Variables Definition and 1000 Threads

How is it possible that the more numbers in an equation, the worse I become at it, where the more variables there are, the easier it is and the faster I can do it? Is there possibly a universal law regarding this, or am I alone in suffering this condition? I love math, but as it turns out, I...

Homework Statement Prove that function has directional derivative in every direction, but is not differentiable in (0,0): f(x,y)=\begin{cases}\frac{x^3}{x^2+y^2},&(x,y)\neq(0,0)\\ \\0,&(x,y)=(0,0)\end{cases} The Attempt at a Solution I have already proved that it has directional...

Homework Statement As shown in the figure below, a particle is moving in a circle of radius R with constant speed v. At some location, the particle is detached from the circle and falls with a parabola path to point A. What is the horizontal range x of the projectile?Homework Equations Writing...

I don't completely understand why the area of the proof circled in red is true. Any advice would be appreciated. https://dl.dropboxusercontent.com/u/33103477/Q1.jpg

A solid marble starts from rest and rolls without slipping on the loop-the-loop track in Fig. 10.30. Find the minimum starting height from which the marble will remain on the track through the loop. Assume the marble’s radius is small compared with R. Solution: In the question, why is the...

"Critiquing" separation of variables method for PDE. I am currently taking a course in PDE's and it has been very "applied" and not so much theory based. I can say its been separate this separate that separate this separate that… Enough! We are always "separating variables" and it always...

I have two more loosely based questions about PDEs and the separation of variables technique: In the intro of this chapter the author imposed that we "assume" the the solution to a set of special PDEs is: U(x,t) = X(x)T(t) where X and T are the eigenfunctions. My question is how did...

Homework Statement find the minima and maxima of the following function: ##f:\mathbb{R}^3 \to \mathbb{R} : f(x,y,z)=x(z^2+y^2)-yx## The Attempt at a Solution after computing the partials, i see ∇f=0 for every point in the x-axis: (a, 0, 0) The Hessian is: ( 0 0 0 ) ( 0 2a -1...

Homework Statement Obtain the Taylor series ez=e Ʃ(z-1)n/n! for 0\leq(n)<\infty, (|z-1|<\infty) for the function f(z)=ez by (ii) writing ez=ez-1e. Homework Equations Taylor series: f(z) = Ʃ(1/2\pi/i ∫(f(z)/(z-z0)n+1dz)(z-z0)n The Attempt at a Solution The first part of this...

Homework Statement utt = uxx -(25/4)cos((5/2)x) ux(0,t) =1 u(pi,t)= pi u(x,0)=x ut(x,0)=0 Homework Equations u(x,t)=v(x) + w(x,t) The Attempt at a Solution This is what I did so far: u(x,t)=v(x) + w(x,t) u(x,0) = v(x) +w(x,0) when t is large: vxx - (25/4)cos((5/2)x) = 0 vx =...

http://postimg.org/image/8jqk9q6rp/ Can someone explain what "independent system displacement variables" are? http://postimg.org/image/eypl6edhh/ What are the independent system displacement variables in this diagram? thanks

Homework Statement f(x,y) = exp(-x^2 +xy -y^2) transform with x =(1/sqrt(2)) *(u – v), y = (1/sqrt(2))* (u + v) . Homework Equations Jacobian The Attempt at a Solution Jacobian = 1 f(u,v) = exp(-(u^2)/2 -(3v^2/2) double integral f(u,v) du dv the bounds would be...

3x + 4y + 2y = 1 The solutions for x, y, and z is { ( (1/3-4l-2m) | 3l | 2m ) }, where y = l and z = m. I've tried this method, presupposing y = l and m = z, then it came to I. l = (1 - 3x -2m) / 4 II. m = (1 - 3x -4l) / 2 If I try to put in either (I) or (II) to x, it would come...

Hello MHB, I understand taylor series proof with one variable but how does it work with Two variabels? is it pretty much the same? The one I understand is Taylor's theorem - Wikipedia, the free encyclopedia Go to proofs Then it's the one under "Derivation for the integral form of the remainder"...

Given a function: z(x,y) = 2x +2y^2 Determine ∂x/∂y [the partial differentiation of x with respect to y], Method 1: x = (z/2) - y^2 ∂x/∂y = -2y Method 2: ∂z/∂x = 2 ∂z/∂y = 4y ∂x/∂y = ∂x/∂z X ∂z/∂y = (1/2) X 4y = 2y One or both of these is wrong. Can someone point out...

Homework Statement I have the equation: x^2 + 2*x*y + 5*y^2 - 4*x - 6*y +7 and I have to find the minimum value I'm getting something that looks half like the correct answer, but not quite right... Homework Equations The answer from the answer book is: [x + 2*(y - 1)]^2 + (y + 1)^2...

Homework Statement There are a set number of marbles in a bag; the marbles consist of two colors. We are given the mean number of marbles of color 1 in the bag, as well as color 1's standard deviation. We are then asked to find the mean and standard deviation of color 2.Homework Equations How...

Homework Statement Hey guys, I have this problem which I am having a hard time solving. $$u_{tt} -x^2u_{xx} = 0$$ $$1<x<2 \hspace{4mm} t>0$$ $$u(x,0)=0$$ $$u_t(x,0)=g(x)$$ $$u(1,t)=0=u(2,t)$$ Homework Equations $$u_{tt} -x^2u_{xx} = 0$$ $$1<x<2 \hspace{4mm} t>0$$...

Hello, I've been trying to solve a system of equations but I'm getting a lot of troubles when I tried to insert inside a matrix a numeric variable. This is my code. I've tried both schemes, i.e., (1) introducing all elements of the matrix by hand (real numbers) and (2) introducing numeric...

Can you please help me find the density of the following functions? The density of an absolutely continuous random variable X is: fX(x) = { (3x^2-1)/12 if 1<x<2 { 1/2 if 2<x<3 { 0 elsewhere Find the density of Y where Y = 4X-2 Find the density of M where M = (X-2)^2 Thank you!

Homework Statement Solve for k: k2 - 16k < 0 In the answer it has 0 < k < 16, I do not know how they get there from the original question.

Could the "hidden variables" be encoded in the observer? The hidden variables that have been proposed to dictate the action of quantum outcomes, Could they be in observer dependent as opposed to encoded in the particle? We know the observer is an integral part of the process. Has this...

Hi all, For this problem, I have checked all possible factor that may cause NaN in variables such as - division by zero --> not found - undefined variables - set initialization for variables - ep, hr,ht - parameter setting --> double precision problems checked, no issue but still...

Done editing I hope. Homework Statement If Jf = 0 everywhere, then (as we showed in class), one can express H as the gradient of a scalar potential, W. W satisfies Poisson’s equation with ∇⋅M as the source. Use this fact to find the field inside a uniformly magnetized sphere. (Griffiths has...

Hi I'm having a bit of trouble with this question: Use separation of variables to find all the possible separable solutions to the partial DE equation for [FONT=times new roman]u(x,y) given by [FONT=arial] [FONT=times new roman]yux - 3x2 uy = 0 [FONT=times new roman].I try [FONT=times new...

Find cov(Y,Z) where Y = 2X_1 - 3X_2 + 4X_3 and Z = X_1 + 2X_2 - X_3 Information given E(X_1) =4 E(X_2) = 9 E(X_3) = 5 E(Y) = -7 E(Z) = 26 I tried expanding cov(Y,Z) = E(YZ) - E(Y)E(Z) but can't figure out how to calculate E(YZ)

Homework Statement Show that if C is a positively oriented simple closed contour, then the area of the region enclosed by C can be written (1/2i)/∫C\bar{}zdz. Note that expression 4 Sec. 46 can be used here even though the function f(z)=\bar{}z is not analytic anywhere. FORMATTING NOTE: SHOULD...

(I wasn't sure how to title this, it's just that the statement resembles Chebychev's but with two RV's.) Homework Statement Let \sigma_1^1 = \sigma_2^2 = \sigma^2 be the common variance of X_1 and X_2 and let [roh] (can't find the encoding for roh) be the correlation coefficient of X_1 and X_2...

Hello everyone! The problem: $X,Y,Z$ are random variables that are dependent and uniformly-distributed in $[0,1]$, and let $\alpha$ be a given number in $[0,1]$. I am asked to compute the following: $\text{Pr}(X+Y+Z>\alpha \;\;\; \& \;\;\; X+Y\leq \alpha)$ What I have so far...

Homework Statement Let X_1, X_2, X_3 be iid with common pdf f(x)=exp(-x), 0<x<infinity, 0 elsewhere. Evaluate P(X_1<X_2 | X_1<2X_2)Homework Equations f(X|Y) = f(x,y)/f(y) The Attempt at a Solution Since P(X_1<X_2) is a subset of P(X_1<2X_2), the intersection (edited, at first said union)...

Solve given differential equation by separation of variables \frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8} So separate x and y terms (xy-2x+4y-8) dy = (xy+3x-y-3) ugh I'm stuck:(

Homework Statement Isolate for the angle. Do not sub in numbers, isolate the angle, θ . Use of trig identities required. Homework Equations m_{2}g=m_{1}gsinθ-μm_{1}gcosθ We are given the trigonometric identities: The Attempt at a Solution I have attempted everything from squaring both...

Hi, I am struggling trying to find the (equation of the) pdf of the sum of (what I believe to be) two non-central chi-squared random variables. The formula given on wikipedia (http://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution) shows that the random variable associated with...

Homework Statement Two RVs X1 and X2 are continuous and have joint pdf f_{X_1,X_2}(x_1, x_2) = \begin{cases} x_1+x_2 &\mbox{for } 0 < x_1 < 1; 0 < x_2 < 1 \\ 0 & \mbox{ } \text{otherwise}. \end{cases} Find the pdf of Y = X_1X_2.Homework Equations I'm using the transformation "shortcut' that...

Homework Statement Let us choose at random a point from the interval (0,1) and let the random variable X_1 be equal to the number which corresponds to that point. Then choose a point at random from the interval (0,x_1), where x_1 is the experimental value of X_1; and let the random variable...

Homework Statement Homework Equations Y=1/2*(X1-X3)^2+1/14*(X2+2X4-3X5)^2The Attempt at a Solution For (a) part, I have only learned to find the moment-generating function of Y, but not finding the p.d.f. Moreover, the examples I have seen only involves random variables Xi to the power 1, but...

\[ \alpha^2T_{xx} = T_t + \beta(T - T_0) \] where \(\beta\) is a constant and \(T_0\) is the temperature of the surrounding medium. The initial temperature distribution...

Homework Statement By changing variables from (S,t,V) to (x,\tau,u) where \tau = T - t, x = \ln\left(\frac{S}{K}\right) + \left(r - \frac{\sigma^2}{2}\right)(T-t), u=e^{r\tau}V, where r, \sigma, \tau, K are constants, show that the Black-Scholes equation \frac{\partial V}{\partial t} +...

Homework Statement Using the technique involving variable separation, solve the following differential equation and use the initial condition to find the particular solution \frac{dy}{dt} = \frac{1}{y^{2}} y(0) = 1 Homework Equations The Attempt at a Solution To be honest...

Homework Statement lim (x,y)\rightarrow(0,0) f(x,y)=2*x/(x^{2} + x +y^{2}) Homework Equations used different paths like y=k*x ,where k is a constant and y=k*x^2 The Attempt at a Solution Got an answer 2 but solution says does not exist. Can anybody convince me that why limit does...

I need to find the f'(x) when f(x)= A/B+C (ex) so I used the quotient rule to get: (B+Cex)(1) - A(B+Cex)/(B+Cex)2 is this right so far? and if it is, how do I simplify it more?

Quantum Phys Homework: I am given a function: $$f(x)=\frac{1}{10}(10-x)^2\,;\,0\leq{x}\leq{10}$$ and $$f(x)=0$$ for all other \(x\). I need to find the average value of \(x\) where $$\bar{x}=\frac{\int_{-\infty}^{\infty}x\,f(x)\,dx}{\int_{-\infty}^{\infty}f(x)\,dx}$$ I am not really even sure...

Solve the DE by using separation of variables \frac{dy}{dx} = e^{3x+2y} Break up e^{3x+2y} = e^{3x}e^{2y} Move x's and y's to their own side of the equation. \frac{1}{e^{2y}} dy = e^{3x} dx Integrate both sides of the equation to get \frac{-e^{2y}}{2x}=\frac{e^{3x}}{3}+C I don't know how to...

Solve the differential equation by separation of variables x \frac{dy}{dx} = 4y becomes \frac{1}{4y} dy = \frac{1}{x} dx Integrate to get \frac{1}{4} \ln{|y|} = \ln{|x|}+C I'm stuck here because I want to raise e to the power of both sides of the expression like e^{ \frac{1}{4} \ln{|y|}} =...

Homework Statement Three yearly losses. First: Exponential Second & Third: Weibull Losses are independent. Find the 95% VaR of the min loss Homework Equations The Attempt at a Solution My first thought was: Let L be total loss, A be first Loss, B be second loss, C be third...

-2x - 9y + 3z = -8 I set parameters, and i get x= 4 - 4.5s + 1.5t y = s z = t But the database I'm using says it's incorrect...

Hi all, Suppose I declare X in the main program. Then in the following subroutine: Call example(list of arguments) ------------------------------------ subroutine example(list of arguments) x=y+z end subroutine ------------------------------------- I have two options: (a)...

i have a simple enough question Find the MGF of a continuous random variable with the PDF: f(x) = 2x, 0<x<1 I understand MGF is calculated as: $$M(S) = \int_{-\infty}^{+\infty} e^{Sx} f(x)dx$$ which would give me $$\int_{-\infty}^{+\infty} e^{Sx} 2xdx$$ but how would i compute this...

Let $p(x,y)$ and $q(x,y)$ be two polynomials with coefficients in $\mathbb R$. Define $P=\{(a,b)\in\mathbb R^2 : p(a,b)=0\}$ and $Q=\{(a,b)\in \mathbb R^2:q(a,b)=0\}$. Now assume that there is a sequence of points $(x_n,y_n)$ in $\mathbb R^2$ such that: 1. $(x_n,y_n)\to (0,0)$. 2. $(x_n,y_n)\in...

Consider the following solution to the steady state heat diffusion problem on an infinite y domain. \[ T(x, y) = \sum_{n = 1}^{\infty}c_n\exp\left(-\frac{\pi n}{\ell} y\right) \sin\left(\frac{\pi...