Elementary Definition and 558 Threads

Let me preface by saying I am a physics major. So I am coming at differential forms from the perspective of physics, i.e. work, flows, em fields, etc. My question is this. My understanding is that a basic 1-form dx, dy, or dz takes a vector v = (v1,v2,v3) and gives back the corresponding...

Homework Statement http://img42.imageshack.us/img42/8172/carxp.jpg Homework Equations In my solution The Attempt at a Solution My attempt: http://img208.imageshack.us/img208/6526/xxxxoh.jpg The actual solution http://img403.imageshack.us/img403/5579/carsol.jpg...

Hi I've been reading that muons are supposedly leptons (elementary particles), in the past confused for mesons (hadronic particles). They are clearly not mesons, which are composed of a quark and an antiquark. But I've also read that muons decay to an electron and two neutrinos of different...

It is supposed that the smallest posible black hole (BH) has mass of Planck's mass. But obviously one nucleon (or an electron) also acts with gravitational force. If we assume that the smallest possible BH has really Planck's mass, is here any contradiction that a electron acts with...

Ok, so I am taking my first course in linear algebra, and even though I am not a math major (physics major actually), I can't help but wish my teacher and text were more rigorous. So let me start by telling you all the problem I am having: (First question) My book states the following...

They say that a photon has two degrees of freedom, its two polarization states. Does that also mean that the electron has only two degrees of freedom, its two spin states? What about the frequency of a photon, is that not a degree of freedom? Or the three space directions that a electron can...

I have a polyethylene cylinder exactly double the diameter and length of a toilet paper cardboard tube, attached inside the cylinder 3" from the topside of the cylinder I have a tightly secured round vented 10 Micron plastic carbon filter disc encompassing the entire inside diameter which only...

I was just thinking, as I do sometimes when my brain won't shut up and... If an electron is an elementary particle, and a positron is an elementary particle, why do they share so many properties, and yet are different slightly in almost every way. All the mass measurements show that the...

Homework Statement Let \mathcal{C} be a category such that, for each object c \in Ob(\mathcal{C}), the slice category \mathcal{C}\,/c is equivalent to a small category, even though \mathcal{C} may not be small. Show that the functor category [ \mathcal{C}^{\text{ op}}, \bf{Set}] is an...

(dy/dx)^2 + y^2 + 4 = 0; Show that there are no real valued solutions. (dy/dx)^2 = -(y^2 + 4) dy/dx= sqrt( -(y^2 + 4)) -----> This is the answer I got, I feel it makes sense because the negative under the radical produce an answer with 'i' or an imaginary sol'n and since y^2 is always...

Homework Statement 1. For the system of equations x'(t) = 4y and y'(t) = x, obtain the equation of the trajectory (path in the phase plane) that passes through (2, 0). For this trajectory, what is the equation of the slant asymptote that (x(t), y(t)) approaches as t goes to infinity? 2...

Hello! :) Having a hard time managing to solve ad integral in Landau Theoretical Physics Volume 1 page 28 (3rd edition) (Determination of the potential energy from the period of oscillation) The integral is ∫1/√(E-u)(σ-E) with respect to dE between u and sigma. The book claims that the...

I have decided to attempt to pick up some differential geometry on my own, and I am trying to get some traction on the subject which I do by trying to reduce it to familiar and simple cases. This is a trivial case, I know, but it will go a long way in advancing my understanding. Suppose the...

Why are all particles of a particular type of elementary particle all exactly the same? What kind of a process causes a lot of identical elementary particles to appear? How can a infinitely dense, hot, and small piece of space become a system with finite bounds (on energy, number of...

Hi, I'm wanting to do a fun numeracy exercise for my students. I'm planning to have them construct bottle rockets, take measurements and then calculate/graph how high their rockets get using simple triangulation. From that, I was hoping to get them to calculate what the thrust was of their...

Homework Statement I am using a book that doesn't have any solutions in it, so I would like to be sure that I am doing the problems right before I move on. The question is below: In a programming language, a variable name must start with a letter or the underscore character, and...

can a gas of neutrons said to behave like ideal gas? neutrons almost satisfy all postulates of kinetic theory.(except maybe about Newtons laws) Also can a gas of protons said to be a ideal gas? protons could be said to be simply hydrogen with electrons removed. the electrons don't have...

Alright, I know I'm kind of shaky when it comes to proving elementary things rigorously. I'm looking for for the most elementary (in the sense of using least possible mathematical knowledge) proof that x < \tan x, {} {} \forall \frac{\pi}{2}>x>0 Geometrically ? I can't prove...

Why elementary work is defined as δW=Fdr? My ques. is not on the definition; it is on why it cannot be dW=Fdr?

I am able to use a variety of methods to check to see if a series converges, and I can do it well. However, it's not something I feel like I've intuitively conquered. I don't understand why the series 1/x diverges. I mean, I do, in that I know the integral test will give me the limit as x ->...

During the past week the local TV stations have been reporting on parents camped out in front of a new elementary school, in order to be first in line to apply to put their kid in it next fall. The reason? It specializes in engineering, I kid you not: http://www.greenville.k12.sc.us/ajw/about/

Homework Statement Suppose matrices A and B are similar. Explain why they have the same rank. Homework Equations The Attempt at a Solution So if A and B are similar, then there is some invertible matrix P such that B = P^-1AP. I have been trying to find some way to relate...

I've read everywhere that strings are now taken to be the fundamental particle, but I think that it is taken as one because we cannot go further. After a few years once we can go in we may discover a new elementary particle. I was thinking; isn't energy the fundamental particle? Because even...

Homework Statement Homework Equations addition / multiplication -- showing that the vectors (in this case) aren't closed under addition and scalar multiplication. . . The Attempt at a Solution I really get stuck with proofs: how to begin / where to go / etc. I know that I am...

Homework Statement Prove that if W is a subspace of a finite-dimensional space V, then (dimension of W) is less than or equal to (dimension of V). The Attempt at a Solution I've been trying to prove this by contradiction (assume dimension of W is greater than V and arrive at a...

Homework Statement A worker on the roof of a building that is under construction dropped a 0.125 kg wrench over the edge. another workman on the 8th floor saw the wrench go by and determined that its speed at that level was 33.1 m/s. the first floor of the building is 12.0m high and each...

Homework Statement An urn contains 17 balls identical in every respect except color. There are 6 red balls, 8 green balls, and 3 blue balls. A) you draw 2 balls from the urn but replace the first ball before drawing the second. find the probability that the first ball is red and the second...

I started reading about relativity before doing my first calculus problem, and knew relativity concepts before learning basic physics I concepts. It actually helped me simplify a few problems. I knew that two cars colliding at different speeds was just another description of one car colliding...

Homework Statement if an integer n >= 2 and if n divides ((n-1)! +1) prove that n is prime. Homework Equations a divides b iff b = ma for integers a, b, m. The Attempt at a Solution by contrapositive: Assume n is not prime. Then we have by definition of divisibility...

Homework Statement The 3x3 matrix A is transformed into I by the following elementary row operations R1+2R3 -> R1 R2+2R3 ->R2 2R2 ->R2 R1 <->R2 2R3 ->R3 Find det(A) Homework Equations I assumed to start off with the problem since I was going backwards from I to A. I would do the opposite of...

I need to design a procedure for this lab. I measured the mass of a couple of bags containing the same object in random amounts. Without looking at how many objects are in the bag i have to determine the mass of one object. At first i thought that since each mass measured should be a...

It's been some time that I've been studying abstract algebra and now I'm trying to solve baby Herstein's problems, the thing I have noticed is that many of the exercises are related to number theory in someway and solving them needs a previous knowledge or a background of elementary number...

Homework Statement Consider the following 3 row operations performed to a 4x3 matrix A used to transform it into matrix B: E1: -4R1+R4-> R4 E2: R2<->R3 E3: (1/2)R4-> R4 From there I am asked to find E1, E2, E3. The Attempt at a Solution I assumed the identity matrix I would start...

The truly elementary mass seems to be the Planck mass which is much larger than the masses of the particles that we see in nature. Maybe what we think of as elementary particles are actually just quasi-particles, excitations of the underlying space-time (like phonons are quantised vibrations...

Homework Statement Prove that if P(A) \subseteq P(B) then A \subseteq B, where A and B are two sets and P symbolizes the power set (set of all subsets) of a particular set. Homework Equations The Attempt at a Solution Okay, so here goes. Because it's a conditional, we suppose...

So, I took elementary analysis this summer and I got a 'D,' which was very annoying simply because half of our class got 'F's and it would have made such a big difference if my teacher would have just curved the class. Anyways, I'm not interested in taking any other courses which require...

Homework Statement If 3 | m^2 for some integer m, then 3 | m. Homework Equations a | b means there exists an integer c such that b = ca. The Attempt at a Solution I realize that this is a corollary to Euclid's first theorem, and that there are plenty of ways to solve this. However, I...

elementary particles --their place in atom Homework Statement Do elementary particles reside inside the nucleus alone? Homework Equations The Attempt at a Solution

I am self-studying elementary abstract algebra over the summer, with the book "Abstract Algebra: An Introduction" by Hungerford. It's my first exposure to mathematical proofs (well, short of an introduction in my intro to discrete mathematics), so sometimes I'm not really sure I do everything...

Homework Statement Prove or disprove the following about vectors in \mathbb{R}^n: If A \cdot B = A \cdot C and A \neq O, then B = C. Homework Equations In this example, O represents the zero vector. Let the vectors be represented as: A = (a_1,a_2,\dots,a_n) B =...

I have yet to take Elementary Linear Algebra MATH 341, but I am currently signed up for Intro to Analysis MATH 413. I'm about to complete Elementary Analysis MATH 315. I could take MATH 341 and MATH 413 at the same time, but I'm already signed up for two other economics classes that I feel I...

Elementary questions about connections. I’ve been looking at the Wikipedia article on affine connections with a view to better understanding the choice of Riemannian geometry for our best theory of gravity — a founding choice made by Einstein nearly a century ago. Sadly for me the...

I'd like someone to check this proof out for violations of math law. It seems like hackery to me, but then so does a lot of what my professor says, so maybe it's not. If it's flawed, just tell me why. Please don't suggest other ways to prove this, that's my job this weekend. Thanks :) p.s...

Hello, I am teaching myself Set Theory, and in doing some exercises I came across the problem: Given sets A and B, prove that A \subseteq B if and only if A \cap B = A. My proof, in natural language, is in two parts: 1) Prove that if A \subseteq B, A \cap B = A. By the definition...

Homework Statement Homework Equations The Attempt at a Solution Well, I just want some hint. It seems substitution doesn't work.(I can't think of any suitable substitution)

T/F, Please Help! Elementary Statistics! Homework Statement 5-If a true-false exam contains 10 questions, there are 20 different ways to answer all the questions. Homework Equations There are none for it is a true false question. The Attempt at a Solution I believe this is...

There is a bag in front of me. I am told it contains 100 red balls or 50 red balls and 50 blue balls. If I pick n red balls from the bag and no blue balls what is the probability as a function of n (p(n)) that the bag contains 50 red balls and 50 blue balls. Of course, if n is greater than 50...

Hello, Maybe a strange question here (I'm not 100% current with the standard model), but does the standard model say anything about a change in the ratios of fermions as the universe expands? (I see Generations I, II & III listed)

Homework Statement What strenght do you need to put mass m in the height h? Homework Equations P=\frac{A}{t} The Attempt at a Solution A=mgh so P=\frac{mgh}{t} Is that mean that your strenght is less if you take mass long in the height h?

Homework Statement Let \bigtriangleup ABC be a right angled triangle such that \angle A = 90°, AB = AC and let M be the midpoint of the side AC. Take the point P on the side BC so that AP is vertical to BM. Let H be the intersection point of AP and BM. Find the ratio BP:PC. Homework Equations...