General Definition and 1000 Threads

I recently bought a Tiva launchpad and have been playing around with it for the last couple of weeks. I wanted to interface an OLED module to it and was wondering what the options for this was? There is a booster pack available but this is now sold out, so I suppose that I have to create my own...

Homework Statement A polynomial of degree two or less can be written on the form p(x) = a0 + a1x + a2x2. In standard basis {1, x, x2} the coordinates becomes p(x) = a0 + a1x + a2x2 equivalent to ##[p(x)]_s=\begin{pmatrix}a0\\ a1\\ a2 \end{pmatrix}##. Part a) If we replace x with...

Homework Statement Find the general solution x(t) to the following differential equation: dx/dt = 2t/5xHomework Equations dx/dt = 2t/5x The Attempt at a Solution My solution is: ∫5xdx = ∫2tdt (5/2)x^2 = t^2 + C x^2 = (2/5)(t^2 + C) x = +-√[(2/5)(t^2 + C)] However, when I put the problem in...

Homework Statement A general rotation through angle ##a## about the axis ##\underline{n}##, where ##\underline{n}^2 = 1## is given by $$R(a,\underline{n}) = \exp(-ia\underline{n} \cdot \underline{T}),$$ where ##(T_k)_{ij} = -i\epsilon_{ijk}##. By expanding the exponential as a power series in...

Hello fellow PF go-ers I am having trouble with coordinates in curved space time lately, allow me to demonstrate my issue. Take the metric of flat space in spherical coordinates for example, a diagonal metric with values 1,r^2 and r^2sinΘ. It appears to me that only when we know that the Θ and...

For this question, I have to obtain a general quantization of motion in circular orbits by combining the equations (Where U(r) is potential energy): (mv2)/r= |(dU(r))/dr| With the angular momentum quantization of: mvr= nℏ Then use this to calculate the spectrum for circular motion in a...

In this post i want to discuss good chemistry textbooks vs. bad chemistry textbooks and I'd like some help finding a good General chemistry textbook for university - Undergraduate level. What Is a good introductory chemistry textbook? So i finally found a book in organic chemistry which...

Homework Statement The equation: \frac{dx}{dt}=\frac{t^2+1}{x+2}. Where the initial value is: x(0) = -2. Homework Equations I believe you have to use the method of seperations of variables. The Attempt at a Solution So I multiplied both sides with x+2. Then I integrated...

Hello, I am learning General Relativity through some books like 'Gravity' by Hartle and through some other textbooks. All those books, do not speak of general relativity from the context of differential geometry. I have a fair amount of knowledge of calculus as well as set theory. My...

Hi, I decided to learn about relativity with this book, and I'm looking for people who would like to read it with me and discuss :thumbs:. Since I'm a little busy at the moment the pace will be quite slow, let's say about a chapter each two weeks (or more later for more advanced chapters)...

Hello all. :) I've recently enrolled in coursera courses and I must say I'm loving it! Hence, I decided to ask if any of you ever tried one MOOC (massive open online course) before? I think it's an interesting take on education. Professors (in general) seem more motivated to present the course...

Hello, Can anyone help guide me in order to stabilize my General Relativity background. Little do I know about GR, I know the very simple basics! I feel that I need to start from the first beginning. ANy recommendations? How to start learning this on my own? Do I need to watch videos or read...

Homework Statement A particle's movement is described by \vec{r} in the inertial system IS. Find the velocity of the particle \vec{\dot{r'}} in the system IS', which is moving with arbitrary velocity v from IS. Both inertial systems are arbitrary.Homework Equations For the position vector the...

I am trying to find a matrix A such that $(1)$ can be written as $v^TAv=1$ where $v=(x, y)^T$. $(1)$: $$\left(\frac{x}{a_1}\right)^2 + \left(\frac{y}{a_2}\right)^2 - 2\left(\frac{xy}{a_1a_2}\right)\cos(\delta)=\sin^2(\delta)$$ $$a_1, a_2, \sin(\delta)\neq 0.$$ I am positive that $\cos(\delta)$...

Homework Statement An observer falls radially inward toward a black hole of mass M, which is equal to 3 solar masses, starting with zero kinetic energy at infinity. How much time is measured by this observer as he travels between radii r1 = 6GM/c2 and the event horizon? Homework Equations...

I am writing a paper about SR and GR. I have the following: Special relativity deals with inertial reference frames and flat space. General relativity deals with accelerating reference frames and curved space. Inertial reference frames are only an approximation that applies in a region...

Hi guys... I was wondering if anyone have a sort of a summary of sign conventions in general relativity books. By convention I mean the definition of Riemann tensor, Ricci tensor and signs of stress-energy tensor and signs of einstein field equations for a given sign of metric tensor... I heard...

Hello, I had a question about the method of undetermined coefficients for solving ODE's. I understand it is only useful for certain non-homogeneous functions, and those dictate specific guesses, but what if I had a sum or product of two valid functions, is the guess simply a sum or product of...

Homework Statement Derive a general formula for the horizontal distance covered by a projectile launched horizontally at speed vi from height, h. The Attempt at a Solution vyf = vyi -gt t = vyf/g x = vxi .t = vi cosΘ (t = vyf/g) = [vi^2 sinΘcosΘ]/g

I'm a current junior considering applying to graduate school next year (I'm tossing up between applying for certain applied physics programs and going into finance). I was wondering how much preparation people found necessary to take the general GRE. I'm not sure whether it would be better to...

I'm curious about how the temperature of the CMBR compares to the light and temperature of galaxies in general. Basically, I'm wondering how 'hot' are galaxies and how do they contribute to the CMBR readings. Does the temperature of galaxies compare on some scale? Do we have to account for...

Hello all, I will preface this post with an apology for not putting it in the math/science learning materials section. This would have been the best place to post my question, but for some reason I can't post there. My question is the following: what depth of understanding must I have of...

Homework Statement Any floating homogeneous balloon in a planar uniform wind current will always "tend" to present to the wind flow a section of maximal drag. 2. The attempt at a solution I have three possible solutions to this "problem": 1- Speed gradient justification: When an object...

There's an equation from Dirac's book on General Relativity that I don't get at all. It isn't derived; instead it's treated as almost self-evident, when it isn't. Dirac begins by defining ##p^\mu## to be the "mass 4-current" of a continuous distribution of matter (matter in this case really...

Homework Statement This is not a homework question, rather, I am just trying to clarify a concept and example in my textbook. Ammonia is produced by the reaction of Nitrogen (N2) with hydrogen (H2) as shown in this equation. N2 + 3 H2 --> 2 NH3 The rate of ammonia production is 5.0 x 10-6...

Homework Statement My textbook says that I = (1/3)ML^2 for a slender uniform rod, and I = (1/2)MR^2 for a uniform solid cylinder. So let's say that there is cylinder that is a thin disk with M = 5kg, and R = 7m. And let's say that a thin rod also is 5kg and has a length of 7m. Why don't...

A satellite orbiting the globe at some 300 miles at 18000 mph. Does the clock on the GPS tick slower or faster than the same clock on Earth? 1) the clock is distant to Earth and is under less gravitational pull, resulting in time slowing down less than the Earth clock, therefore ticks faster -...

Finding the area of an irregular polygon with n side is quite easy when we are given the length of all of the n sides and the length of (n-3) specific diagonals. This way, we get (n-2) triangles whose areas can be calculated using Heron's formula and then added up. But what if the length of...

Nothing surprising, but worth repeating. 480k Americans die each year from smoking related illness. Stop smoking...

Hellow everybody! A simple question: exist a general formulation, a solution general, for a PDE of order 2 like: ## au_{xx}(x,y)+2bu_{xy}(x,y)+cu_{yy}(x,y)+du_x(x,y)+eu_y(x,y)+fu(x,y)=g(x,y) ## ? The maple is able to calculate the solution, however, is a *monstrous* solution!

It seems odd to me that we have no general solution to quintic equations yet. Is it possible that it exist any general solutions to equations of the fifth degree (and higher) that just haven't been discovered yet? Or are we certain that it doesn't exist?

Homework Statement The problem is attached as TheProblemAndSolution.png, and everything is typewritten, so it should be easily legible (but you will likely need to zoom into read the text since the image's height is significantly larger than its width). Homework Equations Differential...

Problem statement Given sin theta (sqrt 3)/2 Determine the domain for the following solution https://www.physicsforums.com/attachments/655052) determine each general solution using the angle measure specified. Revelant equations Attempt at solution1What is the reasoning behind that? For...

Hello, Homework Statement find the general solution to cos3θ = sin2θ Homework Equations The Attempt at a Solution I know that sinθ = cos(π/2 - θ) but I am unsure of how to apply this when I have sin2θ. Do I say that sin2θ = cos2(π/2 - θ)? I think not because when I do...

Hi Guys, First post here. I'm just wondering if anyone could lend a helping hand in the following derivation. It is taken from Ishida AIChE J 14 (1968) 311 (also very similar to that derived by Ausman Chem Eng Sci 17 (1962) 323) and concerns the derivation of the general non-catalytic shrinking...

i have a question, that nobody seems to be able to answer : is math actually suited for reality ? Basically the idea is that reality seems to be granular, for example we have planks time. Usually the difference is so small, that is doesn't matter, but if you bring things like infinity into the...

https://www.amazon.com/dp/3642372759/?tag=pfamazon01-20 http://www.springer.com/physics/theoretical,+mathematical+%26+computational+physics/book/978-3-642-37275-9 I have just ordered (actually, my wife did, but she has yet to realize this :biggrin:) this new, comprehensive, advanced book on...

Dear Forum, Does every sequence have a general term? What is the definition of the general term of a sequence? Best wishes

Hey everyone, I was hoping someone could point me towards a good General Chemistry textbook. I just finished General Chemistry I last semester, and I'm taking part II next semester. We didn't have a required text for the class (nor did we even really need one), but I want to get a good...

Homework Statement See Attachment Homework Equations The Attempt at a Solution So basically I will not bother writing the derivation from my notes but ultimately it turns out an approximation of deflected light around a mass body is 2\delta\phi=4GM/R where R is distance of closest...

y"+2y'+y=2e^-t I tried to find the solution for this nonhomogenous diff. Equation but i could not. First i took a function Y(t)=Ae^-t but i was getting 0=2e^-t. To get rid of that i took another y'+y=2e^-t and found the solution y=2te^-t + ce^-t. Noticed that first part of this finding is...

Hello! Tchebysheff polynomials are often defined with trigonometric functions: T_m (x) = \begin{cases} \cos(m \arccos (x)) & -1 \le x \le 1\\ \mathrm{cosh} (m \mathrm{arccosh} (x)) & x > 1\\(-1)^m \mathrm{cosh} (m \mathrm{arccosh} |x|) & x < 1 \end{cases} But they are also polynomials, and...

If a function s(t) exists, does a function t(s) always exist? Are there functions with no inverse relationships? Suppose s = \int^t_a e^{u^2} du Can there be a t(s)?

Homework Statement Find the general solution for the current I(z,t) associated with the voltage V(z,t).Do this by substituting [1] into [2] and [3], integrate with respect to time, and then take the derivative with respect to z. Homework Equations V(z,t)= f+(t-z/vp) + f-(t+z/vp) [1]...

Please view the following... http://www.wimp.com/visualizegravity/ This is the way scientists try to explain the warping of space to explain gravity effects between to objects. The very demonstration requires gravity to work! Why does one object track along the displaced track to begin...

Hi, In classical and quantum physics and even in special relativity, shifting the energy of a system by a constant (i.e. resetting the zero point) changes nothing in the dynamics and is not observable. In quantum field theory, we even have to shift by an infinite (but "constant") energy to...

In other words, can dark matter be reconciled with GR without drastically changing the idea that force is due to space-time curvature? and in the case of the standard model is there any thoughts of how the force of dark matter is transmitted via the exchange of a particle? It seems that this...

Hello, Can someone please help me to understand equation (10) from this article http://arxiv.org/abs/gr-qc/0607020. I do not see how does spherically symmetric tensor must (can) be written in that form. Thanks, Benjamin

I'm trying to do 3 questions, each one a bit more complex than the previous, but all have the same ideas. ( 2) has 1 more term than 1, 3) is with imaginary numbers) Could someone please guide me on how to do them? Am I trying to substitute things into each other? Suppose that the sequence x0...

Homework Statement I have a general question concerning circuits. I am a bit confused as to how to determine when the current is negative. For instance, on circuit diagrams, we are shown arrows that indicate the positive direction of current. Then, when we open the switch on the circuit...