(PROBLEM SOLVED)
I am trying to think of a complex function that is nowhere differentiable except at the origin and on the circle of radius 1, centered at the origin. I have tried using the Cauchy-Riemann equations (where f(x+iy)=u(x,y)+iv(x,y))
\frac{\partial u}{\partial x}=\frac{\partial...
Does anybody happen to know where to find the perturbation theory formulas for the energies and states up to fourth order? I have to do a calculation up to this order and don't want to have to derive them if I don't have to (I know that Wikipedia has high order energies, but they only have the...
Ah! Thank you very much for that insight, it hit me as soon as I read what you had to say. I haven't used that trick in awhile so I think I temporarily forgot about it.
I have just learned the residue theorem and am attempting to apply it to this intergral.
\int_{0}^{\infty}\frac{dx}{x^3+a^3}=\frac{2\pi}{3\sqrt{3}a^2}
where a is real and greater than 0. I want to take a ray going out at \theta=0 and another at \theta=\frac{2\pi}{3} and connect them with an...
Newton's third law of motion is specifically describing forces. If I am at rest and a particle hits me with a force, \mathbf{\vec{F}}, then it feels a force exerted by me equal to -\mathbf{\vec{F}}.
Well you know that by the properties of integrals, you can treat it as two integrals
I=I_1+I_2=\left(\int 1dt\right)+\left(-\int\cos{t}dt\right)
Do you know these integrals? What is the derivative of -\sin{t}?
So you have the function f(x)=\frac{x}{3x+1} and you know that a function is differentiable at a if its derivative exists at a. You also know that
\left.\frac{df}{dx}\right|_{a}\equiv \lim_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h}=\frac{\frac{a+h}{3(a+h)+1}-\frac{a}{3a+1}}{h}
If you simplify...
You can think of it like an infinitesimal form of the Euclidean distance formula. For a function f(t)=\langle x_1(t),x_2(t),x_3(t),\ldots\rangle
\sum_a^b \sqrt { \Delta x_1^2 + \Delta x_2^2+\Delta x_3^2+\ldots } \longrightarrow s=\int_{a}^{b} \sqrt { dx_1^2 + dx_2^2+dx_3^2+\ldots} =...
It is for physics, and I feel like I actually did very well on the writing portion so that should be alright. Thanks for your response; it's hard getting a feel for what carries what weight on applications and what meets the expected standards, especially with the general GRE.
I just took the General GRE and received V: 560 Q: 740. Would it be advisable to take it again, or would the improvement in quantitative not matter that much? Thanks for any advice.
I figured it out now using a Do[] command, but my point was that if you want to multiply many matrices and not write out the long stretch of A1.A2.A3.A4...AN, then you cannot use the product command on Mathematica because that will just multiply the matrices element-wise. I wanted to know if...
I am trying to compute the following,
\prod_{j=0}^{N-1}\left[\hat{I}+\hat{M(j)}\left(\frac{T}{N}\right)\right]
where \hat{I}, \hat{M(j)} are matrices. My problem is that Mathematica interprets this product as element-wise with respect to the matrices, but I of course want it to use matrix...
I think you got caught up in some simple confusion. The Laplace Transform transforms a function of some variable (it could be x or t or whatever) to a function of s by the rule
F(s)=\int_{0}^{\infty}f(t)e^{-st}dt
So in your case f(x)\longrightarrow F(s) and your equation will go...