Derivations Definition and 102 Threads

Alright, this is a pretty low level / silly question but I am having some issues. I would like to get the vertex rule for an interaction that has a field tensor involved like this... \partial_\mu Z_\nu -\partial_\nu Z_\mu do I treat the two Z's as separate fields? For a generic field...

When people talk about harmonic oscillators it seems to me that they always assume either that the relationship of force and displacement is linear, or that it behaves in some sinusoidal fashion. Do you always have to assume one to be able to arrive at the other? Or is there something I'm...

Will anyone give me the derivations for continuty equation of fluid and euler's equation of fluid motion .

Hello, I am trying to derive the harmonic content of a signal passing through a transistor's transfer function. After a Taylor expansion in Mathematica 7, I have the expanded equation and the next step is to reduce everything to first order Sine/Cosine functions. In Mathematica, if I have a...

Homework Statement I have to reverse engineer a derivation in a paper and have no idea where to even start. The amount of terms are overwhelming and I can't imagine how the author even began. Homework Equations The following equations are known...

I'm looking for another derivation of time dilation which does not involve moving clocks or mirrors... I feel like those aren't very clear - is there any other way time dilation has been derived? thanks

Hey all, I was wondering if anyone uses a iPad (or similar device) for taking notes and doing long derivations. I am looking into buying and iPad or a similar device and stop using paper. What do you guys think about this? Ever tried it?

I'm studying the MUSIC algorithm in order to implement it in some project of mine, but I have some difficulties understanding the mathematical derivations done in the original Schmidt paper. For those of you who have access to this paper, I'll appreciate your time and help. The author begins...

Hello everyone, I'm trying to calculate the doppler shift in frequency of a moving source. I'm approaching the problem from two different frames of reference and getting inconsistent results. what am I missing here? consider the special case of transverse doppler effect (θ=π/2). light...

I'm looking for a source online that gives the step by step derivation of common trig identities, such as sin(2theta) = 2sin(theta)cos(theta), cos(2theta) = cos2(theta)-sin2(theta), sin2(theta) = (1 - cos(2theta))/2, ect. I did do 20 minuntes or so of searching online, nothing was exactly what I...

"Simple" derivations I set out trying to derive the big 5 motion laws not only regularly, but calculus-style: dv=adt Integration yields v=at + C, and thus we get v=at+v0. Non-calculus method is just using the definition of a=deltav/deltat and is trivial. dx=vdt x=(v0+at)dt x=v0t +...

Does anyone have a website or perhaps a book that has step by steps on the derivations of some of the physical equations? i.e. Newton's Inverse Square Law for gravity, etc. etc. Any recommendations would be appreciated. Thank you.

I've been reading some material on the Schrödinger wave equation, and quite a few sources claim that there is no derivation for the equation at all. That it essentially falls out of nowhere. This is confusing for me as I have seen some plausible derivations based on de Broglie waves. Are...

My questions here, in order: 1. How do Maxwell's equations demand that c is constant for everyone? People say that his equations "derive" c but I always thought that the permeability variables were experimentally derived. I fully understand the derivation of gamma from the time dilation light...

Hey, So I'm trying to figure out how the matrix representatives of Lie-algebras can act as derivations. In particular, let N \in \mathbb N and consider the Lie group of special unitary matrices \mathfrak{SU}(N). Now we know that the Lie-algebra is the set of skew-Hermitian matrices...

Practicing the derivations of the Motion Equations, and I am looking through my notes that I transcribed from my professor...Im getting caught up on one spot. Im getting all the equations to "pop out" except for this last one, which, I can see; but, the algebra is throwing me off...

I'm just curious about the, sin(a\pm b), \quad cos(a\pm b) identities, is there a simple way to derive them? I have a test in a few days and I don't like memorizing too much. Thanks again!

Homework Statement I have 2 equations. I need to derive two different equations from them. Derive (1): v102= v1f2 + vf22+ 2v1fv2fcos(φ+θ) (2): v2f = v10sin\theta/sin(theta - phi) Homework Equations v10= v1fcosθ + v2fcosφ 0 = v2fsinφ - v2fsinθ The Attempt at a Solution I know for...

Hi, everyone: I am going over J.Lee's Smooth Manifolds, Chapter 3; specifically, Lemmas 3.1, 3.4, in which he states properties of derivations. Lee calls linear maps L with the Leibniz property (i.e L(fg)(a)=f(a)L(g)+g(a)L(f) ) derivations, when these maps are defined in a...

Every textbook i find breezes over the following point: \delta\partial (x) =\partial \delta (x) where delta is just the variation. Someone asked me why that's true and i guessed the only thing i could say was that delta is an operation not a variable so this is more like an algebraric...

I'm trying to understand how my book derives the tangential accelration. I drew a picture because it's kind of confusing to explain. From the triangle we get the tangential and normal components of the velocity. What my problem is (and I think, and hope, it's something simple that I just...

HI, I've been mulling over the derivation of the Lorentz factor gamma in my head for some time now & had worried about it a bit. I've now discovered that what was bothering me was something called "frame-jumping". This is where you use the Pythagorean Theorem to derive Gamma. If you're...

how do i prove the following is a theorem in SD [(A -> B)->A]->A ... i started off by assuming [(A -> B)->A] then assume ~A to try to derive A in the end... but now I'm stuck :( and also: Suppose we dropped from SD the rule for vE, and adopted in its place the rule of Disjunctive...

Here is how my book goes about defining the moment of inertia. Now here's how my book goes about deriving an expression for the angular momentum of a rigid body. From this the book derives that L = Iw My question is in regards to the bolded part. How come in one derivation we assume...

Homework Statement Dimensions: These derivations are not correct ( as stated by the book) I'm just reading my textbook at the moment and I saw this example ( So I don't have work for it myself by the book shows all the steps). ***√[L]/[L/T^2] =√[T^2] Homework Equations The...

I've encountered a definition of the tangent vector via the notion of derivations on the manifold and I have some problems with it. I would actually like to show that every derivation can be expressed as a directional derivative, but I'm not ver successful in doing so. I have this definition...

I've noticed in my physics textbooks that every time the author wishes to prove something, he'll go for a direct proof/derivation. Is there any particular reason for this? I think that I have yet to see any proofs by contradiction/proving the contrapositive/mathematical induction in any of my...

is it necessary to know where to derive all my formulas, as a general rule? i always try to follow them and understand more or less where they came from, because i hate hand waving. i can derive a good chunk of them, especially the ones of mechanics, but some of the messier ones, like the ones...

I am confused by various derivations of the Noether current in various textbooks. However, they either contradict with each other or exist many flaws. For example, originally I thought the best derivation is at the end of the book of classical mechanics by Goldstein. But I found that in the...

Homework Statement Consider a solenoid of length L, transverse area A, total number of loops N Compute the magnetic field B inside the solenoid, assuming that it is uniform and vanishes outside the solenoid, neglect any boundary effects. Working under the same assumptions, calculate...

I have used this equation in the past but have no knowledge of how the equation is formed. I will probably learn about it next year, but that is a long time to wait for a burning question. :shy: Here is the equation I am talking about. I would like be sure that I know what everything stands...

Right I've got an exam at half past 4, tomorrow on a Saturday! I've spent the past few days doing past exam questions and a lot of them I'm able to do or at least work out for myself after a bit of time. Here's a couple I'm really stuck on so some help would be really really appreciated...

Ok I am in my final study for my last exams... and i just want to check with all you guys that i have my calculus right :) Derviations: 1. Lower the power by one, and times by the new power out in front of the term. Coefficinets drop off, and terms with just x become a new coefficient in the...

As far as I know, the tangent space of a manifold at a point is often defined abstractly as follows. First, we define the germ of smooth real valued functions at a point a, which is the set of equivalence classes of smooth functions where two functions are considered equivalent if they are the...

Can someone show me how to integrate any (or both) of these two simple equations. I have written down the equation that needs integrating and the final result and attached them as a pdf. Regards, Andy

I was bored so I make fun with derivations of SI units of many Physics formulas. Note, this should just be called "introductory physics", that means NO calculus (but rate of change designated by the delta symbol) and motion is in one or two directions only. This is high school physics level in...

How did who decide some of the steps to choose for developing the Chain Rule and for developing the derivative of the Sine function? I spent some time during the last few days reading and examing these derivations, and although now I can understand those, the steps taken do not seem very...

Hello, I have been asked to find the magnetic field inside a solenoid (along its axis)using two methods. One is using Ampere's law (and the approximation that the B field is zero outside the solenoid). Here is what I get: B = (uIN)/(L) where I is current, N is the number of loops...

this is not homework help.I want to know. Hello,can anyone suggest why for a dipole m placed in a magnetic field B F=grad(m.B) and N=mxB?

For the following Eo is epsillon zero Homework Statement 41. A solid nonconducting spere of radius R has a uniform charge distribution of volume charge density p = kr/R where k is constant and r is the distance from the center. Show the (a) the total charge on the sphere is Q =...

Are "two line derivations" harmful in teaching special relativity My experience on the forum showed me that some participants do not agree with the simple, “two line” derivations, of the equations that account for relativistic effects like time dilation, length contraction and Lorentz...

Still the "World's Fastest Derivation of the Lorentz Transformation" http://arxiv.org/abs/physics/0606046 ...apparently in response to A faster than "World fastest derivation of the Lorentz transformation" http://arxiv.org/abs/physics/0602153 , ...which is apparently a challenge to...

i have no idea where to start: can someone help me mathematically derive the following? -22 degree halo and 46 degree halo -sundogs -coronas -sunrise/ sunset -silver linings -sun pillar (graphics would be greatly appreciated) if you find any helpful links please cite...

aristarchus was the greek astronomer who was the first to find out the distance between the Earth and the sun. he observed that when the moon was exactly half full; the Earth (E), moon (M), and sun (S) formed a right triangle with the right angle at the moon. then how did he found out that the...

Hi all, Does anybody know some reference (even internet one) that explains in detail the derivation of Maxwell´s velocity and/or energy distribution on an ensemble of atoms/molecules ? References to Fermi-Dirac distributions and Bose-Eisntein´s are also welcome. Best Regards, DaTario...

Hi, I have a problem and I am stuck to one question: The area of a triangle is given by the formula: A=1/2*b*c*sin(θ ) At time to, we have bo=10 inches, co=20inches, θo=pi/3 a) Find the area of the triangle at to I found 50*sqrt(3) b- find the rate of change of the area with...

Hello. I am in confusion because I cannot understand which formula will be used in this and that derivation,because there are many formulas of physics.Then how we come to know that this specific formula must be used in this derivation It is a great confusion for me. Please solve my problem...

(Any help whatsoever is greatly appreciated) I am looking for good online sources to help me understand relativistic formula's for the equations of Maxwell, and all the stuff that follows from it (like Cherenkov radiation). I realize that's a pretty vague description, so if there is no...

Principles of sound reasoning. For the following argument, derive the conclusion: B & C (A \leftrightarrow B) v (C\rightarrow D) (A v E) \rightarrow H (D & C) \rightarrow I (IvJ) \rightarrow H Conclusion is H. I know I am supposed to make some provisional...

I'm taking a first course in modern physics and were currently discussing special relativity. My professor keeps using four-vectors in derivations and proofs, and requires us to use them, but he hasn't developed the theory behind them; that is he's only showed us how to manipulate them. The...