/sci/ - Science & Math

[Anonymous No.14571673]

ITT: most overrated textbooks

[Anonymous No.14572464]

>>14571673
It's not overrated, but entirely worthy of the praise it receives from Physicists and Graduate students.

An example of an overrated textbook would be Gilbert Strang's Linear Algebra book.

[Anonymous No.14572470]

>>14572464
L&L are garbage books. They are poorly written, contain many false theorems and nonsensical proofs. Pretty much any modern book is a better alternative than L&L.

[Anonymous No.14572506]

>>14572470
Name one in the OP book

[Anonymous No.14572542]

>>14572506
Have you not read the book or are you just a brainlet? I posted mistakes in this book many times on /sci/.

[Anonymous No.14572546]

>>14572542
not that anon, but i don't browse /sci/ religiously. can you share?

[Anonymous No.14572550]

>>14572542
If you can't cite any supposed false theorems or nonsensical proofs when asked to do so I have no reason to believe what you're saying. It's as useful a claim to me as people here stating they know how to prove the Riemann Hypothesis.

[Anonymous No.14572553]

[Anonymous No.14572556]

[Anonymous No.14572567]

>>14572546
Just search warosu archives.

[Anonymous No.14572614]

>>14572567
okay, and what should i search for? you do realize search engines are useless if you don't know what you're searching for, right? what key words should i look for? any specific posts?

[Anonymous No.14572652]

>>14572614
>Do you have the book with you?
>So, according to Landau, since two functions which differ by total derivative give the same equations, the only way in which the equations could be the same is if the functions differ by a total time derivartive.
>In essence, Landau is asserting here that if P=>Q then Q=>P.

>Is he retarded?

[Anonymous No.14572655]

>>14572542
I’ve found errors in classical theory of fields, some of their relativity stuff is wrong in early chapters. But they are simple typos, not horrendous errors you can’t reconcile easily. The books are fantastic. Is it possible you’re just a bit jel?

[Anonymous No.14572679]

>>14572655
If you've only found those errors then the material flew way over your head or you didn't read the books.
The books are unusable garbage.

[Anonymous No.14572705]

All of them textbooks are rubbish

[Anonymous No.14572774]

>>14572652
This isn't necessarily a mistake if it turns out that P<=>Q (I don't know whether the two imply each other in this case or not). It's possible that Landau is just omitting a proof, not necessarily making a logical mistake.

[Anonymous No.14572818]

>>14572774
If he was omitting the proof then he would say so, or at least just state the result outright without explaining why. But that's not what he did, he referenced a specific section as the proof of it which proves nothing of the sort, meaning he actually thinks P=>Q is the same as Q=>P.

[Anonymous No.14573053]

>>14572818
Well generally speaking, physics is more about building physical intuition than rigorously proving mathematical statements. So if it turns out that P and Q do not imply each other, then that is a logical mistake. But if it turns out that the proof of this was omitted because the author felt it was unnecessary, that's more forgivable. I see where you're coming from though.

[Anonymous No.14573063]

>>14573053
>I see where you're coming from though.
No you don't. Read my post again.

[Anonymous No.14573417]

>>14572556
Care to elaborate? Was tossing up between Aluffi and Dummit & Foote for an abstract algebra text. I was under the impression that Aluffi introduces category theory which is a bonus or is it really a meme and learning category theory is better served by an actual book?

[Anonymous No.14573430]

[Anonymous No.14573454]

>>14571673
This fucking garbage, Lemay is better
I can't remember if Zemansky was also a meme compared to Haliday

[Brainlet No.14573617]

I leave it as am exercise to the student to discover the concepts that I didn't feel like developing. You should be able to do this.

[Brainlet No.14573623]

I leave it as an exercise for the student to merely re-discover the concepts that I don't feel like discussing. You should be able to do this.

[Anonymous No.14574092]

>>14571673
Almost all the later textbooks just copied L&L and localized or modernized it. Particularly the problems, you can trace those right back to L&L most of the time.

[Anonymous No.14574319]

>>14572506
There is one by Cambridge university press but fuck knows the author

[Anonymous No.14574538]

>>14572679
Nah, pretty sure you’re jel.

[Anonymous No.14574559]

>>14574538
We all know lots of wikipedia links = good physicist.

[Anonymous No.14574736]

>>14572556
I agree with this. I went into this book a bit and found out that category theory is really just boring with no good applications. If I were to describe what category theory studies, I'd describe it as "how to move commas in and out of parentheses"

[Anonymous No.14574739]

>>14573430
Wrong

[Anonymous No.14574742]

>>14571673
Everything by Lang is way overrated. He tends to write the 3rd or 4th best book in every field. Good enough to acquaint with a topic, but clearly inferior to other texts like Rudin, Peter Lax, Royden, David Lay, etc

[Anonymous No.14574746]

>>14574559
Anyone who works in physics sees phenomena named after Landau everywhere. But I’ll humor you, what formulae/phenomena/theorems have you had named after you?

[Anonymoose No.14574770]

>>14574746
You're asking him to breach anonymity?

[Anonymous No.14574916]

>>14574770
You think 4chan is actually anonymous? The FBI, CIA, ADL and SPLC get all your IP logs connected with your comments

[Anonymous No.14575051]

>>14574916
Roaming IP phone posters will inherit the earth.

[Anonymous No.14575137]

>>14574742
This except Algebra which is the best.

[Anonymous No.14576236]

>>14573623
Please don't crap all over Griffiths, you brainlet.

[Anonymous No.14577340]

>>14573430
This was the first book that introduced me to the beauty of proofs. It’s unfortunate though because his proofs are very slick and definitely spoils you.

[Anonymous No.14577347]

>>14577340
I've only done chapter 1 but his proof of the cauchy schwarz inequality was an absolute mess

[Anonymous No.14577375]

>>14577347
All of his proofs aren’t going to be beautiful, but there are certainly many gems in there. These are the ones that you look at and admire and essentially add to your tool box.

[Anonymous No.14577539]

>>14572652
>>14572818
No, he's not asserting P=>Q implies Q=>P (this is obviously stupid to think so). He just omitted a step, and you're well aware of this, you just like to think you're very smart because you spotted a small logical omission in a book written by a physicist who you know full well is much better than you are.

[Anonymous No.14577594]

I'm surprised this piece of shit wasn't posted yet

[Anonymous No.14577616]

>>14577539
>you spotted a small logical omission
Fill it in then for me please, if you think it's such a small omission.

[Anonymous No.14577642]

>>14577594
I don’t think anyone ever thought this was overrated. It’s pretty bad and everyone knows it.

[Anonymous No.14577660]

>>14577642
the only place I know where people think it's bad is here.
in my uni everyone uses it and it's the recommended book by calculus professors

[Anonymous No.14577768]

Anything shilled by /sci/ is a meme and you shouldn't follow its recommendation

[Anonymous No.14577914]

>>14577660
For comparison, this is the textbook I used for multivariable calculus (I can’t find the textbook for single variable):

https://marian.fsik.cvut.cz/~svacek/math2/SCR_M2A.pdf

The single variable calculus text was very similar in format. This textbook is what’s used for engineers. I don’t think Stewart’s text is sufficient unless you only want a watered down understanding of calculus.

[Anonymous No.14578334]

>>14572652
Well, I have to admit you've really got a point, this proof is wrong. I think that Landau's books are more "physical" and sometimes they can be sloppy about the mathematical details, which for a physicist can be a useful approach. However this specific example is actually pretty bad now that I examine it carefully.

[Anonymous No.14578388]

I'm surprised that I agree with a lot of posts in this thread.

Maybe I shouldn't be surprised, given that there's only a few books of which I'd say they are good.
Mostly German authored books.

[Anonymous No.14578561]

>>14578334
It isn’t bad, Landau is referring to invariance under galilean transformations. In this case the only possible difference in the Lagrangians given the frame is moving with some infinitesimal velocity is a total time derivative. In the page following his statement you can see easily that the new Lagrangian yields the old plus a total time derivative, all such Galilean transformations of the coordinates yield this form. He misspoke and was sloppy with his arguments but nothing he said is wrong or unphysical. The guy is a faggot.

[Anonymous No.14578585]

>>14572470
>brainlet filtered by landau
You will never be a real physicist

[Anonymous No.14578604]

>>14578561
>In this case the only possible difference in the Lagrangians given the frame is moving with some infinitesimal velocity is a total time derivative
Why?
> all such Galilean transformations of the coordinates yield this form
Why?
Please formulate carefully what you think Landau meant to say.

[Anonymous No.14578609]

>>14578585
Correct. I like being precise and dislike philosophy-speak.

[Anonymous No.14578626]

>>14578388
I like Anglos better than Germans on average. Germans tend to veer too far into autism
The absolute best books are American ones written before like 1980 though. Most recent American textbooks are too pussified to be useful compared to their yuro counterparts.

[Anonymous No.14578640]

it does not matter how much you will shill those books by LL on /sci/, /lit/ or any other board, you will remain a pseud at the end of the day. you haven't even fully read one work of him in your entire life, most likely only read not more than 25% or half of mechanics.

[Anonymous No.14578761]

>>14577594
what's an alternative to it?

[Anonymous No.14578905]

>>14578609
>Correct. [insert cope]

[Anonymous No.14579114]

>>14572652
Based

[Anonymous No.14579282]

>>14577616
It's obvious as fuck. The only missing comment is that the only way the action would vary under a Galilean transformation is by addition of a total derivative with respect to time.
You're stupid as fuck if you think he was actually implying if implies only if.

[Anonymous No.14579388]

>>14573430
BASED

[Anonymous No.14579492]

>>14578561
I didn't say that the statement is wrong or unphysical, just that I don't think the derivation is correct.

[Anonymous No.14579551]

>>14579282
>The only missing comment is that the only way the action would vary under a Galilean transformation is by addition of a total derivative with respect to time.
Why is that true?

[Anonymous No.14579572]

>>14578640
Why would I want to waste my time reading garbage?

[Anonymous No.14579580]

>>14579572
You're here, aren't you?

[Anonymous No.14579615]

Meh, most texts are overrated. Anytime anyone recommends a single text on a subject, you should be suspicious since they probably don't know shit. There are typically multiple passable texts on a subject that if you study side by side will give you a great awareness of a subject (especially of different notation styles in the case of math).

Also, I'd argue the majority of these texts are garbage merely because they don't have good computational examples to step through. It's literally 2020, why are we holding onto textbook conventions of the 80s? Everyone has a computer and you should know how to code. Simulations, numerical algorithms, graphs, etc. should be expected and incorporated into most of these texts (especially if they are at all application focused). It's so strange that many math texts feel stuck in the past.

[Anonymous No.14579678]

>>14579580
I live here.

[Anonymous No.14579822]

>>14579615
Applied Mathematics: Body and Soul (Vols 1-4)
Hoffman, Johnson, Logg

Computational Differential Equations - eriksson, estep, johnson

[Anonymous No.14580502]

>>14572818
>>14572652
>>14579114
>>14578609
>>14572470
>>14579572
>meaning he actually thinks P=>Q is the same as Q=>P
This is trivial since P<=>Q turns out to be true as that anon said, Lamport showed 30% of maths papers have minor "errors" like these. You don't even have proof of this in the original Russian version, it might as well have been butchered in translation.
Nothing there warrants you to shit on Landau, undergrad faggot, and 99.9% of the time, if an assertion P=>Q is made and consecutively claimed to be the same as Q=>P, it is elaborated on later on. Same thing with L&L denoting certain quantities "kinetic energy" and "potential energy" before even introducing the concept of energy (in which case you might as well ask why it would be called energy. It's a pedagogical style wherein you are given snippets of the whole thing early on that is elaborated on later on in the book. Nobody is an autistic robot who needs everything to be written linearly).

In any case, I'd recommend you stop dabbling in theoretical physics if the idea of exhaustively explaining virtually all physical phenomena is unreconcilable with not introducing said concepts perfectly, mathematically rigorously and I'd recommend you read mathematical physics books, like Abraham and Marsden, Takhtajan, Dütsch, etc., instead (granted you aren't a LARPing undergrad too retarded for pure math).
Note that this is exactly why mathematicians are usually terrible at physics: They wind up in some pandaemonium, confused about how to prove a certain thing to be the case, all the while not realizing physics is not math but only has a very strong mathematical backbone, which is integral, mind you, but still doesn't assimilate it.
For the record, even the hardcore mathematical physics books, like Deligne et al., quickly give up on mathematical formalism.

Now go on and read the more rigorous books and shut up. No need to shit up /sci/ with such low-quality trash.
>>14578604
>>14579551
Maybe read the book?

[Anonymous No.14580921]

>>14577616
kys

[Anonymous No.14581010]

>>14580921
I am not who you are replying to, but this does not seem like a small omission. I don't think anyone ever tought Landau is wrong, but what he presents as a proof is a little hand-waving,

[Anonymous No.14581048]

>>14581010
I'd honestly be surprised if you could find another instance of something like that.

[Anonymous No.14581121]

>>14580502
>Maybe read the book?
Where in the book does it explain it?

[Anonymous No.14581150]

>>14573623
Griffiths is fine, Jackson is shit.

[Anonymous No.14581203]

>>14580921
>that pic
HAHAHAHAH Thanks for making me laugh bro. It's the definition of mindless (and incorrect) symbol pushing without understanding what they mean.
Actually, now that I looked at Landau's book again, I realized that he wasn't just wrong, he was not even wrong. What he wrote simply makes no sense.
Let me explain.
Look at pic related. L is a function of three variables: q, q' and t. They are a priori numbers and NOT functions. I.e. L is not a functional (it's not the action), it's a regular function of three (two of which are vectors) arguments.
What would it mean to say that the function L' is L + d/dt f(q,t). You talk of total time derivatives only when you assume the other arguments are also functions of the variable w.r.t. which you're taking the derivative, but in this case we're only talking about functions L, L' which do NOT take functions as arguments, so it makes no sense to say they differ by a total derivative. You could say that two functionals I, I' which take as inputs FUNCTION q(t), q'(t) differ by a total time derivative and that would make sense, but to say this about Lagrangians is just plain meaningless gibberish.
Suppose we write
[math]
\frac{df (q, t)}{dt} = \frac{\partial f}{\partial t}(q,t) + \frac{\partial f}{\partial q}(q,t)\frac{dq}{dt}(t)
[/math]
Then the condition on L' becomes
[math]
L'(q, q', t) = L(q,q',t) + \frac{\partial f}{\partial t}(q,t) + \frac{\partial f}{\partial q}(q,t)\frac{dq}{dt}(t)
[/math]
but this makes ABSOLUTELY no sense as q is just a vector and not a function of t.
Landau truly was a brainlet of epic proportions. I'm surprised he could even function.

[Anonymous No.14581250]

>>14581048
I agree it's a bit cumbersome. Maybe Arnold does something similar, I'll have to check.
>>14581203
What are you talking about, nigga, of course [math]\mathcal L[/math] is not a functional as its arguments are the values of [math]q[/math], [math]\dot q[/math] and [math]t[/math], but if the values of the coordinates that you insert in [math]\mathcal L[/math] depend on time what he wrote is absoltely correct. This is something any physicist would do every day multiple times a day.
It's like saying that if [math]f = f(x)[/math] and [math]x = x(t)[/math] you can't take the derivative [math]\frac{\text{d}f(x(t))}{\text{d}t}[/math] because [math]f[/math] is not a functional.

[Anonymous No.14581253]

>>14581250
This, it's just chain rule shit.

[Anonymous No.14581274]

>>14581250
Bro you just keep making it worse for yourself lmao.
>t's like saying that if f=f(x)f=f(x) and x=x(t)x=x(t) you can't take the derivative df(x(t))dtdf(x(t))dt because ff is not a functional.
f(x(t)) is now a function of t and just t (while implicitly we have in mind the function f which is just a function of x), because f has been composed with x(t).
But L is not a priori a function of only t (in which case a total time derivative may be applied), it's a function of three variables, and only becomes a function of just t after a particular function q(t) is chosen and q(t), q'(t) are inputed as arguments.
To see how ridiculous what Landau wrote down is, let's just take an example.
Let's say we only have one degree of freedom, so L is a function of just three real numbers. Say we also know as Landau asserts that
[math]L'(q, q', t) = L(q,q',t) + \frac{\partial f}{\partial t}(q,t) + \frac{\partial f}{\partial q}(q,t)\frac{dq}{dt}(t)[/math].
We try to calculate L'(1,2,3) and find
[math]L'(1,2,3) = L(1,2,3) + \frac{\partial f}{\partial t}(1,3) + \frac{\partial f}{\partial q}(1,3)\frac{d1}{dt}(3)[/math] which is ridiculous, unless you interpret the derivative d1/dt =0 and make the last term equal zero, in which case it's just a partial derivative not a total derivative (because a total derivative doesn't even make sense in this context) and then what he wrote down next is simply WRONG, because under nice assumptions any L can be written as a partial derivative of another function (just integrate w.r.t. t).

[Anonymous No.14581278]

>>14581253
Have you genuinely never taken analysis or even calculus? You clearly don't understand the concept of a function and how function composition works. Landau fanboys are so retarded holy shit.

[Anonymous No.14581285]

>>14581203
>>14581274
Oh no Landaubros we got too cocky...

[Anonymous No.14581303]

>>14571673
If this was the textbook that the russians learned from no wonder they didnt get to the moon lmao.

[Anonymous No.14581309]

Holy shit, brainlet OP thinks this is wrong. Its literally derived correctly and there is NO inconsistency. YOU LITERALLY POST THE PROOF. Regarding L&L, the relativity section of the second book is one of the best and most concise texts on special relativity I have ever read. If you think otherwise, you are a fucking brainlet.

[Anonymous No.14581324]

>>14581309
>Holy shit, brainlet OP thinks this is wrong. Its literally derived correctly and there is NO inconsistency
How's sub-100 IQ life for you?

[Anonymous No.14581350]

>>14581324
You tell me since you're unable to understand a simple proof that is intended for first year undergrads. You literally don't even understand the formulation of the second paragraph.

[Anonymous No.14581362]

>>14581350
Consider a function of two real variables mapping to R, f(x,t). What does it mean for f to be a total time derivative?

[Anonymous No.14581376]

>>14581362
It's literally just application of the chainrule you fucking brainlet

[Anonymous No.14581388]

>>14581376
lmao @ you getting mad. Chain rule applies to when you have a composition of several functions. In this case you just have a single function f(x,t). So let me repeat the question: what does it mean for f to be a total derivative w.r.t t? Does it make sense to say that?

[Anonymous No.14581394]

>>14581388
Of course it makes sense, if your variables depend on time, which the configuration coordinates do. If they don't, then it just becomes a partial derivative.

How can you not even understand the chain rule yet accuse one of the most influential textbook of a false proof. Walking Dunning Kruger definition.

[Anonymous No.14581401]

>>14581388
In fact, dont ever look up derivation of E-L eqns. or you will start malding about that too.

[Anonymous No.14581405]

>>14581394
I understand the chain rule which is why I said that it only applies when you have a composition of function. You said something about variables depending on time, which is true after the function f(x,t) is composed with some function x(t), in which case talking about the total derivative of f(x(t), t) makes sense, but you have to realize that's a different function from f(x,t), because it depends on only one argument while the latter depends on two arguments. Similarly, g(x,y) = x^2 - y^2 is a different function from h(y) := g(y^2, y) = y^4 - y^2. Do you understand what I'm saying? Now take the simple example of g(x,y) = x^2 - y^2. What does it mean to say that it's a total derivative of a function h(x,y) w.r.t. y?

[Anonymous No.14581408]

>>14581401
I looked at it, it's not completely rigorous but it doesn't pretend to and it makes sense. This example I'm showing you doesn't fundamentally make sense. It's just plain nonsense, whether you're speaking mathematically or physically. It's complete gibberish. Landau basically confused himself.

[Anonymous No.14581413]

What's even funnier to me than a world-renowned physicist writing literal gibberish in the THIRD EDITION of his book are the swaths of brainlet fanboys defending it completely ignoring the point that I'm making and just repeating what Landau wrote. Quality entertainment.

[Anonymous No.14581418]

>>14581405
The total derivative is defined even for any differentiable function, do I have to show you an example of chain rule application?

Are you literally asking if generalized coordinates depend on time? Bro...

[Anonymous No.14581427]

This is unironically hilarious.
>>14581418
Please answer me first if f(x,y) = x^2 - y^2 is a total time derivative w.r.t. y and explain why/why not.

[Anonymous No.14581429]

>>14581413
People are defending it because you are literally raising an issue that doesnt exist, in fact there are bigger issues with mechanics I could name, but this one is not it and it seems the text completely flies over your head.

[Anonymous No.14581432]

>>14581427
Yes, it is. If you don't understand why, you need to review the fundamental theorem of calculus. I hope that calms your 'tism.

[Anonymous No.14581439]

>>14581432
Can you please write down the function whose total derivative w.r.t y is f, please?

[Anonymous No.14581447]

>>14581429
That's a good way to solve an issue. Just deny it exists.

[Anonymous No.14581453]

>>14581439
Tsk tsk tsk, do I have to do everything for you... Assuming x,y are time independent, it's x^2*y - y^3/3 + C.

[Anonymous No.14581467]

everybody in this thread is a virgin

[Anonymous No.14581475]

>>14581453
Hold on to your seat, cause I'm about to blow your mind.
According to Landau logic, if g(y) is any function, then as f is a total derivative w.r.t. y, let's say [math]f(x,y) = \frac{dh}{dy} [/math] we have
[math]\int_{0}^{1} f(g(y), y) dy = \int_0^1 \frac{d}{dy} h(g(y), y) dy = h(g(1), 1) - h(g(0), 0)[/math].
Taking [math]g(y) = y[/math] this gives us
[math]0 = \int_0^1 (y^2 - y^2) dy = (y^2 *y - y^2/3 + C)|^{y=1}_{y=0}= 2/3[/math]. Truly an astounding result!
Such is math when you are a physicist like Landau.

[Anonymous No.14581494]

>>14578761
spivak

[Anonymous No.14581501]

>>14581475
You're quite incoherent, and very sloppy in your attempt to show anything, much more so than Dau. Where does f=g suddenly come from, and also it seems quite clear that you are still confused by the time dependence of generalized coordinates. That is why I assumed in my previous post y independence of x, of course it doesn't work if you break it by using a result with that assumption and then taking x = y.

Once again, it comes down to your own lack of understanding.

[Anonymous No.14581514]

>>14581501
>Where does f=g suddenly come from
It doesn't. I didn't assert that.
>couldn't understand my simple demonstration
I guess you can pride yourself in being as retarded as mr. Landau.

[Anonymous No.14581523]

>>14581203
Re-reading this post again it is now absolutely clear to me that you are a fucking retard who cant grasp the concept of generalized coordinates. You better not continue reading these books, because if q,q dot time dependence flies over your head, you won't be able to understand most of the material

[Anonymous No.14581527]

>>14581523
You need to go back to functions 101, learn about what they are and how function composition works. Also please read
https://en.wikipedia.org/wiki/Total_derivative

[Anonymous No.14581532]

>>14581514
>taking g(y) = y
>next line is integral of g^2 - y^2 instead of f(g,y)
Seems like we're done here, I've now identified that you are stuck on misunderstanding of generalized coordinates and chain rule.

[Anonymous No.14581536]

>>14581532
f(x,y) = x^2 - y^2
f(g(y), y) = f(y,y) = y^2 - y^2 = 0
What's so hard to understand here?

[Anonymous No.14581540]

>>14581527
You should do the same, maybe then you will understand the chain rule and you may have a shot at these books.

[Anonymous No.14581545]

>>14581540
I understand the chain rule perfectly well. I promise you that I know more math than you ever will in your life. I'm just amused by how confused you are.

[Anonymous No.14581546]

>>14581536
You fucking retard holy shit. Q and Q dot are fucking functions of time, write down the total derivative of the Lagrangian.

[Anonymous No.14581554]

>>14581546
You are so dumb lmao. The lagrangian is a function which takes any quantities Q and Q', they don't have to be functions of anything.

[Anonymous No.14581564]

>>14581554
Yes, if understanding that generalized coordinates depend on time means being dumb, then I'm very glad that I'm not smart like you, maybe then I would be solving non existing problems too.

For the last time for any Anon looking to understand the issue of OP's rambling - L is a function of q(t), q_dot(t) and t. And the total derivative of these quantities follows the chain rule. The derivation in L&L is correct, but this autist thinks that q,q_dot are not functions of time, which is clear from this post >>14581203

[Anonymous No.14581573]

>>14581564
It's even more funny because it's clearly implied in the paragraph 2 of the picture, where the coordinates q^(2) and q^(1) are written like this EXPLICITLY to make sure that the reader understands their value is given by the integration bounds. OP is a larping undergrad unfortunately. No quality in this thread whatsoever.

[Anonymous No.14581581]

>>14581564
newcomer to the thread. you don't seem to understand what anon is saying. see this post here
>>14581475
f(x,y) = x^2 - y^2.
he sets f(x,y) = f(g(y),y)) where g(x) = x (by extension, g(y) = y)).

the last piece of information is his y^2 * y term in the integral... that *is* the chain rule, you buffoon.

[Anonymous No.14581595]

>>14581581
I understand it, and I repeat that the issue is that he uses the total differential that is valid ONLY if the function x does not depend on y, but then he is surprised when he sets x = y and bullshit comes out.

This is literally all boiling to his inability to understand that q is a function of time, there is no issue whatsoever with the derivation in his picture.

[Anonymous No.14581596]

>>14581564
>Yes, if understanding that generalized coordinates depend on time means being dumb
But I understand that too. Oh my fucking god why is it so hard to get my point across to you. It's so unbelievably frustrating.
I know chain rule. In taking a total derivative of a function you assume that all the arguments are actually functions of the variable you're taking a derivative with respect to.
My point is that even though a lot of times the inputs you put in L(q, q', t) are values of functions of time, they need not be, as L is a function of THREE variables, not just time. That means you can have many different choices of q(t), not just one, and L will output the answer for a particular value of t just as well. Now again, let's just look at the simplest case of one degree of freedom, where q(t) just just a function R-> R and L(q, q', t) is just a function RxRxR -> R. Now this is crucial to understand. L is a function of three independent variables which can be whatever numbers you choose. It just so happens that we care about the case when one of the variables is (generalized) position and the other derivative of position. To clarify things, let's rename the variables, and write L as L(x,y,z), as x,y,z are allowed to be ANY real numbers and L is supposed to be defined on any pair (x,y,z).
Now IN THE CONTEXT of L being a function RxRxR, PLEASE explain what it means for it to be a total derivative w.r.t. the last argument z. It simply makes no sense. It only starts making sense AFTER you've chosen that for the first two arguments you will input some function q(t) and some other function q'(t), resulting in a function dependent ultimately ONLY on t, that is, t - > L(q(t), q'(t), t). But THIS IS NOT THE SAME FUNCTION AS L. L has three arguments, but this function has only ONE(1) argument. The latter function being a total derivative makes sense, but the former function DOES NOT.

[Anonymous No.14581603]

>>14581595
>and I repeat that the issue is that he uses the total differential that is valid ONLY if the function x does not depend on y,
It's literally the opposite. The whole purpose of total derivative w.r.t. t is that you assume that all the variables of a multivariate function depend on t. THAT'S THE WHOLE POINT OF A TOTAL DERIVATIVE.

[Anonymous No.14581606]

>>14581596
But nigga its strongly implied that he is considering only functions of time, as is clear from the final result where notation implicitly assumes this.

[Anonymous No.14581611]

>>14581606
He's considering the Lagrangian, which is DEFINED to be a function of THREE VARIABLES, the position, velocity, and time. (the first two of which are vectors but nevermind that). It's NOT a function of just time. It only becomes a function of time only when you CHOOSE a path q(t) and input q(t), dq/dt for the arguments in L. But then it becomes a DIFFERENT function, which is NOT the lagrangian.

[Anonymous No.14581612]

>>14581603
Then why are you using an incorrect result which works iff x does not depend on y? Dau does not do anything like this whatsoever and it is clear only functions of time are considered.

[Anonymous No.14581618]

>>14581595
>the total differential that is valid ONLY if the function x does not depend on y
>his inability to understand that q is a function of time,
bruh what. so how is what L&L did valid with the total derivative, via your own argument?

[Anonymous No.14581620]

>>14581612
He says
>some function f(q,t) of co-ordinates and time
>co-ordinates AND time
>AND
It's not just time.

[Anonymous No.14581622]

>>14581611
Bro, you do realize that time dependence in generalized coordinates is implicit for all Lagrangians, right? What the fuck do you think Euler-Lagrange equations are if thats not the case? There is literally no scenario where time dependence is not implicit in any Lagrangian.

[Anonymous No.14581623]

>>14571673
>>14572553
>>14572556
>>14573430
Wrong.

[Anonymous No.14581634]

>>14581622
>Bro, you do realize that time dependence in generalized coordinates is implicit for all Lagrangians, right?
Yes I do, but that's irrelevant to my point. Lagrangian is still a function of a pair of vectors and time, which is why what he wrote makes NO SENSE whatsoever.

[Anonymous No.14581658]

>>14581634
The mathematical precision is lacking, but he is talking about the action, which is a functional and in which case we are assuming an explicit q(t) dependence, in which case this argument is, while a bit sloppy, correct in that the action will only change with a total derivative under the integration.

[Anonymous No.14581660]

>>14577594
Amazed at how many top notch universities use this garbage.

[Anonymous No.14581663]

>>14581658
Btw, if you really wanna get mad about really fucking sloppy and im quite confident that even incorrect math in mechanics, read the section on multiple scale perturbation theory in the section on nonlinear oscillators. Nevertheless, the books are excellent and timeless physics textbooms because they adress exactly the types of problems that arise in research and show the typical ways how to approach them. Math is sloppy af tho, thats without a doubt.

[Anonymous No.14581671]

>>14581658
I guarantee you there is no way to make what Landau wrote precise, because it's just nonsensical gibberish.
>but he is talking about the action
Action is independent of time. Integrating over time eliminates the free time variable.
>correct in that the action will only change with a total derivative under the integration.
We're talking about two different things here. I don't care about showing that if the equations of motion stay the same, the lagrangian differs by a total time derivative. That's a separate issue. My issue is with the implication that adding a total time derivative to the lagrangian doesn't change the equations. I'm saying this is not even wrong because it's total gibberish, and there's no way to make this make sense.

[Anonymous No.14581675]

>>14581663
>if you really wanna get mad about really fucking sloppy and im quite confident that even incorrect math in mechanics
Incorrect math is not that bad, sometimes I read math textbooks with mistakes in them and correct them myself. I don't even care about nonrigorous, intuitively justified math in physics, as long as I understand what the author is doing. My problem is with not-even-wrong, totally gibberish "math", which is there because the physicist doesn't understand the mathematical concepts involved and ultimately spits on rigour.

[Anonymous No.14581684]

>>14581675
I think it can be reconciled by specifying f as only a function of time, not q,t. Then it is correct. This similar result to keep invariance of the action by only considering some divergence term is also performed in derivation of Noether's theorem and the principle is the same.

[Anonymous No.14581687]

>>14581475
Your missing some important steps here, anon... most importantly at no point prior to substituting out for h do you define what h is in terms of g(y) and y.

[Anonymous No.14581696]

>>14581684
>I think it can be reconciled by specifying f as only a function of time, not q,t. Then it is correct
I agree, that would make sense. But then Landau wants to say that the converse is true, so what do you make of the converse? If two lagrangians give the same equations (whatever that means, let's say it means q(t) extremizes the action w.r.t lagrangian 1 iff it extremizes w.r.t. lagrangian 2) what can we then say about the lagrangians? How would you rescue the paragraph, if at all?

[Anonymous No.14581697]

>>14581687
I took the definition of h from the previous anon. It's h(x,y) = x^2*y - y^3/3 + C, so h(g(y), y) = g(y)^2 * y - y^3/3 + C

[Anonymous No.14581714]

>>14581696
It's quite simple I would say, the change in the Lagrangian must be such that the variation of the action difference is zero, which means that the additional term must satisfy E-L eqns. on its own, that is the equations of motion are not changed by this additional term. You could probably then figure out how this function must be a total derivative, because the variation is zero on the boundary.

[Anonymous No.14581715]

>>14581714
>You could probably then figure out how this function must be a total derivative
Again with this nonsense...

[Anonymous No.14581717]

>>14581715
But it's true, look up the derivation of Noether's theorem, it's exactly the same business, where you get that the change to the Lagrangian must be a total derivative and this is something that is done by every university where quantum field theory is being taught, Landau is not at fault for regurgigating this principle :)

[Anonymous No.14581719]

>>14581717
>change to the Lagrangian must be a total derivative
You mean a function of time only? What the fuck do you mean?

[Anonymous No.14581725]

>>14581719
Not necessarily, in field theory the action is a four-dimensional integral over Lagrangian density and a symmetry transformation is such that it changes the Lagrangian density only up to a four-divergence of some function that can depend on the spacetime coordinates. So, yes, the only requirement in the case we discuss here is that it is a function of time.

[Anonymous No.14581728]

I really really strongly recommend that you look up various derivations of Noether's theorem, because that is exactly what Landau talks about in paragraph 2.

[Anonymous No.14581732]

>>14581728
In the abstract, maybe. but you're wrong. landau wishes he had half of noether's rigor.

[Anonymous No.14581739]

>>14581732
Yes, well that's the way of physics. Sometimes shit is being done with zero rigor, but if it works it's good physics.

[Anonymous No.14581740]

What about this? I'm not saying this is nonsense, but why is it true that the second term is a time derivative only if it's a linear function of the velocity v?

[Anonymous No.14581746]

>>14581475
>Assuming x and y are independent...
>Immediately makes x dependent on y

[Anonymous No.14581758]

>>14581740
I think it's because then you have f*g' = (f*g)' which is a total time derivative if f is independent of time.

[Anonymous No.14581768]

>>14581728
I just marathoned the derivation in
>https://en.wikipedia.org/wiki/Noether%27s_theorem#:~:text=Noether's%20theorem%20or%20Noether's%20first,1915%20and%20published%20in%201918.
and had no problem with it. Nowhere does it talk about the lagrangian being a total time derivative or any nonsense like that.

[Anonymous No.14581776]

>>14581768
No total time derivative, but the change in the Lagrangian is a four divergence for a symmetry, which is a similar concept, in the field version of the theorem

[Anonymous No.14582383]

I am believing the schizo on this one

[Anonymous No.14582439]

i too am rooting for the schizo

[Anonymous No.14582475]

this thread proves why physicists are complete fucking retards

you can't compete with mathchads

[Anonymous No.14582605]

>>14582475
>>14582439
>>14582383
>>14581697
>>14581475
>>14581675
>>14581715
>>14581634
>>14581596
>>14581554
>>14581540
>>14581447
Oh please, faggot.
Hope the moderators remove this garbage thread.

[Anonymous No.14582658]

>>14582605
I hope the mods ban you for being a mass replying faggot.

[Anonymous No.14582667]

>>14582658
not my problem you shit up the thread with a simple misunderstanding that could've been cleared up had you just read the fucking book, underage

[Anonymous No.14582677]

>>14582667
Its not a misunderstanding. The quote you posted is from a different context and is irrelevant here.

[Anonymous No.14582678]

>>14582677
no, it's not. It's from the same section and serves as a definition of q.

[Anonymous No.14582686]

>>14582678
It's a definition of q(t) for that particular paragraph, where we have chosen a lagrangian and trying to see what the paths minimizing the action w.r.t. that lagrangian look like
In the later paragraph he talks about how changing the lagrangian changes the equations of motion. Changing the lagrangian here means not changing it for one particular path as a function of time, but for ALL POSSIBLE paths, because by using the Lagrangian for all possible paths is how you get the equations of motion (note the [math]\frac{\partial L}{\partial q}[/math] in E-L equations indicating that L is viewed as a function of q, not just t). That means we don't choose a path, and we look at the lagrangian as a general function L(x,y,t) for ANY generalized coordinate vectors x,y.

[Anonymous No.14582694]

>>14582686
>It's a definition of q(t) for that particular paragraph
No, you just assumed that. Ignoring that definition leads to a contradiction later on so the definition holds until the end of the section. If q(t) is the function for which S is a minimum, then q is necessarily that for the later part of the section. As S needs to be extremal for it to denote a possible path. Hence "ALL POSSIBLE paths" necessarily implies q=q(t).

[Anonymous No.14582702]

>>14581203
Holy shit you're a retard.
I'm so glad Landau filtered you from ever doing physics at a serious level.

[Anonymous No.14582711]

>>14582694
>Ignoring that definition leads to a contradiction later on so the definition holds until the end of the section
I'm not ignoring it, I'm saying it doesn't apply here because we're talking about the general form of the lagrangian, and how equations of motions change when you change the lagrangian. That means we view the lagrangian as a function of THREE VARIABLES, q, q' and t, not just ONE variable t.

[Anonymous No.14582715]

>>14581758
Huh?
Let's say we have f(q,t) such that
[math]\frac{\partial L}{\partial v^2} 2v*\epsilon = \frac{df}{dt}(q,t)[/math]. How does that imply that the LHS is a linear function of the velocity?

[Anonymous No.14582771]

>>14582711
>I'm not ignoring it, I'm saying it doesn't apply here
It obviously does.
>how equations of motions change
there aren't equations of motions in the first place if S isn't extremal, as in if q=/=q(t).
As I said, it's a necessary condition you chose to ignore.
q dot is not an arbitrary variable either. It's precisely defined in the introduction, which you should definitely review.

I won't waste any more of my time with you.

[Anonymous No.14583049]

>>14582715
It does not, but the reverse implication is true, i.e. if it is a linear function of velocity, then it is simply a total time derivative if other factors do not depend on time, like I've shown in the previous post

[Anonymous No.14583053]

>>14583049
So you're saying Landau is wrong in this part too?

[Anonymous No.14583059]

>>14583053
No, he's right. The term of such a form is a total derivative indeed only if it is a linear function of velocity, and I have shown above the reason for this.

[Anonymous No.14583074]

>>14583059
>The term of such a form is a total derivative indeed only if it is a linear function of velocity
You literally said this is wrong a post ago and that a converse is true:
>It does not, but the reverse implication is true, i.e. if it is a linear function of velocity, then it is simply a total time derivative if other factors do not depend on time

[Anonymous No.14583076]

>>14583074
Well, if it was not clear what I meant then it should be clear from my last post. Once again, f*g' is a total time derivative if f does not depend on time, because then it equals (f*g)', which is a total time derivative, therefore if g' is velocity, f must not contain any additional total time derivatives, i.e. velocity

[Anonymous No.14583087]

>>14581203
This can easily be corrected though. Just rewrite the equation as [math] L'(q, \dot{q}, t) = L(q, \dot{q}, t) + \frac{\partial f}{\partial q} \dot{q} + \frac{\partial f}{\partial t} [/math]

[Anonymous No.14583088]

>>14583076
But Landau claims that IF the term is a total time derivative, THEN it's a linear function of the velocity, which is the other way around from what you say.

[Anonymous No.14583092]

>>14583087
Here q bar is an arbitrary vector. How do you take a derivative of an arbitrary vector? Moron.

[Anonymous No.14583094]

>>14583092
I don't see any q bar here. What are you talking about?

[Anonymous No.14583098]

>>14583088
That is also correct since the form of the term is given and alredy linear in velocity, the text obviously means that there must not be any additional velocity terms. I dont see any issue in this part.

[Anonymous No.14583100]

>>14583094
Sorry my bad. I meant [math]\dot{q} [/math].

[Anonymous No.14583107]

>>14583100
You're not taking any derivative of q to get [math] \dot{q} [/math]. You're just letting the linear functional [math] \frac{\partial f}{\partial q} [/math] act on the vector [math] \dot{q} [/math]

[Anonymous No.14583111]

>>14583107
Ok that actually makes sense mathematically, I didn't think about it that way. And then I see that the claim about action not varying is true as the second variable is always intended to be a time derivative of the first in the action. But how then do you prove the converse? That if the equations are the same, then the difference L' - L is of this form.

[Anonymous No.14583121]

>>14583088
you're genuinely retarded

[Anonymous No.14583123]

>>14583111
Where is he claiming that the converse is also true?

[Anonymous No.14583127]

>>14583123
Here:
>>14572652

[Anonymous No.14583128]

>>14572652
>$2

[Anonymous No.14583131]

>>14583127
Well okay I don't have the book but that actually does seem wrong or at least not properly explained

[Anonymous No.14583134]

>>14583131
At least I maybe figured out what he meant by a total derivative of the lagrangian, which is something I've never seen before, and only makes sense because he implicitly assumes one of the arguments is a derivative of the other when it doesn't have to be in general. So yeah, I admit to being wrong when I said that there is no possible interpretation that makes sense.

[Anonymous No.14583830]

>>14582605
It's better than a slow board

[Anonymous No.14584322]

>>14581303
They beat the USA though in almost every other aspect of the space race.

[Anonymous No.14584328]

>>14581467
And?