Derivations Definition and 102 Threads

Hi everyone, I’m Manuel. I studied physics originally and now work mainly in AI. Recently I’ve been combining both interests in an open project called TheorIA (Theoria Dataset), which collects structured derivations in theoretical physics, formatted so they can be used for reproducibility...

I am having some trouble following the derivation of the partial derivative of internal energy with respect to volume at constant temperature. The fundamental property relation is given by: dU = TdS - PdV The text I have shows the result of taking the partial derivative with respect to volume...

Please, I am looking for a simple example of derivation on ##sl_2##, if possible, I try to use identity map, but not work with me, A derivation of the Lie algebra ##\mathfrak{g}## is a linear map ##\delta: \mathfrak{g} \rightarrow \mathfrak{g}## such that ##\delta([x, y])=[\delta(x), y]+[x...

I have been reading Wikipedia’s derivations of the Lorentz Transformations. Many of them start with the equation of a spherical wavefront and this reasoning: - We are asked to imagine two events: light is emitted at 1 and absorbed somewhere else at 2. For a given reference frame, the distance...

Hi I’m looking for a textbook that shows the derivations of equations such as the different forms of the schrodinger equation fully and step by step.

This is a pedagogical /time management / bandwidth / tradeoff question, no argument that learning the complex exponential derivation is valuable, but is it a good strategy for preparing for first year Calculus? my 16YO son is taking AP precalc and AP calc next year and doing well, but struggled...

Hello! According to the attached proposition on ##C^\infty## manifold space of derivations ##D_m M## is isomorphic to Tangent space ##T_m M##. Cited here another proposition (1.4.5) states the following 1. For constant function ##D_m(f)=0## 2. If ##f\vert_U=g\vert_U## for some neighborhood...

[Moderator's note: Thread spun off from previous one due to topic shift.] Please forgive my ignorance, I've never studied group theory systematically up to now, so I'm not aware of all the concepts and symbols that have been used up to now. Yet, I'm interested in the derivation of the Lorentz...

The effect of temperature change in Le Chatelier's Principle is given by the equation $$ \log \left(\frac{\mathrm{K}_{2}}{\mathrm{~K}_{1}}\right)=\frac{\Delta \mathrm{H}}{2.303 \mathrm{R}}\left[\frac{1}{\mathrm{~T}_{1}}-\frac{1}{\mathrm{~T}_{2}}\right] $$. How to derive $$ \log...

Hello! So what I've tried to tackle this problem is derive the equation,set it equal to zero,find a value for v and than put it in the second derivation.So when I derive this I get $$ \frac{v^2+9-v *(2v)}{v^4+8v^2+16)} $$ Now if i set that equal 0 and try to find a value for v I get this. ##...

My lecturer was going through a derivation, and I'm a bit stumped as to what kT/hc actually signifies. Like what is it...

Greetings I'm currently designing a lab-script intended for comprehension and use at an undergraduate level. I was extremely frustrated during my undergrad to be dealing with a plethora of uninspired and dull experiments so I decided to take a slightly unconventional (or extremely conventional...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Theorem 2.2 and the remarks after the theorem ...Theorem 2.2 and the remarks after the theorem read as follows: My questions on the above text from Tu are as follows...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Tu's section on tangent vectors in $$\mathbb{R}^n$$ as derivations... In his section on tangent vectors in \mathbb{R}^n as derivations, Tu writes the following: In the...

G'day, Would anybody else agree that derivations of key results in physics texts - school or college level - proceed in a manner that betrays no compunctions in the mind of the author about fore-knowledge of the pre-known form of the final expression? I have a strong conviction that the great...

I understand that it is useful to learn and remember the derivations of formulae in most cases. However, I tend to forget the derivations of several formulae, especially those in optics and dynamics. For a moment, let's forget the examinations. I wish to pursue higher studies in applied...

It is assumed that entropy increases in the universe. However, the fluid and acceleration equations are derived assuming that. TdS=dE+pdV where dQ = TdS. But dQ is usually set equal to zero to derive these equations. Hence since T is non zero, dS should be zero and so there would be no...

I study ncert physics class 12. Is there any special way you rote learned all the diagrams and derivations? (for example they ask in board exam that explain the working and principle of cyclotron and draw its diagram. Very hard to remember.)

Guys I have the following homework problem to solve: There are 2 given points in a plane. If we take a point-like object with mass m and take it to the "higher" point what path should it go on to reach the other point in the shortest possible time. Only gravitational force affects our point-like...

Hello everyone. I was reading Einsteins 1916 original paper on GR, the "The foundation of the general theory of relativity". There are some derivation that he did but I didn't quite understand. It would be nice if someone can give me some direction or some guidance on it. Here is the link to...

My text of physics, Gettys's, proves that the magnetic field on the axis of a solenoid, in whose loops, of linear density ##n## (i.e. there are ##n## loops per length unit), a current of intensity ##I## flows, has the same direction as the loops' moment of magnetic dipole and magnitude ##\mu_0...

Homework Statement I've been looking at examples of motion derivations for my class, and it's honestly just very confusing. I heard Dynamics should prep you for this but I must have had a very poor course because we never had to understand geometry and physics to this degree... Homework...

hi, I really want to dig valuable things out of quantum theory, also I have a big eagerness to see the derivation of formulas to understand the logic of this topic. Could you recommend me some nice books which may meet my needs I expressed at the beginning ?

Hi. I would like to ask a simple question. Here is the link of the file I study on. Immediately before the formula 4.9 for Biot number. Lc=V/As but I cannot understand it and I think it is not clear enough. How it appears, for what the word "characteristic" stands for, for example a pipe? For...

Homework Statement A straight circular plastic cylinder of length L and radius R (where R ≪ L) is irradiated with a beam of protons so that there is a total excess charge Q distributed uniformly throughout the cylinder. Find the electric field inside the cylinder, a distance r from the center...

I do not get some points of this proof about the time derivative of a unit vector $\hat{u}$ (costant magnitude) which is following a precession motion. The picture is the following. I want to prove that $$\frac{d\hat{u}}{dt}=\vec{\Omega}\wedge \hat{u}.$$ I'm ok with almost all the proof except...

Homework Statement Derive Cholesky Decomposition for a 3x3 matrix Homework Equations IN: S is Real matrix with dimensions 3x3 and is Symmetric and semi-definite Out: L is a Real matrix with dimensions 3x3 such that S=L*L^t L is lower-triangular The Attempt at a Solution We learned this in...

I am reading John M. Lee's book: Introduction to Smooth Manifolds ... I am focused on Chapter 3: Tangent Vectors ... I need some help in fully understanding Lee's conversation on directional derivatives and derivations ... ... (see Lee's conversation/discussion posted below ... ... ) Lee...

Hello, Please take a look at this handbook of derivatives and integrals: http://myhandbook.info/form_diff.html http://integral-table.com/downloads/single-page-integral-table.pdf I would appreciate it if someone could point me in the direction of exemplary books that derive these...

Hello! I understand what specific heats are and how to derive them. I just feel that I'm missing a little something in the methodology. Consider the 1st law of thermodynamics and the definition of enthalpy: 1) dU = δQ -δW = δQ - PdV 2) H = Q - VP For the derivation of CV, dV = 0 and the...

Homework Statement Using the special relativity formulae p = mv / [1 - (v/c)2] E2 = p2c2 + m2c4 derive linear relations between: (i) momentum and mass; (ii) energy and mass; (iii) energy and momentum, which involve only c, c2, β = v/c, and γ (= 1/sqrt(1 - β2)) The attempt at a solution I am...

Any advice on my derivation layout?

(Change in momentum is the area under a force against time curve.) (Force is the time derivative of momentum.) Using separation of varibles, you get Fdt=dp. Integrate both sides, you get that the integral of Force with respect to time is equal to p. This seems to imply that p, momentum, is...

I don't understand how some terms are derived. How did the last term of 3-47 originate? How did 3-49 get so many terms from just one term in 3-41? Why integrate from V to infinite? That is not intuitive. Thas a functions are unusual because the absolute values of U,H,S cannot be computed...

Hi Guys, new poster here. I am currently doing a practical report on Uniform Circular Motion, where we had to swing a rubber stopper around attached to a length of string and mass. I have to do a write up, including the background theory. I have searched everywhere but I have found no clear...

Homework Statement I am wondering if anyone knows of a document that shows derivations of specific values in Physics? For example, I need to find μs and am given the distance traveled and time (1.2 km in 17 sec). Homework Equations I know the equation for μs, Ffriction=μs⋅FN. The Attempt...

I have been studying potential steps and barriers as well as reflection and transmission coefficients and how to derive them. Most of it makes sense to me except for one thing: As we know, the normal Schrodinger equation is: (-ħ2/2m) (∂2Ψ/∂x2) + v(x)Ψ = EΨ For a step potential however, my...

Hey, I just had the chance to extract the gravitational lensing caused by a massive point using Fermat's principle. I was wondering though, is there any other way to do that? Also is the light's time delation induced by the "refraction index" n (Saphiro delay) connected to "gravitational time...

Hi, I understand when I study a physics topic, it's very important that I solve as many problems as I can possibly can and it's also very important to internalise all the techniques used to solve problems in that topic. However, I was wondering if the same applies for the derivation of formulae...

Hello Everyone, I have read many derivations of Einstein field equations (done one myself), but none of them explain why the constant term should have a $$c^4$$ in the denominator. the 8πG term can be obtained from Poisson's equation, but how does c^4 pop up? Most of the books just derive it...

Loosely speaking a derivation D is defined as a function on an algebra A that has the property D(ab) = (Da)b + a(Db). Now, if we define the map ad_x: y \mapsto [x,y] and apply this to the Jacobi identity we get ad_x[y,z] = [ ad_x(y),z ] + [ y, ad_x(z) ] . This does not look quite like the...

Hello In textbook by Kobayashi and Nomizu derivation of rank k in space of all differential forms on a manifold is defined to be operator that is linear, Leibnitz and maps r-forms into r+k-forms. By Leinbitz I mean, of course: D(\omega \wedge \eta)=(D \omega) \wedge \eta + \omega \wedge (D...

Hi. I'm a self-learner, and I'm doing an introductory QM from Griffiths. My question is should I memorize all the derivations and proofs in the book or I just have to memorize the final results? Another point is that I have nobody to ask about my solutions to problems or to help me in the hard...

Homework Statement Hello, this isn't really a h/w problem that fits the template, but here seems the most sensible place to post. I am writing a paper (not original research) and part of the requirements is that I include a "comprehensive discussion of the relevant theory (including...

In some books, when discussing the relation between partial/directional derivatives and tangent vectors, one makes a generalization called a "derivation". A derivation at ##\vec{a} \in \mathbb{R}^n## is defined as a linear map ##D: C^{\infty}(\mathbb{R}^n) \to \mathbb{R}## which for ##f,g \in...

hi so basically my question is derivation of derivation of the quadratic case of the terminal velocity I have attached the pictures in picture 1 I don't know I think the book has error in his derivation @ equation 2.4.13 shouldn't it be + instead of negative ?? & in second picture their...

The traditional Schrodinger equation is written as Laplacian ψ+constant(E-V)ψ=0 the above equation derivation is based on the formation of hydrogen after the combination of proton and electron. E is said to be total energy and V potential. energy of hydrogen atom. On solving the value of E...

Are there derivations of the taylor, Fourier and laurant series?

I've recently come to the conclusion that I might have made some mistakes along the way. I'm going into my senior year of EE and something just doesn't feel right about my abilities. Over the last couple semesters, I've fallen into the "plug and chug" mode of solving problems. I have some issues...

Homework Statement I need the derivations of gravitational potential energy and kinetic energy (without using calculus)Homework Equations PE = mgh \\ KE = {1 \over 2}mv^2 The Attempt at a Solution Potential Energy: Work done = Fs But... F=ma So substituting that in becomes mas where a is...