The Single Basic Concept found in (Almost) All Fundamental Physics Equations.
Вставка
- Опубліковано 27 чер 2024
- If you can understand Partial Derivatives, you can understand what most fundamental physics equations are trying to tell you.
In this video, we take a look at normal, "total derivatives" as well as "partial derivatives". We start by understanding that a total derivative is used to measure the rate of change of one quantity with respect to another, even if that change is not constant with the second quantity. This is a very basic principle in calculus that was worked on by both Leibniz and Newton.
The example given here is that of a car moving along a road. Even if the car does not move equal distances in equal time intervals, we can calculate its velocity at every point in time if we are able to calculate the total derivative of the car's displacement (position) with respect to time. In essence, the total derivative measures the rate of change of displacement with respect to time.
However, in some cases there are quantities that depend on more than one variable. In this video we look at the height of a surface sitting above the x-y plane, and the height at any point along the surface depends on both the value of x, and the value of y, at that point. This means we have a quantity h (representing the height) that is dependent on two variables - x and y.
However, we may want to measure simply how the height changes with the change in one of the variables, without accounting for its change due to the other variable. This is where our partial derivatives come in. Firstly worth noting that the letter d's used to represent normal derivatives become curly d's if we want to represent partial derivatives.
The partial derivative dh/dx (for example) gives us the rate of change in height of the surface, as we move along the x direction, for a constant value of y. In other words, we can find the gradient of the surface and how this changes over x, having chosen a single value of y that we can move along. Similarly, partial dh/dy shows how the height of the surface changes as we move along the y direction at a constant value of x. In each case, we can choose the constant value of the variable(s) held constant and the formula for the partial derivative will account for this.
This is different to the total derivatives dh/dx and dh/dy because the total derivatives actually account for any interdependencies between x and y too - for example if y was a function of x then total dh/dx would be different to partial dh/dx.
Partial derivatives are used in many different fundamental physics equations. In this video we look at a few different examples - the Classical Wave equation, the Schrodinger equation, the Heat equation, and the Euler-Lagrange equation. Each of these uses partial derivatives to represent relationships between quantities that may be dependent on multiple variables, but that we only want to study one variable's dependence on. In other words, each of these equations is a partial differential equation.
Thanks for watching, please do check out my links:
MERCH - parth-gs-merch-stand.creator-...
INSTAGRAM - @parthvlogs
PATREON - patreon.com/parthg
MUSIC CHANNEL - Parth G's Shenanigans
Here are some affiliate links for things I use!
Quantum Physics Book I Enjoy: amzn.to/3sxLlgL
My Camera: amzn.to/2SjZzWq
ND Filter: amzn.to/3qoGwHk
Timestamps:
0:00 - Total (Normal) Derivatives
4:47 - Partial Derivatives and the Curly D's
9:22 - Fundamental Physics Equations Using Partial Derivatives
Videos Linked in the Cards:
1) • Why Lagrangian Mechani...
2) • Why You Should STOP Us...
Live that you’re doing more mathematical topics! Keep it up
Having this explanation as a first lesson in calculus would be a great boon to any student! Nice work Parth.
I am certainly interested in more Legendre discussion from here. 🙏
Parth back at it again hell yeah! 🔥
🔥🔥🔥🔥🔥
Thanks for explanation about basic concept in derivative. I really enjoy watch this video and have a new perspective about understanding the concept.
If we understand the meaning of every equation, I think physics is fun to study. 😅
Again, thanks for your video Mr. Parth. Keep up the good work. I'm the new subscriber here.
🙏
This is great helpfully
Always love your content
Amazing content!
Very well done mate
I like to see that at some point in the future!
Nice video 😊
Thank you !
Would love to know more about wormwholes and the theory behind it from you
I live your videos where you explain mathematical terms. Also could you maybe look into doing a video about the 2022 Nobel prize for physics?
❤❤❤ So helpful.
What do you think about making a video about operators in shrodinger equation, how to deal with them in this?
Hey Path. I'm a physics student in my third year. I'm struggling a little with my statistical mechanics course. Could you make a video about the partition functions Z and Q?
I second this. Hope he makes one.
I love Lagrangian mechanics, it's so simple even though it has absolutely no right to
to be WHAT?
@@azzteke misstyped lol
@@davidurban528 lol what was it you mistyped?
"to be
WHAT???" 😅
Bro, I like this mustache on you. Looks good 👍
Hey Parth... Love your videos❤ Could you do one about Bhabha Scattering?
_Parth ...Grateful to learn from you...👌...I Request you to do a video on Lorentz and Gauge Invariance in detail... because it holds remarkable space in physics_
*I request the above by 2nd time... previously in previous video*
This is the first time I request you to cease requesting.
@@bon12121 If we need something we have to ask...who else will ask...?...it's a kind of respect we are giving to the educator, who shares his/her perspective.
At 11:47, I got got stuck on the RHS (Right-Hand Side) of the eq. I saw the time derivative of something that already had a time derivative, q_dot.. It made me think that it might relate to the second partial derivative of q-space, acceleration. But I don't know if diferenciation (sp) distributes over multiplication, like it does over addition.
Didn't you learn the product rule??
i think you should also mentioned the total differential
Sir, In the book introduction to electrodynamics, 3rd edition (Griffiths), is stated that
figure 1.18 c indicates a positive divergence. Could you please explain this in the context of your video about the first Maxwell equation.
Yes, make the vid, make me happy
So you never have d2t in the denominator, right. And dt2 is not a square in any way, just a notation. Thanks for confirming.
just voting for more on Euler-Lagrange ... plus all the physicsy stuff others have requested here. thanks.
Can u make conceptual videos on stat mech?
I'm currently learning partial derivatives in calculus 3 and it's surprisingly easy
the struggle is the partial differential equations. my calc 4 class here is ordinary differential equations, and that's plenty complicated right now
@@ekt2656 yeah I'll be taking different equations next semester if I pass my cal 3 course. Is multiple integration difficult?
@@real_michael as good as you need to be at integration (you get some pretty nasty functions sometimes), its not so much multiple integrals but just all the properties of all the different forms that ODEs can come in. For first orders we learned: separation of variables which is pretty intuitive, exact method, "by integrating factor" (idk if thats the proper name), bernoulli, riccati, and other misc subs. For higher order derivatives, we actually only did linear eqns and for that we did undetermined coefficients, trial sln y = e^\lambda x, euler sub x = e^t, variation of parameters, and more. rn we're doing systems of odes which is like the above but like vectors kinda sorta as far as i get it now.
i had to know a bit about lin alg although i havent taken it in regards to linear independence, determinants (the wronskian), matrix multiplication, linear operators (D operator), and condition?/property? of a singular matrix. also had to know euler's identity the e^itheta one like the back of hand.
next we do the laplace transform which im excited for!
i hope you enjoy the class next semester!
@@real_michael NO.
How can i contact you about a research I am conducting requiring your input? I am far from a physicist or scientist in the telluric field but I am an expert in cosmology and would love your input on something of an unconventional nature. Thank you.
Huh. They are all zero normed split-complex (or hyperbolic quaternion) derivatives, ||∂u/(∂x/c+j ∂t)||=0 where j²=1?
That suggests a few things to me:
First, ∂u could be the norm of a split-complex (or hyperbolic quaternion) value which could give you are more complicated (and possibly interesting) form of these equations without that norm.
Second, mapping to Euclidean space-time would give you a non-zero norm and a zero proper time interval? That implies the wave is moving at the causal limit, c, right? That's the only circumstance under which 𝛼(v) ∂t = 0 where Lorentz's 𝛼(v)=√(1-v²/c²). Either that or ∂u is constant with repect to ∂𝜏, which it would have to be if ∂𝜏=0 but wouldn't *necessarily* need to be true otherwise. Except 𝜏 and t aren't independent parameters of the function u.
Third, it implies ∂u/∂x is the derivative of ∂u/∂t with respect to 𝜃=Arg(∂u/(∂x/c+j ∂t)) and vice versa due to the relationship between cosh 𝜃 and sinh 𝜃.
Hello there, i am an engineering student from India. You are like a God to me that i hadn't understood any of the Maxwell equations explained in our college but i saw your playlist, they are awesome. Thank you very much sir 😊.
If you like these kinds of videos then try also Mithuna's channel called "Looking Glass Universe".
Today only I start this chapter
Hey, you have a beautiful moustache, I suspect it's inspired by Ram from RRR...
No - inspired by Paul Dirac or Louis de Broglie or maybe even Renee Descartes. Who knows.
Please ✔️ few words more on x=Beta.t^3 ❓️ at 2:56
I am 13 years old and I need to solve Schrodinger equation and wave function in mathematical form can you do it in mathematical form
10:03 Should have used different coefficients.
Show Us The QUIRKS! Show Us The QUIRKS!
I thought video contain Legendre polynomial ,
How to ask you a question on physics? what is your contact email?