General Definition and 1000 Threads

Hi I thought I remember reading that transmitting power over 800km's is passed the break even point for DC vs AC. And I read that modern rail is starting to use 25KV AC, but aren't many networks bigger than that, specifically in NSW Australia, the according to wikipedia it's 815km, I'm not sure...

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I am trying to gain a full...

Homework Statement A pipe diameter changes from 0.5m to 1m in a length of 1m in a pipe diffuser . If a discharge Q flows from 0.5m diameter towards 1m diamater , obtain the general expression for velocity at the pipe cross section . Homework EquationsThe Attempt at a Solution since we know...

Goodmorning everyone, is there any implies to use in general relativity a metric whose coefficients are harmonic functions? For example in (1+1)-dimensions, is there any implies for using a metric ds2=E(du2+dv2) with E a harmonic function? In (1+1)-dimensions is well-know that the Einstein...

I am reading general and special relativity from a book and I am stuck with these lines please can someone provide its detailed explanation "Einstein demanded that the special principle of relativity should be valid also for Maxwell’s electromagnetic theory. This was obtained by replacing the...

hi, I know the wave equation in terms of minkowski metric, and we use ordinary derivative in that equation. I also know this wave equation in terms of general metric form using covariant derivative, but I do not know the derivation of it. Could you spell out the steps of derivation?? How do we...

It is known that equivalence principle is good for understaning of general relativity (GR). This means comparison of the elevator and falling in homogenic gravitational field. But, I here somewhere something like "in the higher lever of GR, let us forget on principle of equivalence". How it is...

I have read several times that general relativity has some problems with quantum mechanics and they are not compatible. However, special relativity can be introduced in quantum mechanics mainly by Dirac equations (so I am pretty sure that the problem of passing from a frame where the parameter...

Hello , I'm preparing for the GRE subject test in Physics. I have Irodov's Problems in general physics. I think that this book contains a large number of very interesting and somewhat challenging collection of problems. Is this book suitable for GRE study ? My goal is to get 900+ on the test.

HI, can anyone suggest a good book on general relativity with fairly good mathematics for beginner for self study?

So I have successfully transferred to a 4 year university from a community college. I am majoring in mathematics. I have completed: Calculus 1,2,3, Introduction to Ordinary Differential Equations, Introduction to Linear Algebra, Introduction to Discrete Mathematics. I have also completed...

I have already taken both General Chemistry 1 and 2 at my community colleges. I did not get a good grade, but that was because of I missed a lot of homeworks and projects, but did good on the tests and I understand some of the material that I learned. In general, can you take both of them again...

It's just that I've never properly sorted this confusion of mind, so i would like to sort it out so it 2 different capacitors are in series with a resistor: (let's say 0.15F, 0.45F, 150M ohm) 1. both current and voltage drops exponentially 2. capacitance on capacitors remain same over time? 2...

Hi all, I was trying to understand the time dilation in special and general relativity and after much time of "overthinking" I am pretty much stuck now. My problem is, that what seems to me to be the same premises apparently imply opposite things. In special relativity, for two inertial...

i was trying to learn some trigonometry from some basics ... after understanding terms like , f(x) = sin x , and y = sin x ... i was also getting sort of comfortable with the notations of functions ... i was also wondering , where to improve from here ... ? any good books , sites ...

Homework Statement [/B] In a set of axes where the z axis is the axis of rotation of a finite rotation, the rotation matrix is given by ## \left[ \begin{array}{lcr} &\cos\phi \ \ \ &\sin\phi \ \ \ &0 \\ & -\sin\phi \ \ \ &\cos\phi \ \ \ &0 \\ &0 \ \ \ &0 \ \ \ &1 \end{array} \right]##...

Long story short. Want to know waaaay before I get deep into Aerospace Engineering, what I need to know to do it and if I can, I've already retrieved books on it. Like Fundamentals Of Aerodynamics... Some Calc 2 books.. Calc 1.. etc etc. However I look at Calc 1/2, then look at my Aerodynamics...

I need some help understanding the countability and separation axioms in general topology, and how they give rise to first-countable and second-countable spaces, T1 spaces, Hausdorff spaces, etc. I more or less get the formal definition, but I can't quite grasp the intuition behind them. Any...

I'm new to proofs and I'm not sure from which assumptions one has to start with in a proof. I'm trying to prove the generalized associative law for groups and if I start with the axioms of a group as the assumptions then I already have the proof. From what basic assumptions should one start...

I'm looking for the general form of a symmetric 3×3 matrix (or tensor) ##\textbf{A}## with only two different eigenvalues, i.e. of a matrix with the diagonalized form ##\textbf{D}=\begin{pmatrix}a& 0 & 0\\0 & b & 0\\0 & 0 & b\end{pmatrix} = \text{diag}(a,b,b)##. In general, such a matrix can be...

Given a linear homogeneous 2nd order ODE of the form $$y''(x)+p(x)y'(x)+q(x)=0$$ the general solution is of the form $$y(x)=c_{1}y_{1}(x)+c_{2}y_{1}(x)$$ where ##c_{1},c_{2}## are arbitrary constants and ##y_{1}(x), y_{2}(x)## are linearly independent basis solutions. How does one prove that...

I'm finishing up my general physics 2 course (today actually) and I begin my upper division courses in Fall. I was wondering how you found general physics 2 compared to intermediate modern physics in terms of difficulty? I found physics 2 (basically introductory E&M at my school) more difficult...

What is general relativity all about. I don't know anything about it. I am an undergrad.

Conserved quantities in GR deal with ##p_\mu## not ##p^\mu## and while in Minkowski spacetime its easy to see what each of the components mean (since the metric is so simple) in general relativity I think its not and its starting to confuse me. Why exactly is ##-p_0## the energy in general...

Introduction If Quantum Mechanics is more fundamental than General Relativity as most Physicists believe, and Quantum Mechanics is described using Hilbert Spaces wouldn't finding a compatible version of General Relativity that operates within the confines of a Hilbert Space be of utmost...

Hi everybody! I'm currently studying integrals, and I would like to clarify a few definitions, especially about the criterions of convergence/divergence of an integral. Basically if that's okay for you guys I'm going to list and number a few statements and I'd like to know if they are true or...

I understand that the ansatz to $$(\Box +m^{2})\phi(\mathbf{x},t)=0$$ (where ##\Box\equiv\partial^{\mu}\partial_{\mu}=\eta^{\mu\nu}\partial_{\mu}\partial_{\nu}##) is of the form ##\phi(\mathbf{x},t)=e^{(iE_{\mathbf{k}}t-\mathbf{k}\cdot\mathbf{x})}##, where...

Homework Statement How do I go about finding the most general form of the canonical transformation of the form Q = f(q) + g(p) P = c[f(q) + h(p)] where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and...

How do I go about finding the most general form of the canonical transformation of the form Q = f(q) + g(p) P = c[f(q) + h(p)] where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and conjugate momentum in...

Suppose ##x_1(t)## and ##x_2(t)## are two linearly independent solutions of the equations: ##x'_1(t) = 3x_1(t) + 2x_2(t)## and ##x'_2(t) = x_1(t) + 2x_2(t)## where ##x'_1(t)\text{ and }x'_2(t)## denote the first derivative of functions ##x_1(t)## and ##x_2(t)## respectively with respect to...

Homework Statement Find the general expression for the adiabatic relationship between P and V Homework Equations start with ##(\frac{∂P}{∂V})_s## expression for adiabatic relationship between V and T: ##(\frac{∂V}{∂T})_s = \frac{-C_v}{\frac{RT}{V}}## Relationship between S and T...

Homework Statement edit: I figured out my mistake Here's the entire problem. But I don't yet need help with all the steps. I'm getting off on the wrong foot (as usual)a We have shown in class that ideal gas adiabats have the form: ##P_I(V_i)^γ = P_f(V_f)^γ## with the heat capacity ratio: ##γ...

Hi everybody! I'm currently preparing a math exam, and I'd like to clear up a few points I find obscure about limits of sequences, my goal being to more or less determine a method to solve them quickly during the exam. Hopefully someone can help me here :) I'll number the questions so that it's...

My goal is to develop an intuitive understanding of the math underlying general relativity and ultimately be able to take a book like Wald or Carroll and, as someone on these forums commented once, “be able to casually read it while sipping my morning coffee and listening to the news.” :) So...

What are some good general textbooks on the properties and solution of systems of partial differential equations? I'm most interested in the general theory of vector and tensor valued PDEs like Maxwell's, Navier-Stokes, and the bulk equations governing elasticity and deformation of solids, etc...

Homework Statement This question has four parts which may follow up from each other so I incuded all the parts. The real problem I'm having is with d Consider the function f ang g given by f (x)=( e^x+[e^-x])/2 & g (x) =( [e]^x]-[e^-x])/2 a) show f'(x) = g (x) and g'(x) = f (x) b) find the...

From my studying of QM, I have been learning about state functions that are supposed to describe a particular system. Now for most purposes, it seems that I have been computing the position wave function (or, through Fourier transforms, the momentum) which evolves with time. But I am just...

Can anyone suggest good books and lectures in general physics that can still help in physics nowadays ? And i like to know best authors names in physics .

I had the following question how are the Schwarchzild metric that describes a spherically symmetric matter distribution (such as a star) be compatible with the FRW metric that describes the 'overall universe' that the star resides in/is part of its matter distribution? Then we say that FRW...

Hey! :o I want to solve the differential equation $y'''(x)-2y''(x)+y'(x)=e^x$. I have done the following: Consider the homogeneous equation $y'''(x)-2y''(x)+y'(x)$. $k^3-2k^2+k=0 \Rightarrow k=0 \text{ single root } , k=1 \text{ double root } $ So, the solution of the homogeneous...

Hi all, I've just been made offers to two different institutions - one to study General Relativity and Early Universe Cosmology, and one to study particle physics phenomenology and dark matter at PhD level, and I'm having a hard time choosing! Relativity and Cosmology is Queen Mary University...

I'm a 16 year old whose summer goal is two understand general relativity, but I'm lost on what math to have to understand it, I understand topological spaces and a topological manifold. but then it becomes more complicated math, and I know I simply don't understand because of the mathematics.

The question is to resolve a logical conflict. GR says as we fall into a black hole, an outside observer will see that event come to a stand still as if the falling object is hovering at the horizon. This stand still extends to infinite time. Unfortunately, I've read and hear the term...

This references a specific problem in my Physics class in relations to electrical potential and electrical fields, but I kind of want a more general answer in terms of physics. So obviously, I know that distance is always positive. However, when I was given a problem to solve, there were 3...

I'm trying to understand the nature of coordinate transformations in physics. In classical mechanics, we can transform to a different coordinate frame by means of a Galilean transformation. In special relativity, this is replaced by a Lorentz transformation. I am now wondering whether there...

I used to think that gen ed classes (like literature, humanities, fine arts) were a waste of time. Now, I realize that they have value within a lucrative major. The purpose of college is to be well-rounded academically. It's what makes a college degree different from a 6-month nursing course...

Homework Statement Particles of mud are thrown from the rim of a rolling wheel. If the forward speed of the wheel is v0, and the radius of the wheel is b, show that the greatest height above the ground that the mud can go is b + v02 / 2g + gb2/ 2v02 At what point on the rolling wheel does this...

Here's what I'm confused about: The harmonic series 1/n is divergent (because you're just infinitely adding numbers) but the series (1/2)^(n+1) is convergent. This doesn't make sense to me because by plugging in larger and larger numbers, you are still adding small numbers infinitely which...

Hi everyone. I'm sorry for the long thread. If you don't want to read all the introductory stuff I will mark the part towards the end where my questions are located. I'm trying to find the general formulae for the roots of the equation $$ax^3 + bx^2 + cx + d = 0$$ By using some changes of...

any particular solution plus the general solution to the homogeneous equation. I'm having difficuilty understanding this proof from my lecture notes Theorem : Let T : V → W be a linear transformation. Let w ∈ W and suppose T(u0) = w T(v) = 0. where v ∈ V (the kernel ) to prove: T(u) = w...