Fundamental Definition and 907 Threads

The question: Find the fundamental matrix for the given system of equations, and then find the specific solution to satisfy x(0) = I. x' = \left(\stackrel{1}{5}\stackrel{ -1}{ -3}\right)x My solution: I found the eigenvalues to be r_{1}= -1 + i and r_{2}= -1 - i I then found the...

Homework Statement Okay, basically why does (a_{}n + b_{}n) ignore the Fundamental Theory of Polynomials? Homework Equations ... I could post them here, but basically when n is odd (a_{n} + b_{n}) = a series that looks like this: (a+b) (a_{n-1} b_{0} - a_{n-2}b +a_{n-3}b_{2} + ... +...

Homework Statement Without computing A, find the bases for the 4 fundamental subspaces. [1 0 0][1 2 3 4] [6 1 0][0 1 2 3]=A=LU [9 8 1][0 0 1 2] Homework Equations N/A The Attempt at a Solution There was an "example" in the book. It just showed the answers. It was: [1 0...

IDK if my understanding is right...but as far as I understand physics...all the fundament forces shares 2 characteristics - attraction and repulsion...now, here are my questions.. 1. Assume there are only 2 uncharged atoms in the universe...would they come together or go apart or stay where...

Thermodynamics! Finding a fundamental equation. This is the question: "While he Gibbs free energy G is the fundamental function of the atral variables (T,p,N), (T=temperature, p=pressure, N=number of molecules), growing biological cells often regulte not the numbers of molecules N, but the...

[SOLVED] fundamental theorem of algebra Homework Statement Theorem: If F is a field, then every ideal of F[x] is principal. Use the above theorem to prove the equivalence between these two theorems: Fundamental Theorem of Algebra: Every nonconstant polynomial in C[x] has a zero in C...

I was just going through the derivation of the euler - lagrange equation that rests on the proof of the fundamental lemma of the calculus of variations which states the following: If a function g(x) vanishes at the endpoints i.e g(a) = 0, g(b) = 0 and is continuously differentiable within...

Hi all In Paul Tipler's book on modern physics (with Ralph LLewelyn) I read an explanation for the formation and stability of a molecule, which is based on Pauli's exclusion principle. This principle was responsible for a term in the energy equation, which yields also (naturally) a term in...

what are the fundamental symbols in logic? maybe this is a vague question but that's cause i don't know anything about logic. are they \neg \wedge \vee? do we define the material implication in terms of these symbols? basically I'm having trouble understanding the paradoxical nature of...

Hello, I have a little problem. I´ve calculated the fundamental matrix of a EDO system, such that: M(t) = P * exp( J*t) where J is a diagonal matrix: J = [-3 , 0 ; 0 , 1] and P = [1 , 1 ; 3 , -3] The problem arise when I try to find the inverse matrix of M. What I do is this As we know the...

http://www.nature.com/news/2007/071220/full/news.2007.389.html this just came out in Nature News, comment? To be sure, they are talking about how many DIMENSIONAL fundamental constants you need. The main bunch of constants that people always want to measure and to explain are the...

For the first fundamental theorem of calculus, I don't quite understand it... I think I got the integral part, but not the interval [a,x]... can you guys help me? thx

Homework Statement Find F'(x) if F(x)=\int_{0}^{x^3}(\sin (t^2))dt The Attempt at a Solution Here's what I did: F(x)= -\cos (t^2)\biggr]^{x^3}_{0} and I get: F(x)= -\cos (x^6) +1 F'(x)= sin (x^6)(6x^5) However, the book's answer is F'(x)= 3x^2 \sin(x^6) How did...

Homework Statement In order to decrease the fundamental frequency of a guitar string by 4%, by what percentage should you reduce the tension? Homework Equations f = sqrt [T/(m/L)] / 2L I believe that is the equation that relates frequency to tension... The Attempt at a Solution...

Homework Statement There are two versions of the fundamental theorem of algebra, one that says a polynomial of degree n has n roots and the other that says a polynomial can be factored into linear and irreducible quadratic factors. Is there a quick way to see how they are the same...

Homework Statement Find the derivative of cost/t (dt) evaluated from 3 to the sqrt of x The Attempt at a Solution using the fundamental theorem of calculus, I have [cos(sqrt x)]/(sqrtx) I know I have to use the chain rule but I don't know how to go about it from here. Any tips?

Via [Ilqgs] email list: POSTDOCTORAL POSITION AT PENN STATE IN FUNDAMENTAL GRAVITATIONAL THEORY The Institute for Gravitation and the Cosmos expects two openings for post-doctoral positions starting fall 2008 in the areas of general relativity and quantum gravity. Successful...

Hey guys...I always tend to ask a lot questions...so I was wondering if you guys know of some books out there which is very fundamental and explains its reasoning on every step of its way as if it was made for kindergarten but covers advanced topics? Fields I am interested in...

how do i interpret this geometrically F^\prime(x) = \lim_{h\to 0} \frac{F(x+h) - F(x)}{h} = f(x) that the change in area with respect to change in "width" is the "height"? i don't think that's right.

Homework Statement A string with a length of 2.5m has two adjacent resonances at frequencies 112 Hz and 140 Hz. Determine the fundamental frequency of the string? A. 14 Hz B. 28 Hz C. 42 Hz D. 56...

So, here is what I have: Gravitation F = -G\frac{m_{1}m_{2}}{r^{2}} Weak Interaction ? Electromagnetism F = -\frac{q_{1}q_{2}}{4\pi \epsilon_{o}r^{2}} Strong Interaction ? I'm thinking of all of these things as actual calculable forces; but I cannot...

Homework Statement 1.I have a vector defined by (v1,v2,v3). 2. I want to project this vector on a plane such that a point on that plane is defined by (p1,p2,p3).Also, the normal to the plane is given by (n1,n2,n3) 3.Can anyone help me to the projection of the vector on this plane...

Somewhere along the path, I've realized that I have been going the wrong direction...instead of finding the truth...I was actually trying to say, "I am right and you are not" So the old questions have sprung against and I feel clueless, any sort of help will be highly appreciated. To begin...

I have 2 questions: FIRST I read from John H. Mathews’ Numerical Methods using MATLAB, 3E that the number 1563 can be expanded in form of 10-base expansion as: (1 × 10^{3}) − (5 × 10^{2}) + (6 × 10^{1}) + (3 × 10^{0}) …......... (1) Which results 1000 − 500 + 60 + 3 equal to 563...

We have a periodic signal of period 10 ms and amplitude 2.The signal is a rectangular pulse from -5/2 to 5/2 and 0 from 5/2 to 19/2.This signals fundamental frequency(f0) is 100Hz.It is passed through a filter whose response is 1/(1+jf/f0.I calculated the average power using the trignometric...

My question is which law of Newton is the most fundamental? I am talking of the laws of motion...

I want to find the fundamental matrix for the following system: \dotx = \left(\begin{array}{cc}1/t&0\\0&1/t\end{array}\right)x + \left(\begin{array}{rr}1&1\end{array}\right)u y = (1, 1)x There's supposed to be an x' before the first equal sign but I can't get it to work for some...

Homework Statement Imagine that I throw a ball toward the floor. It hits the floor and rebounds upward. What type of fundamental interaction between the atoms of the floor and the ball causes the ball to rebound upward? a. Strong nuclear b. Electromagnetic c. Weak nuclear...

0, 1, phi (the Golden ratio), e, pi, delta (Feigenbaum's constant) and comparatively many other fundamental, dimensionless mathematical constants occur on the interval 0 to 5. With a potential infinity of numbers to choose from, why does such a confluence exist?

Homework Statement Find fundamental period of x(t)\,=\,cos\left(\pi\,t\right) Homework Equations x(t)\,=\,A\,sin\left(\omega_0\,t\,+\,\phi\right) Which has a fundamental period T\,=\,\frac{2\pi}{\omega_0} The Attempt at a Solution \omega_0\,=\,\pi <---- Right? T\,=\,\frac{2\pi}{\pi}\,=\,2...

Hi...I am new to this forum. Can somebody clear a fundamental doubt i have?:rolleyes: A wave function has a form found by applying Schrodinger's equation. In steady-state systems, arent the system eigen functions, the wave equation of the system? if so is it the energy eigen function or the...

I'm having a bit of a difficulty trying to determine the fundamental frequency in a given function and the harmonics. In the equation below,would the fundamental frequention be 1 (corresponding to the value cos(1x-pi)) and the harmonics amplitude 3 and -4?Also,the values of the frequency of the...

Hi all, reading an article I've encountered the concept of power at the fundamental frequency, google didn't help me. Could you please give to me any hint about this problem? It is at least one week I'm dealing to understand what the "fundamental power" is! there is a kind of wave, express as...

From http://www.us.oup.com/us/catalog/general/subject/Physics/Relativity/?view=usa&ci=9780198567325" I learn that the fundamental identity c^2\text{d}{t'}^2 -\text{d}{x'}^2 -\text{d}{y'}^2 -\text{d}{z'}^2 = c^2\text{d}{t}^2 -\text{d}{x}^2 -\text{d}{y}^2 -\text{d}{z}^2 relates co-ordinates...

Some things are clearly fundamental, and some emergent. As examples of fundamental concepts I could mention energy, momentum and location. An object has a location in space, because its' particles each have own locations. On the other hand some things are emergent, for example behaviour of a...

Fundamental group of RP^n by recurrence!? Homework Statement That's it. Find the fundamental group of RP^n by recurrence. The Attempt at a Solution It's just obvious to me that it's Z/2 no matter n but what is this recurrence argument that I'm supposed to use?

Why is an electron so small and the proton so large? Why does + repel + and all those other combinations? Why exactly does an electric field form? What is + charge? What is - charge?I'm looking for very indepth stuff here.

The theorem of classification of closed surfaces says that any closed surface is homeomorphic to a fundamental polygon in the plane. I was wondering if any fundamental polygon can be made into a closed surface by adjoining an appropriate atlas to it. The topological requirements of a closed...

[SOLVED] Change in Tension &amp; Fundamental Frequency of a String Problem. Show that if the tension in a streched string is change by a small amount \Delta F_T, the frequency of the fundamental is changed by a small amount \Delta f = 1/2 (\Delta F_T / F_T) f. Let T be the intial tension and h...

What are some of the fundamental differences between Classical & Quantum mechanics?

Hi Is there anywhere a list of all constants (with their values) and fundamental equations (which can not be constructed from any other equations) of the standard model? thx einKI

third law is equal and opposite reaction . . . the first law is inertia of mass. From everything I can remember reading, people often talk about the mystery of inertia in bodies . . . well, i finally got around to thinking about this stuff(admittedly), and it seems to me that the first law is...

I don't really understand how Faraday's Law can be one of Maxwell's equations if it doesn't seem all that fundamental to me. An induced emf/voltage is created by the rate of change of magnetic flux with respect to time in a closed loop. Well obviously if a voltage is induced it means an...

I have a big test tomorrow and as I was reviewing, I encountered the following confusions. I hope that someone can help me out. I really appreciate for your help!:smile: 1) http://www.geocities.com/asdfasdf23135/cal0007.JPG The answer is NO. But when I differentiate both sides and...

Simple question: is the fundamental group of a pointed space independant of the base point?

I read on wiki* that a (pointed) topological space is simply connected iff its fundamental group is trivial. But I don't see how this in accordance with the R² caracterisation that U is simply connected iff it is path-connected and has no holes in it. Take the closed unit-disk with a point of...

so now I'm finally getting to grips with the maths of quantum mechanics, I'm getting really confused about what it means physically. sorry this is quite long but it seems like the more i think about quantum mechanics, the more my understanding of it disintegrates. first, does quantum mechanics...

I have a little hard time understanding the definition of a simply connected space in terms of a fundamental group. A space is simply connected if its fundamental group is trivial, has only one element? It's been some time since I played around with homotopy. My understanding is that a set...

Can someone say why it is said that in electrostatics,the test charge may be moving very slowly?Specifically,what is wrong if the test charge moves at a speed which is a significant proper fraction of speed of light?

I haven't taken any abstract algebra course so I do not know if this is the right section to post this question in. Anyway, I am learning differential equation right now and my prof. recently showed factorization of differential operator. For example, let D be the differential operator, he...