Fundamental Definition and 907 Threads

Hi, I've been watching the MIT lectures on single variable calculus, and whilst proving FTC, he mentions that we since we know that: <$> f'(x) = g'(x) </$>, then by MVT we know that <$> f(x) = g(x) + C </$>. I have tried searching for somewhere where this implication is spelled out for me...

Are forces due to fields or are fields an abstraction of forces? Do electromagnetic waves exist apart from as an abstract description of changing fields, which are in turn abstract descriptions of changing forces (or potential of force if there was an object for force to be applied to)?

What do we mean by different fundamental forces having different relative strength? And if we already consider electromagnetic and weak interaction to be different manifestations of the same force, how are their relative strengths different?

Problems with fundamental particles and quarks :( Hi, I have no idea where to post this so I hope its ok... I'm studying A level physics. We have a topic on fundamental particles. Yea couple of questions... 1. Whats the difference between a (insert lepton here)-neutrino, and its...

Is rest mass just an illusion? In Proton, for example, most of the rest mass is relativistic mass of quarks, moving at relativistic speeds. Quarks are quite light, but if we go deeper, the rest mass of quark is also an illusion - all particles have rest mass = 0, and what we call mass is...

Homework Statement Consider a cartesian coordinate q_k and conjugate momentum p_k. The Poisson-bracket for two random functions f=f(q_1,..,q_f,p_1,..,p_f,t) and g=g(q_1,..,q_f,p_1,..,p_f,t) is defined as: \{f,g\}=\sum_{i=1}^{f}\biggl(\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial...

Homework Statement Verify that y1(x) = 1 and y2(x) = x^.5 are solutions of the following y y'' + (y')^.5 = 0. Then show that c1 + c2 x^.5 is not in general a solution of this equation. Homework Equations The Attempt at a Solution I was able to show that both y1 and y2 are...

How do you define what is a fundamental circuit element? I am not really sure, why isn't a transistor a fundamental circuit element. Can u consider a switch a fundamental circuit element or is it a resistor with infinite resistance.

Homework Statement a) Use the fundamental theorem of line integrals to evaluate the line integral: ∫(2x/(x^2+y^2)^2)dx+(2y/(x^2+y^2)^2)dy (over C) Where C is the arc of the circle (x-4)^2+(y-5)^2=25 taken clockwise from (7,9) to (0,2). Explain why the fundamental theorem can be applied. b)...

I would like a reference for a purely algebraic proof of the fundamental theorem of algebra - or if you would like to supply a proof that would be even better.

In a smooth compact 3 manifold there is an embedded loop - a diffeomorph of the circle Consider a torus that is the boundary of a tubular neighborhood of this loop. If the loop is not null homotopic does that imply that the torus is not null homologous?

Is there such a concept in information theory? I.e. Something as complex as language can be reduced to 1's and 0's. Is binary the fundamental unit of information?

I'm just trying to get a few things straight as I delve into the world of quantum physics and string theory. First of all, what does it mean when someone says two forces combine, such as the electromagnetic and weak force as the electroweak force? Does that mean that the particles are the same...

If I take a plane with n holes, would the fundamental group be that of the "bouquet of n circles"? (http://en.wikipedia.org/wiki/Rose_(topology ).) The bouquet of circles is the same as the unit line with n-1 points identified. All three spaces initially appear quite different so it would be...

I am doing some revision and trying to do fundamental groups and I was wondering if the fundamental group of the following space is {1} i.e. all loops based p are homotopic. fundamental group of (X,p) = D^2\{(x,0) : 0<=x<=1} where p=(-1,0)

I just don't get it. Some people, deep down in their hearts, want to see computation as the most fundamental thing ever. This is the reasoning behind the holographic idea, at least from Verlinde. Variable spin makes it possible quantum computation through anyons, yet people still want spin like...

What I understand from the definition of the fundamental group is: Pi1(X.x) is "the set of rel {0,1} homotopy classes [a] of closed paths" Ok, when I think about one [a] it consists of all: 1.Closed paths like a and b with a(0)=a(1)=x & b(0)=b(1)=x --->since they are closed. 2.And since...

Can someone explain to me the fundamental understanding of why, when two hydrogen atoms for example, release energy when they form a covalent bond? I can't seem to comprehend. Here is my reasoning, please see if this makes any sense of I am simply going in the wrong direction, I would really...

What restrictions must we place on a real-valued function F for F(x) = \frac{d}{dx} \int_a^x F'(y)dy to hold, where "\int" is the Lebesgue integral?

I need to calculate the fundamental group of the following spaces: X_1 = \{ (x,y,z) \in \mathbb{R}^3 | x>0 \} X_2 = \{ (x,y,z) \in \mathbb{R}^3 | x \neq 0 \} X_3 = \{ (x,y,z) \in \mathbb{R}^3 | (x,y,z) \neq (0,0,0) \} X_4 = \mathbb{R}^3 \backslash \{ (x,y,z) \in \mathbb{R}^3 | x=0,y=0...

Hello; "S\propto\ln\Omega, where \Omega is the number of microstates" is what a user told me was the fundamental definition of entropy. What is S? Is it the number of macrostates? And where does the ln come from? Can I see an example of where this formula would be used in practice? Thanks.

1. Balboa Park in San Diego has an outdoor organ. When the air temperature increases, the fundamental frequency of one of the organ pipes _____. a) goes down b) stays the same c) goes up d) is impossible to determine 2. v=331sqrt(1+t/273)/ 3. goes up?)

Fundamental frequency! 1. Ultrasound with a frequency of 4.079 MHz can be used to produce images of the human body.If the speed of sound in the body is the same (1.97 km/s) as in salt water, what is the wavelength in the body? Answer in units of m. and 2. On a day when the wind is...

Homework Statement A guitar string has a fundamental frequency of 429 Hz when its tension is 259 N. The string is being tuned to a fundamental frequency of 388 Hz. What is the required tension? Homework Equations v = sqrt(T/u): where v is the speed, T is the tension and u is the...

Why is it that the The fundamental thermodynamic relation dU = Tds - PdV works in general even though Tds > dQ for irreversible processes. Likiewise PdV >/= dW for irreversible processes. Do the two irreversible effects cancel out. How does this happen physically.

Hello, I am thinking of applying for the above course and just trying to gauge how difficult it is really. I have a 2:1 in physics from Cambridge, and although at times I felt like I was knocking my head against a brick wall overall I think I might have pulled to a first if the exams had...

I am reading Munkres and know exactly how to find the fundamental groups of surfaces, using pi_1 and reducing it down to simpler problems. However, I'm completely lost when looking at my final exam it says to find the fundamental groups of matrices! How do you go about doing that! There are...

Homework Statement Using the Fundamental Theorem of Arithmetic, prove that every positive integer can be written uniquely as a power of 2 and an odd number. Homework Equations The Attempt at a Solution Since the FTOA states that any integer can be written as a product of primes...

The 2nd part of fundamental theorem of calculus says: Over what open interval does the formula F(x)=\int_{1}^{x}\frac{dt}{t} represent antiderivative of f(x)=1/x ? By looking at the theorem I would say that f(x) is continuous only for x \neq 0 So I would say that F(x) is defined on...

Verlinde and Jacobson's early work, strongly implies that gravity is emergent. Anyhow, one of Jacobson's and Verlinde's claim in his paper is that since gravity is not a fundamental force, it does not make physical sense to quantize it canonically. So the LQG program is misguided...

Homework Statement For a given rectangular waveguide the cut off frequency of the fundamental mode is 6.5GHz. What is the fundamental resonant frequency of a 30mm long cavity made from the same waveguide? Homework Equations Unsure The Attempt at a Solution I would have...

I'm studying for an exam which is a couple months away and I found an old exam which asks the following: Find the fundamental group of: a) The closed subset in R3 given by the equation x - y^2 -z^2 = in the standard coordinates. b) The closed subset in R3 given by the equation x - y^2 -z^2...

According to Wikipedia, "the first fundamental theorem of calculus shows that an indefinite integration can be reversed by a differentiation." Am I wrong or is this theorem very simple? Indefinite integrals are the same as antiderivatives. So isn't this theorem simply stating that the...

If I draw a random curve over a scalar field, then it is not generally true that the line integral of the scalar field over the curve equals the difference between the value of the antiderivatives of the scalar field at the beginning and finishing points of the curve, as one can clearly see by...

Homework Statement Does the function F(x)=int(sin(1/t)dt,0,x) (integral of sin(1/t) with lower limit 0 to upper limit x) have a derivative at x=0? Homework Equations The Attempt at a Solution I was thinking that F(x) shouldn't have a derivative at x=0 because the integrand isn't even...

What is the Fundamental Theorem of Computer Science? No such formally named theorem exists if I do a google search. But I'm very curious as to what students and professors of Computer Science might think it should be. Anyone?

Hi, Suppose we're asked to find the derivative of the integral f(x)~=~\int_{-13}^{sin~x} \sqrt{1+t^2}~dt Now, the solution apparently looks like this: f(x)^{\prime} = \sqrt{1+sin^2(x)}\cdot~cos(x) Why? Why does the solution contain the upper limit `plugged in` ? A more sensible...

I read a short high-level article about the pilot wave interpretation of quantum mechanics and I have some questions. Is there a good way to formulate that theory so that the only force on a particle is from the pilot wave (inertia, gravity, EM, ... move/effect the wave which in turn...

Homework Statement interested in getting reliable information on the actual strength of the fundamental forces,including the strong nuclear, weak nuclear, electromagnetic and gravitational forces.What is their relative strengths one to another? Homework Equations The Attempt at a...

What is "emergent"; what is "fundamental"? Bee Hossenfelder had an interesting discussion of the term "emergent" back in mid 2008: http://backreaction.blogspot.com/2008/04/emergence-and-reductionism.html There are apparently several ways the term is used in theoretical physics. Several...

So there is a theory out there that seems to model the "four" fundamental forces based upon a higgs-like particle, which the author calls k-particles. He seems to believe that these particles act upon electrons, protons, fermions, etc. to produce forces by the means of k-particle density. It's...

I'm assuming the standard reductionist viewpoint: that chemistry is simplified quantum physics. Of the four fundamental forces in modern physics, what forces play a role in chemical reactions? Is it safe to assume it's solely electromagnetics?

What is the unit of 'strength' of the fundamental forces? When it is said that gravitational force is weaker than the strong nuclear force, how are they compared? What is meant when it is said that the fundamental forces approach each other in strength at higher energies in the early universe?

Homework Statement The fundamental frequency of an open organ pipe corresponds to the note middle C (f = 261.6 Hz on the chromatic musical scale). The third harmonic (f3) of another organ pipe that is closed at one end has the same frequency. Compare the lengths of these two pipes...

Let |\psi_n\rangle\in\mathcal{H}, where \mathcal{H} is Hilbert space, be orthonormal states forming a complete set, and n\in\mathbb{N}. Let |\Psi\rangle=\sum_{n=1}^N c^{(1)}_n|\psi_n\rangle, where c_ns are normalized coefficients and N is either finite or infinite. Let m be an eigenvalue of...

Morning everyone, Studying for a test and having a problem on a practice question he gave us to study with. Here's the question along with the answer: Y' = AY + [e^t e^-t 0] with A = [-1 0 4 -0 -1 2 0 0 1] the...

Homework Statement Okay, so this is some trig I learned last year but have since forgotten. If you can give me the first step, I can solve the rest on my own. The given statement is true and you have to prove why using Pythagorean Identities. csc2\alpha-1 = cos2\alpha ________ csc2\alpha

I just learned about the fundamental theorem of calculus. I can see that this ties together differentiation and intergration, but I was wondering what kind of problems can be solved by using this theorem? In other words, what can the theorem be applied to?

Homework Statement Show that the vectors \overline{x}(t) = \begin{bmatrix} e^t \\ -t \end{bmatrix} and \overline{y}(t) = \begin{bmatrix} t \\ e^(-t) \end{bmatrix} are solutions for \overline{x}' = \frac {1} {1+t^2} \begin{bmatrix} 1+t & e^t(1-t) \\ -e^-(t) (1+t) & t-1...

Homework Statement A particular violin string plays at a fundamental frequency of 294Hz. If the tension is increased 15%, what will be the new fundamental frequency? Homework Equations f=v/2L v=sqrt(T/(m/L)) The Attempt at a Solution 294 = sqrt(T/(m/L))/2L so...