Terms Definition and 1000 Threads

Hey! So I'm self studying mary boas's mathematical methods book and I've come across this integral: \int _{0}^{\infty }e^{-x^4}dx and I'm suppose to write this using the gamma function. The hint given states to let x^4 = u. And the answer is: \Gamma \left( \dfrac {5} {4}\right) I tried...

Homework Statement Show that ##\Sigma \vec F = \frac {d \vec p}{dt} ## Homework Equations ##\Sigma \vec F = m \vec a ## ## \vec a = \frac {d \vec v}{dt} ## ## \vec p = m \vec v ## The Attempt at a Solution We need to prove that ## \frac {d \vec p}{dt} = m \vec a ##. When I physicists...

What is the motivation for defining vectors in terms of equivalence classes of curves? Is it just that the definition is coordinate independent and that the differential operators arising from such a definition satisfy the axioms of a vector space and thus are suitable candidates for forming...

I want to start studying aerodynamics. To get me started, what are the basic terms that I need to know?

I have been trying to solve an integration that i have I am not even sure if it's possible. Here, A, m, alpha, a these are constants. I have tried few methods, but couldn't find any way out. I would appreciate any help.

There are too many terms to describe digital screen or part of it and I am having hard time how to correctly use them. Am I correct to say they relate as follows?: Monitor (physical) | Display (*all figurative after this) = screen = view = window > pane (part of display/screen/view/window)...

Homework Statement For ln(.8) estimate the number of terms needed in a Taylor polynomial to guarantee an accuracy of 10^-10 using the Taylor inequality theorem. Homework Equations |Rn(x)|<[M(|x-a|)^n+1]/(n+1)! for |x-a|<d. The Attempt at a Solution All I've done so far is take a couple...

I hate to ask this but whenever applying a function to the equation, the arguments is the entire one side of the equation right? What I mean is $$ ln|y|=ln|x|+C$$ can be rewritten as $$e^{ln|y|}=e^{ln|x|+C}$$ but not $$e^{ln|y|}=e^{ln|x|}+e^C$$ ? So the entire RHS or LHS becomes the argument...

Hi I have trying to study independently some fairly high level physics but I keep getting bogged down with simple (I imagine for other people) mathematics terms: Here is a partial list of terms I don't get: Operator Argument Mapping ComutatorThere are probably many others. My question is...

when they mean disorder do they mean the range of velocities of the particles increasing as entropy increases? so there are larger differences between the low KE particles and the high KE particles?

when I am adding, subtracting, multiplying and dividing fractions and I get an answer is there a way I can check to make sure my answer is in lowest terms ?

The dimensional term in Planck's law (after getting rid of steradians) is [itex]\frac{h c^2}{\lambda^5}[\itex]Which seems to yield units of J*m/s. However, Wikipedia suggests that the units are J/(m3*s). If wikipedia is right, how do you get that answer?

Homework Statement Suppose everything is moving slowly, How can we find the metric tensor in GR in terms of the mass contained. Homework Equations I understand in case of everything moving slowly only below equation is relevant - R00 - ½g00R = 8πGT00 = 8πGmc2 The Attempt at a Solution None.

Homework Statement w = 1/h ln(l/lo-1) w=-2.6, lo=16 and h =1.5 Find L. Homework EquationsThe Attempt at a Solution Plug in the values 2.6 = 1/1.5 ln(l/16 - 1) Make the log term the subject. ln(L/16 -1) = 1/1.5/-2.6 ln(L/16-1) = 0.666/-0.256 ln(L/16-1) = -0.256 Change the log statement to an...

Hi all, I have some points not so clear for me about the fermions mass terms in SM; first, why ## \bar{\psi}\psi = \bar{\psi}_L \psi_R + \bar{\psi}_R \psi_L ##, that since ## \bar{\psi} = \bar{\psi}_R + \bar{\psi}_L ## and ## \psi = \psi_R + \psi_L ## Where are such terms: ## \bar{\psi}_R...

The question is : Show that the curve defined implicitly by the equation X*Y^3 + x^3*Y = 4 has no horizontal tangent.The answer is : Can someone please explain what steps are used in order to obtain the answer in a simple way for a calculus beginner? This answer is not helping me understand...

Homework Statement What is the commutation relation between the x and y components of angular momentum L = r X P Homework Equations None. The Attempt at a Solution I do r X p and get the angular momentum componants:L_{x} = (-i \hbar) (y \frac{d}{dz} - z \frac{d}{dy}) L_{y} = (-i \hbar) (z...

Hi, I was trying to form a summation for ##y_1## and have provided a solution but do not quite understand how it was formulated. I was trying to look for general patters and besides a ##(-1)^{n+1}x^2n## in the numerator, I'm a little lost on how to find a general term for the denominator. Also...

Homework Statement [/B] Expand (b^2 + y^2)^(3/2) as a Taylor's series In terms of y/bHomework EquationsThe Attempt at a Solution [/B] Hello, I'm clueless on this one. I tried to factor out b^3 -> b^3(1 + y^3), but can't figure out what to do next. Thanks in advance.

Consider a theory with the Lagrangian \mathcal L=\mathcal L_{free} + \mathcal L_{int} . I think if we say \mathcal L_{free} \gg \mathcal L_{int} , this means that the equations of motion will be much near to the free equations. But I'm not sure that we can prove that if in an equation of...

In texts on geometrical optics I have read that an image is formed where light rays converge -- without an explanation of why. Thus I ask, why are images formed where light rays converge? In particular, what is the answer to this question in terms of the wave theory of light (Electrodynamics)...

For the question, If x = 3cos(θ), 0<θ<π/2, express sin(2θ) in terms of x. I confirmed that the following is correct: sin(2θ)=(2x/9)√(9-x^2) But for this next one...the x+1 is throwing me through a loop or something. If x+1 = 3sin(θ), 0<θ<π/2, express cos(2θ) in terms of x. cos(2θ) = fail...

3). A company is to distribute \$36,000 in bonuses to its top five sales people. The fifth salesperson on the list will receive \$6,000 and the difference in bonus money between successively ranked salespeople is to be constant. find the bonus for each salesperson. 4). Find the third term of...

Is this possible? It seems like it should be but, it's difficult to find an explicit relationship between a general function of one variable x (let's say we are only interested in functions that decay to zero as they go to plus or minus infinity) it seems like summing a bunch of gaussians of...

I am a little unclear on why in atomic physics that the total orbital momentum terms have to be specifically singlet or triplet states, for example G -Singlet F -Triplet D -Singlet P -Triplet S -Singlet I think it has to do with the pauli exclusion principle but don't really understand the...

Hello I was wondering what the equation is to calculate the tension in terms of coulombs law an example problem would be http://gyazo.com/1319551eb367990c75ee0a782e38a2c2

1. A spring of spring constant k is attached to a support at the bottom of a ramp that makes an angle θ with the horizontal. A block of inertia m is pressed against the free end of the spring until the spring is compressed a distance d from its relaxed length. Call this position A. The block is...

Homework Statement For my second thread of the day I will give the weirdest problem I've encountered in physics yet. In the mobile what is the inertia of the giraffe mgir in terms of the inertia mm of the monkey? Homework Equations I = md2 The Attempt at a Solution In the picture, the giraffe...

I'm trying to find the azimuthal angle unit vector \vec{\phi} in the cartesian basis by taking the cross product of the radial and \vec{z} unit vectors. \vec{z} \times \vec{r} = <0, 0, 1> \times <sin(\theta)cos(\phi), sin(\theta)sin(\phi), cos(\theta)> = <-sin(\theta)sin(\phi)...

Taken from wikipedia, "If several turns of the wire are made, this becomes where N is the number of turns..." when speaking in terms of flux linkage and coils of a wire. However, in terms of a straight conductor (e.g. transmission lines), flux linkage for a meter long straight conductor has...

Is it one wavelength of EM wave? I have googled for this and I can't find an explanation for what a photon is in terms of EM waves.

Homework Statement I need to find q in terms of f and p. Homework Equations I am dealing with this equation at the moment: 1/p + 1/q = 1/f. The Attempt at a Solution I think I should isolate the q, so that I have the variables p and f on one side of the equals sign, and q on the other side of...

As I understand "Dark Matter" is an _assumption_ of existence of matter in certain space, to explain gravitational effects on the matter around that space. But when it comes to "Dark Energy" it is another assumption to explain why universe is expanding. But by Einstein's theory, mass and energy...

Homework Statement If a car has p litres of petrol in the tank it can travel a kilometres. With v litres of petrol in the tank it can travel b kilometres. Find an expression in terms of v in terms of p, b and a. 2. The attempt at a solution I just cross-multiplied how I was shown in class...

Homework Statement What is the probability that an electron emerging from the plus channel of the first device will end up in the minus channel of the second device? Express your answer in terms of θ. (Refer to the attached image) Homework Equations This uses the outcome probability rule that...

I am would like to solve this differential equation: Where http://ieeexplore.ieee.org.ezproxy.uniandes.edu.co:8080/ielx5/8/6493417/6409989/html/img/6409989-eqdisp-3-small.png Could you give me some practical ideas about the required software and methodology? Thank you very much

this is the given: the problem is the middle term, if the h-bar w outside the set brackets is canceled with the h-bar w of the m/2hw, then there will be a h-bar w that is left introduced from the middle term, i.e. i\frac{w}{m}XP- i\frac{w}{m}PX = i\frac{w}{m}[X,P]= i\frac{w}{m}i\hbar but...

Hey, I just found this interesting exercise and I'd like to know how to solve it. The exercise: Between the numbers 4, 5, 6, ... , n, you can put minus or plus signs ( - , +) to create a term. (n means any natural number) and (the numbers must be in order) Which possible numbers for n can...

Is there a form of the van der waal equation in terms of the Cv of the gas? Is it derivable?

Homework Statement In a physics laboratory the value of g, the gravitational acceleration in the vicinity of earth, has been measured accurately by projecting a ball up an evacuated tube and electronically timing the passage of the ball in its upward and downward flight through two light...

It just occurred to me that induction can be seen as a statement quite analogous to that of "a function whose derivative is 0 on an interval is constant on that interval". Suppose there is a property P about the natural numbers that we want to prove. Then let P: N -> {0, 1} be a function for...

Homework Statement For which value(s) of x is each expression not defined? Homework Equations x^2+3x-6 divided by x^2-x-12 The Attempt at a Solution The answer that was given turned out to be: x^2+3x-6 divided by (-4)(x+3) Restrictions: x ≠ 4,-3...

Ok.. What about this one? $$\frac{1}{y+1}+\frac{2}{x+2}+\frac{\frac{x+2}{y+1}-2}{x+2}$$ this is where I am at: \left(\frac{x+2}{y+1}-2\right)

Or does it always have to have MORE THAN 2 like x^2 +x^2 -4a polynomial can never be x^2 - x-^3 Right?

Homework Statement I found the function V, which is the conjugate harmonic function for U(x,y)=sin(x)cosh(y). I am attaching my work. It turns out to be a two-term function with trig factors. I am then to write F(Z) in terms of Z, but is plugging in x, and y, in terms of Z into my trig...

Hi there. I'm reading Gurtin's 'the mechanics and thermodynamics of continua', and working some exercises of his book. In the section 21: 'The first law: balance of energy', after the derivation of the balance equation, he uses an identity to rewrite the balance of energy. The balance of energy...

Need yout help in understanding these terms Hello everyone, nice to meet you all First of all, please know that English is not my mother language and I work as a translator in training and I have these tools and accessories and I really need to know what they do, could you kindly describe what...

At the end of spontaneous symmetry breaking I get these mass terms: W_{\mu}^{\pm}=\frac{1}{\sqrt{2}}\bigl(W_{\mu}^{1} \mp W_{\mu}^{2} \bigr ) \mathcal{L}_{mass}=\frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{+}{W^{\mu}}^{-} + \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+} So I have...

Homework Statement Express the following signal in terms of ramp, exponential, and parabolic functions, where t should be consistently shifted Homework Equations signal simplification techniques, not known to me The Attempt at a Solution It seems you can express this in terms of...

In Heaviside's Electromagnetic Theory (1895) he says that "The second law of thermodynamics itself needs to be established from electromagnetic principles, assisted by the law of averages..." I attempted to Google whether or not anyone has derived the second law via electricity and magnetism...