Fundamental Definition and 907 Threads

1. Find the derivative of: ∫cos3(t) where a = 1/x and b = ∏/3 This was a part of a question on my first calc exam and I just wanted to know if I did it correctly. We can solve this using the Fundamental Theorem of Calculus, Part II The solution would be to simply plug in the values for a and...

Many texts in deriving the fundamental solution of the Laplace equation in three dimensions start by noting that the since the Laplacian has radial symmetry that Δu=δ(x)δ(y)δ(z) That all that needs to be considered is d^2u/dr^2 + 2/r du/dr = δ(r) For r > 0 the solution given is u= c1/r +...

On page 333 in Section 52: The Fundamental Group (Topology by Munkres) Munkres writes: (see attachement giving Munkres pages 333-334) "Suppose that h: X \rightarrow Y is a continuous map that carries the point x_0 of X to the point y_0 of Y. We denote this fact by writing: h: ( X...

Hi guys I'm wondering about something, currently in our mathematics our number system goes something like this, 1,2,3,4,5... etc all the way to 9, then the whole cycle is repeated when it reaches 10. I believe this method of counting seems to stem from the fact that we have 10 fingers and our...

Question: For the interval x > 0 and the function set S = { 3ln(x), ln2, ln(x), ln(5x)}, construct a linear ODE of the lowest order. My work: Taking the wronskian for this solution set, I get it as 0. Doesn't that mean that a linear ODE for this set cannot be found? I'm very confused here...

Hello, I was unsure if I should post this or on the General Physics thread but since it's about Einstein's gravity, I'll post it here. All right, so the problem is as follows (from Surely You're Joking, Mr. Feynman!): I understand the question being asked. My question is, how you would...

I just wanted to say first of all that I am not looking for any specific answers, just hoping someone could shed a light on the subjects at hand. Is the quadratic formula a specific example of some general root finding algorithm that solves for the n (or n-1?) roots of a nth degree...

If photons emit virtual gravitons (but gravitons don't emit virtual photons) why isn't gravity considered to be a more fundamental force?

It seems to me that luminous intensity should really be put in terms of energy, not a special unit (which itself is based on some arbitrary specification of energy.) The other 5 units and Avogadro's number should be the only fundamental units.

On the atomic level, what is entropy? how can I visualise it? Thanks

Hello everyone, Let r(u_i) be a surface with i=1,2. Suppose that its first fundamental form is given as ds^2 = a^2(du_1)^2 + b^2(du_2)^2 which means that if r_1 = ∂r/∂u_1 and r_2= ∂r/∂u_2 are the tangent vectors they satisfy r_1.r_2 = 0 r_1.r_1 = a^2 r_2.r_2 =...

There is an article in the field of relativity (not homework) that need evaluation, please advise institutes that might do that??

Graphic Design & Science: Fundamental Particles Visualisation Hello my name is Brendon. I'm a graphic designer interested in science communication and currently studying a masters in graphic design. I was wondering if anybody would be able to help me with a few queries with regards to...

Homework Statement The Attempt at a Solution So I know that I must have boundary conditions u(0,t) = 0 and ux(L,t) = 0. My textbook recommends reducing the given boundary conditions to homogeneous ones by subtracting the steady state solution. But, I thought these were already...

Homework Statement This is supposed to be a proof of the fundamental theorem of calculus. I'm not really sure what that proves, but to me at least it does not prove that the area under a curve is the antiderivative of the function and then inserting the upper x value and...

I've completed my Engineering but doing a self study course in Dynamics of Structures and have got a very fundamnetal question concerning solution of differential equation and hope someone will be able to help me. Sorry if its too fundamnetal and stupid! Let us say we have to solve a...

Suppose I know my function G is infinitely differentiable on the closed interval [a,b] and that all derivatives of G (including G itself) vanish at b. For any z in [a,b], I have by the FTC that \int_z^b G'(w) dw = G(b) - G(z). Or, switching limits, \int_b^z G'(w) dw = G(z) - G(b). One...

There are a good number of very fundamental principles that underlie physics (conservation of information, principal of parsimony, time invariance, symmetry, etc.) that don't seem to be listed in modern physics textbooks. Are they codified somewhere?

Homework Statement F(x) = ∫ cos (1+t^2)^-1) from 0 to 2x - x^2 Determine whether F has maximum or minimum value Homework Equations The Attempt at a Solution I tried finding F'(x) = Dx (∫ cos (1+t^2)^-1) from 0 to 2x - x^2) = (2-2x)cos[(1+(2x-x^2))^-1] What do I do...

Homework Statement The pion-zero meson has its mass quoted as 135.0MeV/c2. It decays into two gamma rays: ∏0 → γ + γ b) Assuming the ∏0meson to be initially at rest, calculate the energy and hence the wavelength of the two gamma rays. Homework Equations E= hc/λ The Attempt at a...

dE = TdS - PdV, or equivalently \Delta E = \int T \mathrm d S - \int P \mathrm d V In general this is said to be derivable in the reversible case, however since S and V are state variables, it's also true for the irreversible case. But it can't be true for any irreversible case, since the...

dE = dQ + dW = dQrev + dWrev = dQirev + dWirev. We have for an reversible process, dQrev = TdS and dWrev = -PdV. So; dE = TdS - PdV So this relation is for all changes (irreversible or reversible) since dS and dV are state functions. What doesn't make sense to me is the next part when...

I came across this. I guess you could say. F→∏ A l Z ...or... F→∏ AlZ The third symbol is supposed to be upside down. Does that matter?(The ∏ symbol) And between the symbol A and Z the line is supposed to be a tall line. (Not an L or I) Does this make sense?

Homework Statement Find the fundamental equation of a monoatomic ideal gas in the Helmholtz potential representation, in the enthalpy representation, and in the Gibbs function representation. Assume the fundamental equation S= \frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac {U}{U_0} \right )...

Homework Statement I am having extreme trouble with the following problems: http://i.minus.com/iYs6ix6otGtLV.png Homework Equations For 26: If the first derivative is positive, then the function is increasing. If the first derivative is negative, then the function is...

Okay, say a car is moving at a constant velocity and crashes into a wall. Now, observation would clearly illustrate to us that a destructive force was imparted onto the wall and the car. But how can that be if there there is no force, because there was a constant velocity? I must have some...

Homework Statement Let I := [a,b] and let f: I→ℝ be continuous on I. Also let J := [c,d] and let u: J→ℝ be differentiable on J and satisfy u(J) contained in I. Show that if G: J→ℝ is defined by G(x) :=∫u(x)af for x in J, then G'(x) = (f o u)(x)u'(x) for all x in J. 2. The attempt...

State the Fundamental Theorem: Let F be a vector field. If there exists a function f such that F = grad f, then \int_{C} F \cdot dr = f(Q) - f(P) where P and Q are endpoints of curve C. _________________________________ I didn't receive any credit for this answer. Admittedly...

Vector field F(bar)= <6x+2y,2x+5y> fx(x,y)= 6x+2y fy(x,y)= 2x+5y f(x,y)= 3x^2+2xy+g(y) fy(x,y)=2x+g'(y) 2x+g'(y)= 2x+5y g'(y)= 5y g(y)= 5/2*y^2 f(x,y)=3x^2+2xy+(5/2)y^2 Then find the \int F(bar)*dr(bar) along curve C t^2i+t^3j, 0<t<1 I'm stuck on finding the last part for the F(bar)...

The first fundamental theorem of calculus begins by defining a function like this: http://i.imgur.com/aWXql.png (sorry was not sure how to write this legibly in this post so I just uploaded on imgur) I kind of have a hard time wrapping my mind aruond this. How do you chose a? I...

I have a layman understanding about how the curvature of space describes the motions of planets and other large celestial bodies. What I don't understand is how curved space makes say; an apple fall to the ground. Any help appreciated. Thanks.

Hey! Do we really need recreation or leisure time to function as humans? Could one get away with it and just work all of his life to whatever purpose he/she is set to go for? How does one distinguish between work and leisure time? Was there such a distinction in early humans? Or did one such...

I'm reading Thermal Physics by Kettle and I feel I'm having trouble really grasping what entropy is. From my lower division pretty much entropy can be defined as a measurement of randomness in a system. Like with ice, very little randomness=lower entropy, water, more randomness because the...

Homework Statement The question: The function F(θ,k) is defined as F(\theta,k)=\int_0^θ (f(x,k))\mathrm{d}x Find expressions for \left({\frac{\partial F}{\partial \theta}}\right)_k and \left({\frac{\partial F}{\partial k}}\right)_θ Homework Equations Fundamental theory of calculus Chain...

Homework Statement I'm not sure how pions relate to the strong force. My notes say that only gluons propagate the strong force between quarks - holding a neutron together, and that residual force (I imagine between the quarks of neutrons and protons) holds neutrons and protons together in...

Homework Statement An ideal monoatomic gas is characterized by the two equations PV=NRT and U=\frac{3NRT}{2} in which R is a constant. Find the fundamental equation corresponding to a monoatomic ideal gas. Homework Equations S=\left ( \frac{1}{T} \right ) U+\left ( \frac{P}{T} \right )...

Which and why do you believe will turn out to be more 'fundamental' (in the sense that one will prove to be the foundation of a theory which goes beyond the SM, while the other will be explained away by it). Or maybe both, or neither?

four forces? There are four forces supposedly. But isn't gravity not a force. It appears like a force but what we see as effects of gravity is really a warping of space due to the effects of mass on that area of space. In other words, there is really no force causing things to attract...

Why would the force P not always be equal to 60 kips? (I mean, since the structure is in equilibrium, and the members are rigid, can't we shift the two forces of 30kips each to the line of action of force P and conclude that P is always 60kips?) Thanks for your time.

Homework Statement (please see the attachment) Homework Equations σ=F/A The Attempt at a Solution I just can't figure out how to find the forces in the two members. Actually I thought the force in both members will be the same, but according to the problem statement it clearly...

Homework Statement I know that theoretically when one has the fundamental equation of a system, one can find the state equations and totally solve the system (if I understood well, I could make the analogy in classical mechanics of having the Lagrangian gives you the equations of motion)...

I've been thinking about complex residues and how they relate to the topology of a function's Riemann's surface. My conclusion is this: it definitely tells us something, but it relates more directly to the Riemann surface of its antiderivative. Specifically: A closed contour in the plane is...

Homework Statement Assuming the validity of the fundamental theorem of algebra, prove the corollary that: Every polynomial of positive degree n has a factorization of the form: P(x)=a_{n}(x-r_{1})...(x-r_{n}) where r_{i} aren't necessarily distinct. Homework Equations Fundamental...

Homework Statement Standing sound waves are produced in a pipe that is 1.40 m long. For the fundamental frequency and the first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes if the pipe is open at both ends. Homework...

Homework Statement Using Hund's rule, find the fundamental term of an atom whose last incomplete subshell contains 3 electrons d. Do the same with 4 electrons p. Homework Equations The 3 Hund's rules. The Attempt at a Solution By fundamental term I'm guessing they mean the...

hi, my questions are regarding the fundamental interactions. I don't have much physics knowledge beyond high school but am trying to form my own way of understanding these fundamental interactions. So I have some questions. They may be vague/strange so I will try to clarify if so (though I...

Ok, Please correct me if I'm wrong; Flux lines are a sort of mathematical visualisation of magnetic fields, they do not exist. As such, there still exists a magnetic field between flux lines (?), just in calculations we use flux lines because they are simpler (?). In voltage transformers...

The proof my book gives for the 2nd part of the FTC is a little hard for me to understand, but I was wondering if this particular proof (which is not from my book) is valid. I did the proof myself, I'm just wondering if it's valid. \frac{d}{dx}\int^{x}_{0}f(t) \ dt = f(x) So suppose that the...

I'm trying to find a good way to think about work. From what I can tell, it's what the object experiences, not really what the force does, correct? If a train is heading west and superman grabs it, stops it, and starts pushing it in the opposite direction until it's at the same speed as it...

Please don't be bothered by my question, i know it sounds real elementary and it could easily be researched, but after doing so, i haven't been able to find anything on how or why the natural phenomenon of energy release takes place as chemicals react with one another. If you think about it...