Variables Definition and 1000 Threads

Homework Statement In the problem, we are to consider two candles, call them C1 and C2, with different heights and different thicknesses. Call the height of C1 H1, and for C2, call it H2. The taller candle burns can burn for 7/2 hours, and the short one, 5 hours. After two hours lapses, the...

Okay so I am working on this problem: Solve $$xu_t + uu_x = 0$$ with $$u(x, 0) = x.$$(Hint: Change variables $$x \rightarrow x^2$$.) However, I am not sure how to use the change of variables hint that is given or why it is needed. My thinking is that I could just use the method of...

I wanted to do this integral $$\int_a^b \frac{dx}{1-x^2} $$ and I was able to get the right answer with the substitution u=ix, where i is the square root of -1. But is this a valid mathematical procedure? $$\int_a^b \frac{dx}{1-x^2}=i \int_{-ia}^{-ib} \frac{du}{1+u^2}$$ Do those limits...

Hello, I was looking at Riley's solution manual for this specific problem. Along the way, he ended up with a quadratic inequality: If you looked at the image, he said it is given that λ is real, but he asserted that λ has no real roots because of the inequality. Doesn't that mean λ is...

This is the statement, in case you're not familiar with it. Let ## f_j(w,x), \; j=1, \ldots, m ## be analytic functions of ## (w,z) = (w_1, \ldots, w_m,z_1,\ldots,z_n) ## in a neighborhood of ##w^0,z^0## in ##\mathbb{C}^m \times \mathbb{C}^n ## and assume that ##f_j(w^0,z^0)=0, \...

Invariably in the lay literature when it comes time to show that EPR hidden variables are incompatible with QM, Bell's Theorem is invoked (e.g. Greene's "Fabric of the Cosmos", Zeilinger's "Dance of the Photons", Rosenblum's "Quantum Enigma", ...). I don't see why a simple application of...

Homework Statement dL/dp = L/2, L(0) = 100. Find the solution to the differential equation, subject to the given initial condition. My textbook says the answer is L = 100ep/2, but I don't know how to get that answer (or e for that matter). Homework Equations ? The Attempt at a...

Hi there, I have an equation below for the cost of energy for a house per hour. The house has an energy storage system (i.e.a very large battery) installed. You can charge the battery up and energy from the battery can be used to power the building. For example you can charge the battery...

Homework Statement I'm stuck at one of the derivations for relativistic energy. I've figured out every other single step, but I just can't wrap my head around this one: Prove that: {\frac{d}{dt}} {\frac {mu} {\sqrt{1-u^2/c^2}}} = {\frac {m {\frac{du} {dt}}} {(1-u^2/c^2)^{3/2}}}...

(9x)^-1/2 So, I'm not entirely sure how to go about this question. It's got a negative exponent, so I assume its 1 / something. My guess for the answer would be: 1 / 3x [(25xy)^3/2] / x2y For this question, would I compute 253/2 and then x3/2 y3/2 and then divide by x2y

This is not a homework question but I project I am working on and need someone with more mathematical prowess than myself. I am using a computer program to draw random numbers from two independent distributions, x1 and x2, for two different cases and I want to establish a theoretical...

Equation found in previous question is #: x''=gsin(a)-b(v^2) 1. Rewrite the equation # as a differential equation for v as a function of x. 2. Solve the equation to find v as a function of x. Relevant equations: v=x'=dx/dt, x''=v'=a=dv/dt Attempt at 1: Using the relevant equations you can...

Can someone conceptually explain to me how Temperature and Entropy are conjugate variables? I would imagine that Temperature and Internal Energy would be more appropriate, as I understand Heat flow causes changes in Internal Energy, some of which is used to change the translational motion of...

Homework Statement Find the maxima and minima of: f(x,y)=(1/2)*x^2 + g(y) g∈⊂ (δ⊂ ℝ ) in this region Ω={(x,y)∈ℝ2 / (1/2)*x^2 + y^2 ≤ 1 } hint: g: δ⊆ ℝ→ℝ The absolute min of f in Ω is 0 The absolute max of f in Ω is 1 Homework Equations The Attempt at a Solution I have the...

I am currently reading Calculus Made Easy by S. P. Thompson, and the author's idea of what it means for a variable to "vary" seems fundamentally different from my own, so I was hoping someone could help me correct my understanding. Here is the excerpt I'm having trouble with: Those...

How to write something similar to the following Or is it better to write $$\sum_{n=k ,m=1}^{k+1}$$

Is there a general formula for (total) derivatives of functions of the form f(xy(x)+z(x)? I tried the most simple function of that form f(xy(x)+z(x))=xy(x)+z(x) and the formula I got was \frac{\partial f}{\partial x}+\frac{\partial f}{\partial y} \frac{dy}{dx}+\frac{\partial f}{\partial...

Homework Statement We are given the following table and need to find the E(XY) X|Y y = 17 20 23 35 48 p(x) x = -20 0.02 0.03 0.07 0.02 0.06 0.2 0 0 0.05 0 0.05 0.1 0.2 1 0.05 0.03 0.02 0.07 0.03 0.2 3 0.01 0.02 0.03 0 0.04 0.1 17 0.18 0.04 0.06 0.01 0.01 0.3 p(y) 0.26 0.17 0.18 0.15...

write a linear equation in 3 variables that is satisfied by all 3 of the given ordered triples $(1,1,1), (0,2,0), (1,0,0)$ the examples in book are all on the $ax+by+cz=d$ equation but with just ordered triples there is no $d$ or can it be found from them... otherwise I would solve this by...

Hello, I have a simple question regarding changing variables in a conditional distribution. I have two independent variables r \in \mathbb{R}, r>0 \\ t \in \mathbb{I}, t>0 where r is "rate" (can be any positive real number although most likely to be around 1) and t is "time" (positive...

Are they always independent from each other so that you can multiply their E[X] together to form another E[X] with the same distribution and pmf or pdf?

Hello, I'm getting slightly confused by the following so was hoping someone may be able to clear my problem up. For integrals, if b is the upper limit and a is the lower limit, I will write ∫[b,a]. From the Fundamental Theorem of calculus part 1 we can show that: if F(x) = ∫[x,a]...

Hi all, I need Explanation on the attached image from Van Dalen's Logic and Structure; specially on how the red part follows from the lines before it! Regards.

I'm having troubles with PDE. Apply separation of variables, if possible, to found product solutions to the following differential equations. a) x\frac{\partial u}{\partial x}=y\frac{\partial u}{\partial y} I suppose that: u=X(x) \cdot Y(y) Then: xX'Y=yXY' xX'/X=yY'/Y So xX'/X=yY'/Y=c because...

Homework Statement Let D=\{ (x,y)\in\mathbb{R}^2:x+y< 1;0< y< x\} calculate \int_{D} e^{-(x+y)^4}(x^2-y^2) through an appropriate change of variables Homework Equations \int_{D} f *dxdy=\int_{D} f*Jacobian*dudv The Attempt at a Solution I've tried x+y=u and x-y=v...

Homework Statement Given a sequence of independent random variables {X_n}, each one with distribution Exp(1). Show that Y_n = \displaystyle\frac{X_n}{\log(n)} with n \geq 2 converges to 0 in probability but it doesn't coverges almost surely to 0. Homework Equations Density for each X_n...

Hey everybody I'm developing a computer program that can take a series of data-points and estimate the next local maximum(top) of a sine-curve. My approach to this is to take the formula for a sine-function(f(x)=Asin(\omega x - \phi) + B), and isolate all the variables, and that way I'll...

Hi all; I need some clarification in red part; in how it is deduced from the theorem 2.5.6! I know how the blue is deduced from the theorem but don't even know how to get blue form red in practice!(No algorithm is suggested...) Anyway, any explanation is thanked... Regards.

So I have a list of variables, defined in my workspace, and I'm trying to access them each in turn to compare them to a larger matrix A. The eval function calls each variable in turn, stores it under temporary matrix B, then compares it to matrix A, does the necessary calculation, and stores it...

Hi all, I would like to find the distribution (CDF or PDF) of a random variable Y, which is written as Y=X_1*X_2*...X_N/(X_1+X_2+...X_N)^N. X_1, X_2,...X_N are N i.i.d. random variables and we know they have the same PDF f_X(x). I know this can be solved by change of variables technique and...

Hello, I am trying to understand how to solve a system of two variables (let's say s and p representing two physical quantities), where there is a third-order polynomial representing each. I'm not sure I am describing this correctly in words, but here is the system I need to solve. P = a0 +...

As an electrical engineering student can learning about complex variables be beneficial to me? If so can someone recommend an introductory book that I can read on my own? Also I have very little experience working with complex variables.

hello! I'm trying to understand the following property: Let X and Y be independent random variables z: = X + Y. Then http://imageshack.us/a/img268/9228/71pe.png where fZ (z) is the probability mass function for a discrete random variable defined as follows...

... ... I am curious to know why we have to multiply with e^{-j\omega t} in Fourier transform? What is the purpose of this? I have heard somewhere that the transform is merely a change of variables from one set of coordinates to another. I would like to know more about this. Can you help me?

So I've never really understood this idea of a light-cone. I know there is literature, but what are the most important physical concepts/consequences about this light-cone model of special relativity? Also, could you give a concise explanation of light-cone variables?

Realised I probably posted this in the wrong forum before, should've been here.. I often see a function's differential expressed in terms of convenient partial derivatives eg dU=(dU/dT) dT + (dU/dV) dV And I've seen it written that "any system is uniquely specified by two parameters, such...

Homework Statement When possible express the general solution in explicit form. Solve dy/dx =x^2 /(1+y^2) Homework Equations This is a first order non-linear ordinary differential equation. The Attempt at a Solution dy(1+y^2) = x^2 dx Integration both sides returns: y+ (y^3 )/3=...

Solve each differential equation. Express the general solution in explicit form. y' = (3x^2 -1) / (3+2y) So, I will skip many steps, because they are easy. However, I am stuck in one of the last ones. y^2 +3y = x^3- x +C y(y+3)= x^3 - x +C I have seen the solution for y...

Homework Statement [2 Dimensional infinite square well] Show that you can separate variables such that the solution to the time independent schrodinger equation, ## \hat{H} \psi (x,y) = E \psi (x,y) ## can be written as a product state ## \psi (x,y) = \phi (x) \chi (y) ## where ## \phi (x)##...

Hi! I was wondering: is it possible to have a non-orientable surface in 3D which is parametrized by u and v, with u and v periodic (i.e. is it possible to map the torus continuously into a non-orientable surface in 3D?) If so, does anyone have any explicit examples?

Homework Statement Determine if f(x,y) = ((x-y)4 +x3 +xy2)/(x2+y2) [f(x,y = 0 @ (0,0)] is differentiable at the origin. Homework Equations x = (0,0) The Attempt at a Solution A function is differentiable at x if f(x+Δx) - f(x) = AΔx + |Δx|R(x) Where A are constant...

Hi, Homework Statement The sample space of the following problem is defined thus: all the possible permutations of {1,2,3} including {1,1,1}, {2,2,2}, {3,3,3}. Suppose all results are equally probable. Let Xi denote the value of the ith coordinate, where i=1,2,3. I am asked to determine...

The following is identically 0 which can be readily checked by a simple hand calculation. $\binom{n+1}{k}2^{-n-1} - \binom{n}{k}2^{-n} + \binom{n}{k}*2^{-n-1} - \binom{n}{k-1}2^{-n-1}$ If you enter this in SAGE or Mathematica, using the appropriate script, and use full_simplify() and...

Homework Statement Evaluate the integral: ∫ x^{m}* (ln(x))^{2} It's said as ln squared x. Sorry if I miswrote it.Homework Equations ∫udv= uv - ∫vduThe Attempt at a Solution u= (ln(x)^2) v= x^{m+1}/(m+1) du= 2lnx/(x) dv= x^{m} * dx - ∫2lnx * (x^{m+1})/(x*(m+1)) + [(ln(x)^{2}) (x^{m+1})/(m+1)}...

If we think of a functional as a function of the infinite number of taylor coefficients of the variable function, aren't they then just normal functions, a map between a set of reals to another set of reals.

ℂI am working on an assignment and have come across a question that I'm not quite sure how to approach. Here it is, with my "solution" and reasoning: "[F]ind the limit at ∞ of the given function, or explain why it does not exist. 24. h(z) = Arg z , z \neq 0" (Complex Variables Second...

the random variables X1,X2... are independent and they take 0 and 1 values and they have expected value 0 if we have Y=X1+X2+...+Xn and Z=X1+X2+...+Xn+Xn+1 what is the ρ(Y,Z) for n=46 i know that ρ(Y,Z)=cov(Y,Z)/(sqrt(var(Y)*sqrt(var(Z)) but i need some help on how to find the cov and vars...

Hi, Let's say I'm given X and Y identical independant continuous random variables. We pose Z =X/Y, I remember there is a way to find the density function of Z, altough I can't get to remember how to do it and my probability book is out of town.(And I'm not so sure what to look for in google)...

Dear All, If I have the linear algebraic system where its composed as of matrices in that form K*X=F, what column/row operations should I perform if I want to solve it where some of the X variables are known (targeted values) or if I want to solve when variables are constrained relative to...

we have X,Y variables and we have f(m,n)=P(X=m,Y=n)=C*((1/(a*m*n+15*m+11*n+8))^2) for what value of a X,Y are indepedent? ( its not necessary to calculate C) i know that f(m,n)=f(m)*f(n) if X,Y are independent but how i am going to use this for calculate a?