General Definition and 1000 Threads

Homework Statement Find the general solution of u_{xx} + u = 6y, in terms of arbitrary functions.Homework Equations The PDE has the homogeneous solution, u(x,y)=Acos(x)+Bsin(x) . u_{xx} + u = 6y has the particular solution, u(x,y)=6y The Attempt at a Solution Taking a superposition...

Homework Statement From Mary Boas' "Mathematical Methods in the Physical Science" 3rd Edition Chapter 3 Sec 11 Problem 33 ( 3.11.33 ). Find the eigenvalues and the eigenvectors of the real symmetric matrix. $$M=\begin{pmatrix} A & H \\ H & B \end{pmatrix}$$ Show the eigenvalues are real and...

Nice general collection of high resolution astro images. http://www.holtz.org/Library/Images/Slideshows/Gallery/Cosmic/

Is anyone able to comment on the crystalline structures in the second chapter? Copper's cubic unit of structure is described as a face-centered cubic arrangement with atoms at coordinates 0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0. The iron cubic unit of structure is described as a body-centered...

Hi all, I can't seem to find any historic account of when those two theories got their (quite strange) names. Can someone point me to a source? One of the reasons I am interested in this is the persistent idea in popularizing texts, especially from the 1970's, that Special Relativity could...

Homework Statement A particle P starts from rest at a point O and moves in a straight line. P has acceleration 0.6t m s−2 at time t seconds after leaving O, until t = 10. (i) Find the velocity and displacement from O of P when t = 10. After t = 10, P has acceleration −0.4t m/s^2 until it...

Hello everyone, I have a theoretical question on subspaces. Consider the space Rn. The zero vector is indeed a subspace of Rn. However, if I am not mistaken, the zero vector has no orthonormal basis, even though it is a subspace. I thought all subspaces have an orthonormal basis (or is it...

How to learn "general engineering"? Hi. I'm a third year physics bachelor student. I'd like to learn how to apply my physics knowledge to the design of products. Which skills do you think should I try to learn? Like: 3D design, technical drawing, electronics... In other words: once I know the...

Homework Statement for this question , i dun know which method should i use... can someone enlighten me on this? i sub y=vx then differentiate with respect to x but can't get the ans Homework Equations The Attempt at a Solution

Let's say there's a current going around in a superconducting loop in vacuum. Then the loop gets buried in huge amount of matter, which has the same magnetic susceptibility as vacuum. (when not affected by gravity the matter has the same magnetic susceptibility as vacuum) Will the magnetic...

Hi, I'm going deeper in basics points on general relativity but, instead of swimming directly between the differential geometry, I'm trying to base my knowledge on strong physics bases first. I'm studying both on Wheeler's stuff ( I'm collecting almost all his books ), directly on Einstein's...

Homework Statement i got stucked here. below is the answer given. can anybody help please? Homework Equations The Attempt at a Solution

Homework Statement i can't reduce the eq to y= (X+1)/(x+c ) , which part is wrong? Homework Equations The Attempt at a Solution

Hi, I am supposed to use residue calculus to do the following integral $$\int_{0}^{2\pi}\frac{1}{a+b\cos( \theta) } \mathrm{d}\theta$$ for |b|<|a| i have paremetrise it on $$\gamma(0;1)$$ that is $$z=\exp(i\theta), 0\leq\theta\leq2\pi$$ and obtain the following...

Homework Statement Find the general solution of y'=Ay. Your answer must be a real-valued function. A= \begin{pmatrix} 1 & 1\\ 0 & 1\\ \end{pmatrix} Homework Equations The Attempt at a Solution The first step would be to find the eigenvalues. I forgot the name of the term but if...

Is there a formula for Gaussian integrals of the form $$\int_{-\infty}^{\infty}{x^n}{e^{-a(x-b)^2}}dx$$ I've looked all over, and all I could find were formulas saying $$\int_{-\infty}^{\infty}{e^{-a(x-b)^2}}dx=\sqrt{\frac{\pi}{a}}$$ and...

The concepts of general relativity seem to fit (sorta) well with quantum physics, but how does the quantum world fit with general relativity? Specifically, I'm wondering if entanglement has any grounds that you can derive from GR?

Recently, I've come across Planck's lectures in theoretical physics and I have a couple questions. Although I'm curious about the series as a whole, I'm mostly interested in volume 1: General Mechanics and maybe Mechanics of Deformable Bodies. The Series consists of: General Mechanics...

Homework Statement Find the general solution f = f(x,y) of class C2 to the partial differential equation \frac{\partial^2 f}{\partial x^2}+4\frac{\partial^2 f}{\partial x \partial y}+\frac{\partial f}{\partial x}=0 by introducing the new variables u = 4x - y, v = y. Homework Equations...

Hi, (hope it doesn't seem so weird), I'm looking for a general expanded form of (x+y+z)^{k}, k\in N k=1: x+y+z k=2: x^{2}+y^{2}+z^{2}+2xy+2xz+2yz k=3: x^{3}+y^{3}+z^{3}+3xy^{2}+3xz^{2}+3yz^{2}+3x^{2}y+3x^{2}z+3y^{2}z+6xyz k=4: x^{4}+y^{4}+z^{4}+4xy^{3}+4x^{3}y+4xz^{3}+4x^{3}z+4yz^{3}...

Homework Statement In this question we consider the following six points in R3: A(0,10,3) B(4,18,5) C(1,1,1) D(1,0,1) E(0,1,3) F(2,6,2) a) Find a vector equation for the line through the points A and b b) Find general equations for the line from a c) Find a vector equation for the...

For my own use and consumption, I created a generalization of the nth integral of a function f and I'm posting it here for you look: $$\int f(x) dx = f^{(-1)}(x) + C_1$$ $$\iint f(x) dxdx = f^{(-2)}(x) + xC_1 + C_2$$ $$\iiint f(x) dxdxdx = f^{(-3)}(x) + \frac{1}{2}x^2C_1 + xC_2 + C_3$$...

Hi, this might be a silly question, but it does confuse me when I read about general relativity. From what I know about quantum mechanics, a force always needs a force carrier. For example photons are force-carriers for electric or magnetic force; the so-called ‘gravitons’ are the force-carriers...

What in general prevents plants from rotting while they are alive? Do plants that go dormant in the winter need to spend energy to maintain a defense, say a flower bulb? Thanks for any help!

Theory of general relativity-- Falsifiable? "... Supposing that the bodies act upon the surrounding space causing curving of the same, it appears to my simple mind that the curved spaces must react on the bodies, and producing the opposite effects, straightening out the curves. Since action and...

I am currently a general engineering student and plan on getting a electrical concentration. Would it be better to transfer to a college that offers electrical engineering? Which would have better job opportunities. Also, I plan on getting a masters in EE. Would one degree prepare me more for...

I spoke to someone that said that the reason we know humans originated from evolution is because there is no other scientifically possible explanation. I originally thought the reason we knew humans originated from evolution because we had explicit evidence of human evolution. Although now that...

Edit: Problem solved please disregard this post Homework Statement A particle in the harmonic oscillator potential has the initial wave function \Psi(x, 0) = ∑(from n = 0 to infinity) Cnψn(x) where the ψ(x) are the (normalized) harmonic oscillator eigenfunctions and the coefficients are given...

I apologize if this is the wrong forum but I need access to mathematicians who know what's happening with polygonal math. I created an unproven algorithm (or heuristic) back in 1999/2000 for bounding shapes with polygons. It was interesting because it was fast, general for polygons of any...

In Padmanabhan's Theoretical Astrophysics by defining a ratio for comparing gravitational potential energy with rest-mass energy it is shown that if massive objects with M=10^33 gm are confined to small regions with R= 1km then we cannot use Newtonian gravity because the system has general...

How does General Relativity "contradict" quantum mechanics? I couldn't work out exactly where to post this. I've heard several times that QM and General relativity "contradict" each other and in certain extreme conditions this becomes a problem. Is this right? I've only heard this in very vague...

I'm 19, aspiring to go into professional physics, most probably in the astrophysics branch. I'm mostly attracted to gravity (please do not mind the pun), quantum mechanics, string theory, the remote possibility of FTL travel using Alcubierre Drives (or better technology, someday), fusion, et al...

If we have a function such as, $$e=\sum_{n=0}^{\infty} f(k)$$ Where 'k' can be (almost) any real value we choose and the summation series (although unique for each value of 'k') will always be equal to 'e' exactly, what do we call this?

To my understanding General Relativity is a theory of geometry. Is it mandatory that the next step beyond GR also be a theory of geometry, or is there/could there be something else that is believed to give the same results without using geometry? I hope that makes sense.

How can I explain to someone who has only high school level of education in physics, what is general and special theory of relativity about? Each of them separetelly in one or two sentences please. General theory of relativity … Special theory of relativity ... Thank you.

Greetings, I've been learning about special relativity and most of the learning media included a part of general relativity. From that I learned that space-time is curved and orbits are nothing more than an object following a path in 4D. However I do not understand how those objects may rotate...

1. Why are there an unfixed number of particles? Texts usually present some hand-waving argument with bits and pieces of SR and NRQM thrown together. Are there more rigorous explanations? 2. How can the scalar fields suddenly be opeartors? I never understood this step mathematically, one...

Homework Statement The statement below arises from a marble and track lab, and I'm enthralled to figure out a generalized equation ( variables only ) for energy lost per meter of track. Track is 12 feet long, but can be curved for hills and loops. Using a small section of track and marble...

Hello, I am learning about the general solution to higher order linear non-homogeneous differential equations. I know that the general solution of such an equation is of the form ##y=y_h+y_p## where ##y_h## is the solution to the respective homogeneous equation and ##y_p## is a particular...

Greetings, PF. With many recommendations and just enough confidence in my ability to solve problems, I've recently purchased the renowned Problems in General Physics by I. E. Irodov. With excitement, I opened the book and read the first problem. It took a lot of thinking to solve the first few...

An experiment consists of giving a sequences of patients a risky treatment until two have died, and then recording N, the number who survived. If p is the proportion killed by the treatment, then the distribution of N is: P(N=n)=((n+1)(1-p)^n)p^2 Find a general formula for the MLE for...

Hello all, In Carroll's on page 109 it is pointed out that for derivation of the geodesic equation, 3.44, a "hidden" assumption is that we have used an affine parameter. Some few lines below we see that "any other parametrization" could be used, called alpha, but in that case the general...

I have been teaching myself QFT and General Relativity. The mathematics of those fields is daunting, and I find that what I have come across is very difficult to master. Of course it will take work, but can someone recommend a good text for self-leaning differential geometry with application...

Here I have a problem I am dealing with. I answered the question and have it shown on the picture but I would like a double check on it as I think I am getting wrong values. The circuit is shown at the top of the page. If you can't see the values are 10 ohms for the resistor, 3.2 mF for the...

I'm wondering with the circular fin, with uniform cross section area with given length and diameter. both ends are attached to surfaces. is there a general equation to find the heat rate by convection of the fin side surface. I tried to relate all the conditions and ended up with a equation that...

Find the general solution of The ff. D.E 1.$\displaystyle (2xy-y^2+y)dx+(3x^2-4xy+3x)dy=0$ 2. $\displaystyle (x^2+y^2+1)dx+x(x-2y)dy=0$ i tried both of them using $\displaystyle \frac{\dfrac{\partial M}{\partial y}-\dfrac{\partial N}{\partial x}}{N}$ and $\displaystyle...

Hello! Could you, please, name some(if any exists) good reviews about building the general relativity? In all details: with attempts of building the vector theory of gravitation by Poincare; with long Einstein's efforts of building the scalar version; with prediction some of the effects, like...

Does anyone know if we currently have an infinite series summation general solution for the gamma function such as, $$\frac{1}{\Gamma(k)}=\sum_{n=0}^{\infty} f(n,k)$$ or, $${\Gamma(k)}=\sum_{n=0}^{\infty} f(n,k)$$?

I started university two years ago, aged 30. I'm now 32 and have achieved minors in math and physics. I really want to focus now on theoretical/mathematical physics (I'm particularly interested in particle physics and cosmology) but I'm concerned that, given my age and the nature the field, it...

Is there a single, general, solution guaranteeing method that can be applied to any first degree first order differential equations? I know there are a lot of techniques or should I say categorizations for solving these types of equations, like linear, homogeneous, Bernoulli equations...