.
At around 39:10, Φ should not be 90 + θ but rather 90 - θ, since Φ decreases when θ increases. It works out though, because cos(90 - θ) = sin(θ), which you mistakenly put as cos(90 + θ) = sin(θ).
With the second coordinate system, the way you handled Φ geometrically had some flaws as well, but the components turned out to have the right terms.
But I'm just splitting hairs here.
Great job on this video, and I'm looking forward to the next ones!
Thank you for pointing this out. I was very hand waivey with that part.
@@AndrewDotsonvideos I just realised that cos(90+x) = -sin(x), so shouldn't F_x' = |mg|sin(x)+|f| since the the -|mg| would cancel out the negative with -sin(x)
K0’m
V
My topology teacher's favorite joke was saying that general relatively is invariant under notation
Ian Prado hahaha I’m going to have to remember that one
no such thing as jokx or not
???
I wish I could get it
@@KFlorent13 yea
Andrew: "What's going on smart people?"
me: *looks around my room for other people*
What's going on idiot people
Me: looks around the room for other people
@Asyam Abyan You're doing my job for me!
@@rajaradi802 ahahahahaha
@Asyam Abyan where do I find your motivation speechs
@Asyam Abyan dayum🤣❤️
Originally subscribed for the physics memes, staying for the lectures.
Ok
@@ahmedd798 xvS sz ZZ z's ZZ xx z
Samee, this was so useful
same
same
Okay so far the feedback suggests I need to speak louder when facing the whiteboard, and I was a little hand-waivey with the inclined plane problem (which I recognized while editing the video). I'll be sure to be more careful with my arguments geometrically in the future. I'll also include a reference in the beginning of each video to explicitly state what will be covered so you don't have to watch the whole video to find out. Was debating fitting the whole section on vectors into this one video. Glad I didn't!
Andrew Dotson I'm almost a bit surprised how good this actually is! One more small thing you could consider to make it flawless is to put the audio through some "filtration" program to get rid of the static background noise. Looking forward to watching the rest, especially now that I just finished my exams!
When's the next vid coming?
dude u should get more buffed! your vector views will increase 3 fold Lol
BLAIR M Schirmer Well, you are an arrogant one, for sure. You apparently do not understand the concept of "context." This video is not intended as an introductory course nor for beginners, nor is it designed for people who have no idea of what a tensor. He has other videos designed for that type of audience.
This is not his incompetence, this your damn incompetence for not knowing how to search videos on a channel. It's incredible how people in 2018 were still not aware of how to competently use UA-cam.
BLAIR M Schirmer Also, he DID mention the definition of a tensor very early on in a video, and then talked about it would be absolutely unhelpful to start talking about it immediately. So, looks like you have a bad case of not paying attention, or of being a dishonest prick.
0:00 Important Introduction
___________________________________________ The elements
4:53 Products of vectors and their intuition
6:29 Derivatives in vectors
7:35 the Gradient, Curl and Divergence
___________________________________________ What we do with them
9:20 we begin with coordinates
12:40 representation of a vector r in this coordinate idea
14:24 Basis
18:30 Dot product for the introduction of new concepts: Metric, Kronecker Delta
___________________________________________ Applying this products and ideas
20:28 Dot product between two general vectors
24:21 Cross product between two general vectors
___________________________________________ Quick note if you're not careful with angles
29:36 Comparison Dot product for x component and y component
___________________________________________ Physics problem
33:16 Block on plane intro
35:24 2nd Newton Law for the problem and the first way (non block-local x & y)
42:38 2nd way, we rotate our view so we are inclined with the plane (block-local)
This was a refreshing take on how to interpret dot, cross products and the gradient. I've never been quite as good at applied maths as at pure, so I relish this video and the chance to improve my understanding. Looking forward to learning tensors, I've never seen them before!
Three years later, this is finally useful as I'm starting to self-study GR
As a hobby student who came here through your meme reviews, this is absolutely the most helpful tutorial for tensors on UA-cam. All the other tutorials assume you already know the foundations, but as a hobby student my foundations are full of holes, so it's nice to see things like the Kronecker delta defined by a logical progression than with a bunch of words that don't mean anything to somebody who doesn't have a good foundation to start from.
I’m ready. I’ve been watching this channel for years but I’m ready to tackle tensors once and for all.
AWESOME VIDEO! HYPED FOR THIS SERIES!
*One suggestion*: Even though I know very little, You should've introduced Einstein Summation in the video first, that would've made your notation a lot less cluttered...
For a moment there, I thought you said "Welcome to Tensor Calculus for Fitness".
For a moment there, I was excited...
I was honestly very confused about our first few lessons in mathematical physics because there were so many new terms/symbols introduced (unlike regular math classes) like the Kronecker delta and Levi-Civita, so my fundamentals before tensor analysis is really fragile. This video really helped me review our past lessons, and I can say I have a much better understanding now on matrices and coordinate transformations. Thank you for being a very good teacher. Your explanations are very clear. Xx
absolutely beautiful and concise lecture. Thank you very much! My hope to understand tensor calculus and GR brightens!
Congrats for the great videos man!!
I found a couple of minor errors at min 38.
i) The relationship between phi and theta the way you are expressing them should be: phi = 90 - theta.
ii) This error then cancels with a second one here: cos(90+theta) = sin (theta) !! With the correct phi / theta relationship, you can use instead: cos( 90 - theta) = sin (theta)
I think this is my favorite youtube channel already, so clearly explained!
Andrew. Yeah it's me again lol
Just wanted to make a suggestion for the series
If videos are long (like this one), it might help to write the list of topics to be covered in the video and write clear titles when you are talking about them. Also, I don't know your exact plans, but I would do these videos once a week; you give some time for your viewers to see the latest video on the series and most importantly, to let the ideas sink in (I feel how tough these topics can be for people with no actual university-level education in physics, such as many viewers here). Anyway, great video :)
Thanks for the feedback! I think a list of topics at the beginning would be helpful. I wouldn't be able to make them more frequent than once a week if I tried. I think once a week or once every other week will be how it ends up playing out. Especially once we actually get to the more subtle math.
Straight-forward, helpful, intuitive, and to-the-point explanation - thank you so much
The fact that actual math and physics is actually being taught surprised me, since most (if not all) videos I have seen from this channel are meme/joke videos!
Good tensor-concept applied to static engineering vector (physics transformation vector) as an introduction to real-tensor (Einstein notation) such that layman easily understand from familiar realm understanding the complicated-unknown-tensor realm .Good example of illustration .
Finally, I feel like I'm ready to learn this. So excited!
Two years later, thanks Mr. Dotson!
This doubles as a really informative lecture and sleep aid. Thanks Andrew and I hope exam studying is going well!
The way you draw sigma scratches my brain in just the right way
at 39:14 N of x should be positive . cause cos(90+ θ) = - sinθ
same goes for 47:24
Isn't he still correct since the block is sliding in the negative direction? I think he just skipped a step, otherwise the equation would show that friction + the x component of the normal force is equal to the force, and therefor the acceleration experienced by the block, which is obviously not true. Sorry if I missed something.
I think he made a bouble mistake and got it right. Phi is not equal to 90°+theta, instead it should be 90°- theta. So eventually he got it right. I'm currently at 39:11
Sorry I meant "double mistake". Typo* :'(
@@6900xx θ=0→Φ=90° and θ=90°→Φ=180° so Φ=90°+θ
It's great how you find the angles by thinking about how exactly the rotation is happening and not drawing parallel lines to find similar angles
just wanted to see if there are any comments regarding the whole \phi = 90 deg + \theta and \phi = - 90 deg - \theta and is cos(90 + \theta) = - sin(\theta) or +sin(\theta) caused any confusion and there were some comments were it caused confusion how you dealt with the angles. The whole confusion could have been avoided if you had identified the opposite angle as \theta instead of introducing a new angle \phi. you want to make your life easier that's why you change coordinate systems because equations might have a simpler form in different coordinate systems. you don't want to introduce difficulties by a poor choice of angles ;) .. other than that, great series, keep it up!
This is some good educational shit right here, keep it up!
Rick attitude
I loved your explanation so far, despite only making it a couple minutes in. While some of the notation looked a bit foreign from your explanation I started to understand what the underlying concepts were. Thanks for these great videos! :D
Ethan Hall ticket
Hint: double speed.
A big thumbs up from me Andrew. Taught me more than my hs physics teacher has tbh he's been held back by people bad at physics.
Duncan W hey you're subbed to me :)
These lectures really good. It's useful to go through the notation slowly.
Hi. In time 38.22
θ+ϕ = 90°, just prolong N 'til it reaches the x axis.
Tensors were mentioned in "The Outer Limits" episode The Human Factor (1963) which is one reason why I got to be curious about them.
I feel shame being a graduate student and still having a hard time grasping the nature of tensors, hope you will bring me some different perspectives since group theory and representation in quantum mechanics is just other words for nigthmare to me right now! Love from Paris and be safe
I really like how you explain setting up problems. Could you do more videos on setting up problems? My mind is drawing blanks staring at my practice problems in this classical mechanics textbook.
this series is the best there in the whole youtube .....thanks a lot..
In the second example with the rotated (prime) reference frame, I got confused by the fact that you labeled your x-component as negative in the triangle and your y-component as positive which you changed later. If you use your angles properly, which you mostly did, then you don't need to place the negative sign in front of the components. They'll come out positive or negative based on their angles with respect to the relevant unit vector.
I had to think about the issue with the sign of cosine as you did it in the problem. You're correct in saying that it's an even function, so if I flip the sign of the argument, the sign of the result will remain the same, however, because the angle between the unit vector i-hat and the gravitational force vector is oblique the resulting cosine will be negative. If you flip the sign of the argument, the cosine will remain negative. That was really throwing me for a minute and it's a very easy mistake for anyone to make. Honestly, still having a hard time thinking about how you introduce that to a student without introducing the sign in there in a potentially confusing way. You would've had to write "cos(90º+θ) = -sin(θ)."
I also think it might be helpful to actually draw the unit vector and force vector of interest tail-to-tail. That way you can see what angle you're dealing with better.
Only physics major with a good handwriting is Andrew dotson
DUUUUDE this is pure gold. I just have a minor issue: could you use barred letters when changing to another coordinate system? the primes look the number one (1). Thanks bro.
I think you should have written the Levi-Civita symbol with lower indeces, and the component of the cross product also with a low index, a contravariant symbol. Or, alternatively, kept the upper index on the cross product, but written the Levi-Civita symbol with mixed indeces. This would have been especially useful, since it would have allowed you to seemlessly transition into explaining the Einstein summation convention in later videos in the series.
Also, you should have emphasized in the explanation of the transformation of coordinates that φ = 90° - θ, since it would have driven home the point that sin(θ) = cos(φ).
There is more to be said, but you already acknowledged it in your edits and comments, so it is all good.
0:40....Me to myself: "Do I need to decipher these cave paintings?"
Me to myself: why am I so alone???
@@NovaWarrior77 XD lol
You’re an excellent teacher. 👍🏻 Thanks for the videos.
Hey Andrew, the video is awesome. I had been waiting for it. One small thing though is that the sound is quite feeble... a more sensitive mic or talking a bit louder might help.
Elvie Shane yeah it seemed like the audio was good when I was facing the camera, and then died off once I faced the whiteboard
😭🙌🏾omg I actually love you. Thank you for making my life easier
Minor change: use x hat, y hat, z hat notation because in engineering and physics they are always used instead of the mathematical notation
DocAlex personally I use xhat yhat zhat notation myself. I was just sticking with notation used in the book
DocAlex That's not entirely true. I've used plenty of physics textbooks that use i, j, k. My professors also used that notation, and it even gets used in papers.
Hard to discern if you've never heard of it at 11:50, it is the Kronecker delta: en.wikipedia.org/wiki/Kronecker_delta
(also in the video description, I see it now)
Thank you so much, Andrew.
How is your hairline not receding after stress from physics degree?
john toms 😂😂😂
Because he chose it for a reason
It's called love
@@Wild4lon You dont study physics, do you?
He's not in postdoc yet. That's where you're really up shit creek
That’s why i’m just getting a bachelors lol
Tensor is something that transforms as a tensor
Can You give me the links of all the mathematical physics videos? I like the way you explain the mathematics part.
Thanks man! Just started taking math methods this semester... really useful
just a small remark since you said that a hat almost always denotes a unit vector and you left out the hat when referring to non-unit vectors. the e - notation for vectors, i.e. e_x, e_y, e_z, comes from the word Einheitsvektor, meaning unit vector.
Excellent presentation … so helpful!!!
I love you for this series of lectures
At ~ 38:00 ish you say Nx=-|N|cos(phi), but the - sign makes it positive since cos(phi) will be negative since phi=90+theta>90.
cos(90+phi)=-sin(theta) not sin(theta)
I never sow more complicated calculation for incline plane
Richard Feynman defo taught you dude, yk how to teach, thanks for this series
sos crack amigo! tus videos me han salvado la vida muchas veces. Si alguna vez estas en New York te invito un cafe.
At the beginning of the video when you wrote the tensor transformation equation, I had difficulty determining the difference between which symbol is a prime symbol ( ' ), a number one, or the letter i.
Man, where was this when I took Physics 1?
You won’t see some of this stuff in physics 1 but you will see it in Physics 2 or calculus 3.
Thanks for putting this out dude!!!!
Sup re runnnnnn!!! And i got books lololol thanks again dude🤣🤙
I am saying again you are going to become a great Professor
The currency comparison is awesome.
Edit: but why degrees instead of radians?
I tried modern motion and gravity etc and this helped
Divergence should diverge, so it must be coming from a source rather than going towards a sink.
Have my last exam tomorrow but this couldn't wait :)
thank you thank you thank you for this my good sir
Hey, Andrew!
Nice stuff. But I got stuck with one point concerning a unit vector's length.
You said at around 18:50 like let's consider basis vectors but with a length not equal to one.
What does it mean to a basis vector to have a length different from the unit one? I thought that we measure lengths relative to basis vectors, lengths of which are conveniently thought of as the unit ones. Then relative to what do we actually measure the length of a basis vector?
What's important here is that the basis vectors are not of equal magnitude. Sure you could call the magnitude of one basis vector "1" for convenience but the other basis vector(s) would not also equal one. So relative to any arbitrary magnitude both basis vectors can not simultaneously equal 1 for any units of measurement you could choose.
Starting this Tensor series from today😁😁
First time I have ever seen the levi-civita symbol in super script. I suppose it doesn't make much a difference but that was my one issue in the video not already mentioned in the comments.
amazing! Andrew, thank you :)
All good math is obnoxious. That’s why regular people hate maths. Lol thx, pal, solid review.
Hey, i have a question i really like your videos and am interested in math, in what order should i learn math, like in highschool it is basic algebra, trigonometry, taking derivatives, doing integrals ect. how would you approach university level math, diffirential equations ect.
Calc I, Calc II, Calc III, Differential Equations / Linear Algebra, Partial Differential Equations. And maybe throw complex variables in there somewhere if you're feeling froggy
They should call it the kronecker sameness. Because calling it the kronecker delta makes you think it would be true (1) when there is a difference between the inputs.
I found the begging confusing but at the end I understood everything, thank you for this very helpful video
No one's begging here fucker
@@raghavdodla1376 woah calm down young man
Hi. Just wanna ask if the series can prepare me well to dive in Sean Caroll’s GR textbook.
woohoo! I'm happy I landed here.
Is the Levi Civita symbol related to the sign of a permutation used when you define determinants and stuff?
Hello Andrew did u make a video about derivation of the energy-momentum tensor of electromagnetic field,if not plz can u make one,and thnk u alot ur videos really help me.
excellent clarification.
Excelente aula.
You are love Sir
Sir I have a humble request :- please make me understand "the general relativity and special relativity" easily....❤
do you want to understand what they are or do you want to understand the difference between them?
great. but as a W&M alumn, I must ask... ODWHO?????
Hey can I ask what about Physics motivates you to major in it? I'm currently in high school and I want to decide whether I should major in Physics or Engineering. Some insight would be very much appreciated
he has a video on that very topic. It is called So you want to be a physics major (ua-cam.com/video/Y9RnTpIl8TY/v-deo.html). You should also watch this other great video I found on the topic (ua-cam.com/video/Kk8q500rYo4/v-deo.html), I warmly recommend it. I'm also a high school student, so if you want to talk about it, I'd be happy to. If you are interested I can send you my contact information...
Whatever you do, learn as much CS as possible
Ian Prado Can you elaborate? Thanks for the feedback btw.
Dominik Clemente Thank you for the feedback
CS will always help you in your career or be necessary for your career. I struggled in CS when I was in college and I regret not taking more courses.
Excelent video! Thank you!
Do you know anything about differential geometry and forms? If so you should really do a series on forms because they really interest me
We'll definitely get to forms eventually.
Andrew Dotson Awesome, thanks dude! You're the best!
Cos(90+θ) isn't = sin(θ)
Extremely useful for me
at 47:38 isn't "phi" the angle between -mgy and |mg| not -mgx and |mg|? If it was between -mgx and |mg| it would just be 90°-"theta"?
i would just like to know if the directional derivative tells us how much the function is changing in the direction of the normal vector? the gradient itself tells us the direction in which it is changing the most.
Are you going to be covering forms as well?
can you do a video on 4-gradient please!
Your excess of knowledge is sometimes your biggest problem in explaining things. Stay with the subject! Having knowledge isn't a guarantee that you can transfer that knowledge ;-) But I like anyone who tries to share his knowledge with others. What I don't like, might be usefull for someone else.
As a math major I can't help but be deeply deeply disturbed by your use of the word scalar.
From The first derivation, if I want to solve the N2L, how do I eliminate the normal force in the equations of motion?
"So you're going through all of this physics and then you see *F=ma* and you're like 'wait, really? since when?'" haha lmao
can you derive einsteins general theory of relativity equation?
That is way beyond the scope of these videos.
@@AlchemistOfNirnroot Well, uh, not anymore i guess
@@vishwangoosethemongoose1114 only took 2 years :D
@@AlchemistOfNirnroot that deserves a hearty teehee :)
If someone used a left-handed coordinate system, would it change the formula for how to calculate the determinant?
I like when he calls me a smart person even though my intelligence is average. :)