Derivation Definition and 1000 Threads

I'm trying to work through a derivation and am getting some funny results. For example, when trying to compare some expressions, Mathematica was telling me they weren't equal, and when I worked them out by hand, I new they were equal. I then tried something like this: ExpandAll[x] ===...

hi, i just need help with a step in a derivation in my thermodynamics book (indicated by the red arrow) http://i.imgur.com/C8k3xzT.jpg firstly, what's the point of a -(q+N) term if they're just going to cancel it out with a +q and +N? basically i want to know how the terms inside...

I'm studying linear elasticity and I came across an equation that I having problems figuring out the derivation. I want to understand this in case I may need to know it later in the course. The equation is as follows: \frac{\partial^2e_{zz}}{\partial x \partial y} = \frac{\partial}{\partial...

Alright. Physics Internal. I am investigating a physics principle applied into a practical way. Radar Guns and the Doppler Effect. Now the issue is, firstly, that I have encountered two equations to give me the perceived frequency of a wave with a moving observer and stationary source. I am not...

Hello, I have a doubt on how to differentiate a complex function f:ℂ→ℂ defined as follows: f(z)=zz^* where the * stands for complex conjugation. According to this source (at the very end of the Section, where it says: "...As this is a complex value, G*(f) acts as a constant...") the result...

Homework Statement Find the derivative of the function f(x)=cos(√x) by first principles Homework Equations f'(x)= lim as h tends to zero of [f(x+h)-f(x)]/h The Attempt at a Solution Problems arise immediately, since I have no idea what to do with the expression cos(√(x+h)), I've...

The normal form of Green's function is ##\oint_c\vec F\cdot \hat n dl'=\oint_{s}\left(\frac{\partial M}{\partial x}-\frac{\partial N}{\partial y}\right)dxdy## I want to get to \oint _cMdy-Ndx=\oint_{s}\left(\frac{\partial M}{\partial x}-\frac{\partial N}{\partial y}\right)dxdy Let ##\vec...

##F = G \frac{ m_{1} m_{2}}{ r^{2} } ## Where does the formula come from? And why does it work that way? How would it relate to Newton's Second Law? ##F = ma## Using Newton's Second Law, is it possible to get the Law of Universal Gravitation?

I was working on the derivation of the riemann tensor and got this (1) ##\Gamma^{\lambda}_{\ \alpha\mu} \partial_\beta A_\lambda## and this (2) ##\Gamma^{\lambda}_{\ \beta\mu} \partial_\alpha A_\lambda## How do I see that they cancel (1 - 2)? ##\Gamma^{\lambda}_{\ \alpha\mu}...

Sorry if this is the wrong place to ask this, but I think linear algebra is the best place to ask my question. Feel free to move this thread elsewhere if I am wrong. I would like to know how I can use linear algebra to help me figure out when I am deriving an equation if the derivation I...

I know that the potential energy of a dipole in a constant electric field is P(dot)E=PEcos(θ), but I can't seem to find how they got here; its not in my textbook. If anyone knows why please tell me.

Hello everybody! This is the derivation (for a single particle). \tau = F_{\perp }r \ = ma_{\perp}r \ = \alpha mr^2 \\ \text{if }\ \tau = I\alpha \text{ where } I \text{ is resistance to accleration then } \\ I = mr^2 I'm curious what the problem with this is because I haven't...

\vec{\tau}=\vec{F}x\vec{r} \vec{F}=\vec{E}q \vec{p}=q\vec{d} \vec{\tau}=(\vec{E}q)xr=\vec{E}x\vec{p} so then how do we end up with \vec{\tau}=\vec{p}x\vec{E}?

I'm kind of new to special relativity, I mean beyond what they tell you in survey courses. In any case, I've heard there was a relationship between energy and time in special relativity (I've actually heard someone say the "time component" of energy), and I've always been fascinated with E = mc2...

Hey, In a derivation of relativistic energy (in Physics for Scientists and Engineers, 5th edition, Serway and Beichner) they use a method of integration by substitution: Given that F=\frac{dp}{dt} and relativistic momentum is given by p=\frac{mv}{\sqrt(1-(v^2/c^2))} W=∫F...

Homework Statement I want to derive the trig identities starting with rotation on the plane. Homework Equations One rotation through a given angle is given by $$x' = xcosθ - ysinθ $$ $$y' = xsinθ + ycosθ$$ The Attempt at a Solution What if I wanted to rotated through any...

I am reading the article Mirela Vinerean: http://www.math.kau.se/mirevine/mf2bess.pdf On page 6, I have a question about e^{\frac{x}{2}t} e^{-\frac{x}{2}\frac{1}{t}}=\sum^{\infty}_{n=-\infty}J_n(x)e^{jn\theta}=\sum_{n=0}^{\infty}J_n(x)[e^{jn\theta}+(-1)^ne^{-jn\theta}] I think there is a...

Hello all, my teacher assigned a problem related to the yang-mills equation in my general relativity class and I just wanted to ask a couple of questions about this problem. I believe it is a simplified version of the Yang-Mills you encounter in particle physics. Basicly assuming that...

Humidity is known as mass of water vapor/mass of dry air Hs (saturation) = (Mw/Ma){Ps/(P-Ps)} P is total pressure Ps is saturation pressure what is the derivation for this equation?

In reading Weinstock's Calculus of Variations, on pages 261 - 262 he explains how Schrodinger apparently first derived the Schrodinger equation from variational principles. Unfortunately I don't think page 262 is showing so I'll explain the gist of it: "In his initial paper" he considers...

The vector magnetic potential is given \vec A=\frac{\mu I}{4\pi}\oint\frac{e^{-j\beta R_1}}{R_1}dl' After a few steps, the equation becomes: \vec A=\frac{\mu I}{4\pi}e^{-j \beta R}\left[ (1+j\betaR)\oint\frac{dl'}{R_1}-j\beta\oint dl'\right] The Book claim the second integral obviously...

I am trying to resolve some long standing problems I have encountered with blackbody radiation. Namely, the derivation of the radiation energy flux equation $$J=\sigma_{B} T^4$$. I understand the derivation of the energy density of photons in "a box". $$U/V=const. T^4$$ I do not understand the...

For directional derivatives: Let \hat{u}=<a,b,c> be the direction. Thus, \frac{∂\hat{u}}{∂x}=\frac{\sqrt{a^2+b^2+c^2}}{a} and so on. So, \frac{∂x}{∂\hat{u}}=\frac{a}{\sqrt{a^2+b^2+c^2}}=a Thus, \frac{∂F}{∂\hat{u}}=\frac{∂F}{∂x}a+\frac{∂F}{∂y}b+\frac{∂F}{∂z}c=∇F \bullet \hat{u}.

I am reading 'Classical Dynamics: A Contemporary Approach' by J. Jose, and I am confused about a step in the author's development of potential energy for a system of many particles. He begins by writing down a term equivalent to the total change in kinetic energy of the system: \sum_i...

As learning laser fundumentals, I've just reviewed the boundary conditions for electromagnetic waves. However, I came back to a point that confused me in the past and want to get it clear now :) One of the boundary conditions, regarding the magnetic fields parallel to the medium-interface...

This is probably a stupid mistake I am making, but I can't figure it out. My apologies in advance... I am familiar with the text-book derivation of the Lorentz transformation (I don't have any problem with it). It starts out stating: x2+y2+z2-c2t2 = x'2 + y'2+z'2-c2t'2 meaning that a...

A potential energy function for a two-dimensional force is of the form U = 3.21x3 y - 5.79x. Calculate the force that acts at the point (1.47m,1.42m). Enter the x-component first and then the y-component. -2.38×101 N -1.02×101 N I know in order to find the force components of this energy...

Hi! I am trying to understand the statistical mechanics derivation of the ideal gas law shown at: http://en.wikipedia.org/wiki/Ideal_gas_law inder "Derivations". First of all, the statement "Then the time average momentum of the particle is: \langle \mathbf{q} \cdot \mathbf{F} \rangle=...

Dear all, I have been spending 12 hours on this and cannot seem to come up with a solution. We derive Helmholtz Free Energy (A) from the second law of thermodynamics. dS(Total) = dS(system) + dS(surrounds) we try to express dS(surrounds) with properties of the system. Assuming...

Hamiltonian is in the form ##H = H_0 + \lambda W##, where ##\lambda \ll 1## and ##W## is the perturbation. Assume the eigenstates ##\mid \psi(\lambda) \rangle## and engenenergies ##E(\lambda)## can be expanded in a power series of ##\lambda##. $$\mid \phi(\lambda) \rangle = \mid 0 \rangle +...

Can any ine tell from where i can get this information If a single turn circular coil generates a magnetic field around it how can we calculate the induced voltage in a single turn circular coil located at a distance of d

In the derivation of drift velocity i have seen two variations and want to know which one's correct. s=ut +\frac{1}{2}at^{2} Assume that the drift velocity of any electron in any conductor is : v_{d}=l/t Due to the electric field the acceleration of electrons in any conductor...

No, this is not for a homework. Please don't delete the thread. CDF(Z) = Prob(Z < z) CDF(Y) = Prob(Y < y) where y = f(z) PDF(Z) = \frac{d(CDF(Z))}{dz} PDF(Y) = \frac{d(CDF(Y))}{df(z)} Now, it is known from various internet sources and wikipedia that: E(f(z))=...

Hi, I have recently been studying waves, and I understand the transversal wave formula y=Asin(w(t-x/v)) which gives the y coordinate of a point at x along the x-axis in the instant t. However, Wikipedia (http://en.wikipedia.org/wiki/Longitudinal_wave) gives this as the equation for...

I understand how to derive the divergence in polar. Ok, so I have the formula. But what I am confused about is this: say u=(0,0,w(r)), so as you can see the third component of this vector u is in fact a function of r. If I plug this into the polar divergence formula, I get zero, fine. But...

well,i found this article and i find it simple to understand. But is this article totally correct? Here is the link:http://m.sparknotes.com/physics/specialrelativity/kinematics/section2.rhtml

The natural logarithm can be expressed as lim n(x^(1/n)−1) n->ifinity Can someone please derive this for me? I've tried using the limit definition of e^x and then applying f^-1(x) but i can only get ((n*x)-1)^1/n any help is greatly appreciated thanks!

I'm trying to follow Wald's derivation of the Komar mass on page 288. We start with an asymptotically flat static space-time with killing vector ##\xi^{a}##. Let ##\Sigma## be a hypersurface orthogonal to ##\xi^{a}## and let ##S\subseteq \Sigma## be a topological 2-sphere. The quantity ##F =...

Homework Statement In a textbook I have, What is Quantum Mechanics?-A Physics Adventure, second edition,1996, Page 54, states that h=kβ, where h is Planck's constant; k is Boltzmann's constant, and β is Wien's constant. I have multiplied Boltzmann's constant times Wien's constant, but it does...

I'm trying to derive the Geodesic equation, \ddot{x}^{α} + {Γ}^{α}_{βγ} \dot{x}^{β} \dot{x}^{γ} = 0. However, when I take the Lagrangian to be {L} = {g}_{γβ} \dot{x}^{γ} \dot{x}^{β}, and I'm taking \frac{\partial {L}}{\partial \dot{x}^{α}}, I don't understand why the partial derivative of...

I was reading Griffiths's book on quantum mechanics. In chapter 6, he tried to derive the spin-orbit coupling using a classical approach. H=-\vec{\mu}\cdot \vec{B} 1. Finding the relation between \vec{μ} and \vec{S} He consider a spinning charged ring with mass m, radius r, total charge...

The signal length from satellite to the Earth station (AC) can be found as [SIZE="2"]2(H)/[{sin^2(theta)+(2(H)/R)}^1/2+sin(theta)] Due to the Earth projection where "H" is satellite height and and R is the Earth radius My question is Can you help me to derive this equation? how they...

Does anyone have a link or a reference to somewhere where these rules are explicitly derived for phi-four theory?

Derivation: http://s24.postimg.org/nhiqgg4qt/untitled.png How did they get ΔV=Ed? (d=width of the conductor) Sorry, I'm really rusty on my physics. Finding it quite difficult to review.

Hi all! I was reviewing some basic quantum mechanics, and I was trying to 'derive' the equation -i \hbar \frac{\partial}{\partial x} \psi_{(t,x)} = <x| \hat{P} | \psi > using the commutator relation, and the form of the identity operator. OK, I know that the proper, mathematical way to prove the...

Homework Statement In torricellis theorem why we take P1=p2=atmospheric pressure? Homework Equations The Attempt at a Solution

Im trying to understand this concept of deriving an expression for (\frac{\partial T}{\partial P})s in terms of T, V, Cp, \alpha, and \kappaT (\frac{\partial T}{\partial P})s is evaluated by measuring the temperature change and the specific volume change accompanying a small pressure change...

Homework Statement Please help me as I am quite confused in Bernoulli's theorem derivation...In my textbook,it is considered that Fluid Moves from a Greater height h1 to lower height h2,The pressure on upper end is positive,while at the lower end,it is negative,i.e against the motion of...

Hello friend, I want to know how to derive lorentz transformation. Even though i have book that derived lorentz transform,i am not able to understand. I hope you give me an easy derivation of it!

Two boxes are side by side on a floor with friction, from the left a Force acts on them. To be more concise about the picture it is this one on this website: http://hyperphysics.phy-astr.gsu.edu/hbase/f2m2.html#c1 I don't understand how the acceleration is derived. Especially i don't get...