Variables Definition and 1000 Threads

Homework Statement Prove with \epsilon-\delta: Lim_{(a,b)\rightarrow(0,0)}\frac{sin^{2}(a-b)}{\left|a\right|+\left|b\right|}=0 Hint: \left|sin(a+b)\right|\leq\left|a+b\right|\leq\left|a\right|+\left|b\right| Homework Equations 0<\sqrt{(x-x_{0})^{2}+(y-y_{0})^{2}}<\delta and...

Homework Statement f(1/u,0)=1 and f(0,1/u)=-1 for all positive (integer) values of u. Prove whether or not the limit as (x,y) ->(0,0) exists. Homework Equations none. The Attempt at a Solution I argue that 0,0 is not in the domain of the function, but this neglects the behavior of f(x,y)...

Homework Statement I'm trying to show that U(X+Y) = X in distribution, where X and Y are independent exp(λ) distributed and U is uniformly distributed on (0,1) independent of X+Y.Homework Equations The Attempt at a Solution X+Y is gamma(2,λ) distributed. But I can't figure out how to deal with...

Hi, The change of variables theorem states that given a diffeomorphism g:A \rightarrow B between open sets, and a continuous function f:A \rightarrow R, then \int _A f = \int _B f \circ g |Det Dg| given that either one of the integrals exist. I was wondering if anyone here could help explain...

I have an assignment where we have to ask the user for a number of data points which then we will graph a linear regression. Enter the number of input data points: 7 Enter [x y] pair for point 1: [1.1 1.01] Enter [x y] pair for point 2: [2.2 2.30] Enter [x y] pair for point 3: [3.3 3.05]...

Hi, I have some experimental data from a colleague which has been collected with different values for 7 parameters. It isn't nice, as in it's not as if 6 of the parameters were held fixed while the seventh was adjusted. Beyond that, I don't have much data. I'm not up on my statistical...

Not really a specific problem, but just a general question: Does anyone have any good references (preferably online) for solving E&M problems with this method? I'm using Griffith's Electrodynamics book for my class and I'm trying to get ready for a final. This is the only part I'm having...

Homework Statement Locate and classify the critical points of f(x,y) = (x-y)(xy-1). Homework Equations The Attempt at a Solution I found the partial derivatives with respect to x and y and I got: ∂f/∂x = -y2+2xy-1 ∂f/∂y = x2-2xy+1 After setting them both equal to zero I can't...

I have read in different places something like the following: Hermitian operators have real eigenvalues Hermitian operators/their eigenvalues are the observables in Quantum Mechanics e.g energy I am not sure what this means physically. Let us say I have a Hermitian operator operating on a...

I have such MATLAB problem: I create variables R1 RF R2 and w so: Code: syms RF R1 R2 w then I write expression: Code: 3*R1*w*(RF + 200)/((R2*w*29*i + 3)*(3*R1*w - 2*i)) which gives: Code: (3*R1*w*(RF + 200))/((3*R1*w - 2*sqrt(-1))*(R2*w*29*sqrt(-1) + 3)) why sqrt(-1) and not i...

Hi! I have a problem with the following equation: log(D)-b*log(K) = b*log(z)-log(c) I would like to get D and K on one side of the equal to sign, so that: f(D,K) = g(b, c, z) Is this possible? Peter

Hi, I'm new to MATLAB and programming, but I hoping to find out if I can have a variables in my program take on certain values only for certain time intervals. For example, I am using ode23s to solve some equations for me, but for the time interval [0,10] I would like one of the variables...

Homework Statement solve dy/dx=e^(3x+2y) by separation of variables The Attempt at a Solution \frac{dy}{dx}=e^{3x+2y} \frac{dy}{dx}=e^{3x}e^{2y} e^{-2y}dy=e^{3x}dx \int e^{-2y}dy=\int e^{3x}dx e^{-2y}=-\frac{2}{3}e^3x + C -2y = ln(-\frac{2}{3}e^{3x}+C)...

Hi, I wrote some code on a computer at school. dim = 50; Ediff = ConstantArray[0, {dim, dim}]; \[Lambda] = .5; steps = 10; Ediff = ConstantArray[0, {dim, dim}]; L = 1; For[xs = 1, xs <= dim, xs++, For[ys = 1, ys <= dim, ys++, Ediff[[xs, ys]] = Ediff[[xs, ys]] +...

Hi, guys, Why do we assume Lagrangian Density only depend on field variables and their first derivative? Currently, I am reading Ashok Das's Lectures on Quantum Field Theory. He says (when he is talking about Klein-Gordon Field Theory): "In general, of course, a Lagrangian density...

I have seen the following "extension" of discrete random variables definition, from: pediaview.com/openpedia/Probability_distributions (Abstract) "... Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf)...

Homework Statement Let x=ts^2 -1 and y=ln(s)-t Use the chain rule for functions of two variables to determine ∂f/∂t at (s,t)=(1,1) The Attempt at a Solution y=ln(s)-t ∂f/∂t= ∂f/∂s X ∂s/∂t -1 t=x+1/s^2 ∂t/∂s= -2(x+1)/s^3 ∂s/∂t=s^3/-2(x+1) ∴ ∂f/∂t= s^2/-2(x+1)...

I have an equation that I am trying to change the variables of, it has the form; \frac{d}{dt} W = g \frac{\partial}{\partial y} U + h x \frac{\partial^2}{\partial y^2} Z Where W, U and Z are my dependent variables (This equation is just one of 3 coupled equations but have written...

i just came to learn that the intensive gas variables like pressure and temperature don't depend on the system size. now suppose , i sliced out a gas container into an imaginary plane and i got the extensive variable of volume and internal kinetic energy to be halved.. but why shouldn't the...

Im using NDSolve. I need to be able to update a variable inside NDSolve each time NDSolve takes a step. "rand" is the variable I want to update each step. I want it to be a different number each step. The below is an example that illustrates what I have currently happening ("rand" does not...

Homework Statement Use separation of variables to find the solution to Laplaces equation satisfying the boundary conditions u(x,0)=0 (0<x<2) u(x,1)=0 (0<x<2) u(0,y)=0 (0<y<1) u(2,y)= asin2πy(0<y<1) The Attempt at a Solution I am able to perform the separation of variables...

Quick question about Grassman numbers and change of variables. Suppose you have the function: f=\frac{c\epsilon_{ij} }{2!} \psi_i \psi_j and integrate it: \int d\psi_2 d\psi_1 \frac{c\epsilon_{ij} }{2!} \psi_i \psi_j =c Now change variables: \psi_i=J_{ik}\psi'_k to get: \int...

Hi guys, I have this doubt but i am not sure, if i have an uniform distibution can i conclude that the events or random variables are independent? Thank you

I'm brushing up on differentiating multi-variable functions subject to a constraint and was curious about the notation. In particular, why the derivatives change from complete to partial derivates. I've illustrated the question with an example, below. My specific question w.r.t. the example is...

The normalization condition is: ∫|ψ|^{2}d^{3}r=1 In spherical coordinates: d^{3}r=r^{2}sinθdrdθd\phi Separating variables: ∫|ψ|^{2}r^{2}sinθdrdθd\phi=∫|R|^{2}r^{2}dr∫|Y|^{2}sinθdθd\phi=1 The next step is the part I don't understand. It says: ∫^{∞}_{0}|R|^{2}r^{2}dr=1 and...

Hello, I've been trying to solve the following limit for the last hour or so. I'm pretty much at a loss as to how to solve it (I need to do a lot of these kinds of problems, but I need to understand how to approach them first), so any pointers in the right direction would be appreciated...

Hi, I am a master student comes from USM in Malaysia. I don't know my problem should placed on differential forum or high energy physics forum. Anywhere, My current study is high energy physics subject and my main study is focus on monopole instanton solution in static form which did not...

I am a high school student who has finished calculus, multivariable calculus, and differential equations, but I feel as though the treatment I received of those topics was rather inadequate and shallow - lacking mathematical rigor, so to speak. Can anyone comment on the quality of those two...

Hi folks, I'm hoping to get your opinions about something. If i were given two linear equations and needed to solve for x and y using the methods of "substitution" and "elimination", what algebraic structure should i use? I can solve the systems just fine, but I'm trying to "explain" each step...

Homework Statement Find the area in the positive quadrant of the x-y plane bounded by the curves {x}^{2}+2\,{y}^{2}=1, {x}^{2}+2\,{y}^{2}=4, y=2\,x, y=5\,x The Attempt at a Solution This is a graph of the region: http://img21.imageshack.us/img21/2947/59763898.jpg One thing I was...

Could you pls advise me any reference (textbook for example) where I can find how to calculate maxima minima of function of several variables... or drop a couple of lines here.. Thank you

Homework Statement a) \int\int_{B}\frac{\sqrt[3]{y-x}}{1+y+x} dxdy, where B is the triangle with vertices (0, 0), (1, 0), (0, 1). b)\int\int_{B}x dxdy where B is the set, in the xy plane, limited by the cardioid ρ=1-cos(θ) The Attempt at a Solution a) Let ψ: \left\{u = y-x, v =...

Homework Statement Evaluate \iiint_\textrm{V} |xyz|dxdydz where V = \{(x,y,z) \in ℝ^3:\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} ≤ 1\}Homework Equations Change of Variables Theorem: \int_\textrm{ψ(u)} f(x)dx = \int_\textrm{K} f(\Psi(u))|detD\Psi(u)|du Examples: 1) For a ball of...

Homework Statement The precision in MATLAB is approximately 2*10^(-16), is there a way that my computations can be calculated using a smaller precision? Homework Equations The Attempt at a Solution if i want to calculate the sum of pi^2*j where j=1:20 but i want it to be...

Homework Statement Solve the system of equations for x, y, and z. ------------------------- 4x^4+8y^4+z^4=9 x^8+y^8+z^8=1 -------------------------- Homework Equations The Attempt at a Solution Both equations can be rearranged and factored (difference of squares). I've tried it and it doesn't...

Homework Statement A 35 kg child is jumping on a pogo stick. If the spring has a constant of 4945 N/m and it is compressed 25 cm, how high will the child bounce? Answer: 0.45 m Need help substituting the right variable. Homework Equations ETi= ETf Egi + Eki + Eei = Egf + Ekf + Eef...

Hi, Please I need your assistance on this MATLAB code. I will really appreciate it. R=0.492; Pw=0.3708; for r=1:5; for teta=10:10:360...

[FONT=arial narrow]Dear friends, I have divided the time into slots of fixed size. And i toss a coin of probability of heads 1/2 in the first slot. In the next slot, i toss a coin of probability of head 1/4, and in the i^th slot i toss a coin of prob of head 1/2^i. I do this until i get a...

I'm not sure if it's OK to post this question here or not, the Calculus and Beyond section doesn't really look very heavily proof oriented. I'm trying to prove that if continuous complex valued function f(z) is such that the directional derivatives(using numbers with unit length) preserve...

Hi all. I was thinking on how we can maximize a function with the following form: F(y, x1, x2,..., xn) with y=f(x1) I know that I should use the total derivative to find out the effective rate of y, but I don't see how gradient and Hessian should be organized in this context. For...

Homework Statement dP/dt=P-P^2 Homework Equations The Attempt at a Solution I know you can separate this and after i did that and did my partial fractions i got t + C = ln(P) + ln(1-P) but i don't know what to do from here i figure you take the e of both sides at some point...

Homework Statement Solve the equation (x & y are integers): (x^3+4)(xy^2-x^2y+3y^2-12)=x^6 Homework Equations The Attempt at a Solution xy^2-x^2y+3y^2-12=\frac{x^6}{x^3+4} \\ xy^2-x^2y+3y^2-12=x^3-4 + \frac{16}{x^3+4} \\ 16 \geq x^3+4 \\ x^3 \leq 12 That's all I can...

Homework Statement Compute P(X=k l X+Y=p)Homework Equations The Attempt at a Solution No idea. Kind of understand page #1. Although it seems like there's a lot of unnecessary stuff. Could have gone straight from the top to the bottom. And I don't know why/if you even have to substitute the...

Homework Statement The problem is int(y^3 dx-x^3dy) with the region as x^2+y^2<4 and c equal to the boundary. we are supposed to integrate along C+. This may be unclear since I don't know how to type it up in latex however here is a link to the HW assignment. The problem is problem number...

Homework Statement X1 and X2 are two independent discrete random variables with P(X1 = k) = c3-k P(X2 = k) = d4-k for k in natural numbers and where X1, X2 in natural numbers is almost always valid. 0 is not include in N. Find constants c and d. Homework Equations The Attempt...

Good day, I have this problem that appeared in some practical problem that I'm working on. I basically want to find the boundaries of a,b,c,d for which the following inequality is satisfied, if a,b,c,d \in ℝ^+ and the inequality is: -2 \cdot d + c - a \cdot (c \cdot d)^2 + a \cdot c +...

Homework Statement Solve the following equation: (2x-y)dx+(4x+y-6)dy=0 Homework Equations Solve for M and N as a linear system of equations; and x_t = u + h y_t = v + k The Attempt at a Solution M = 2x-y=0 N = 4x+y-6=0 2x=y 4x+2x=6 6x=6 x=1 y=2 ∴ x_t=u+1 \\ dx=du...

Ok, so I have this written in my notes and while going over it I have a few questions: Suppose cubical boxes are made so that the length, X (in cm) of an edge is distributed as f(x)=\frac{1}{2} for 9≤X≤11 0 otherwise What sort of distribution will the volume, Y, of the boxes have...

- Jim Hefferon: Linear algebra Theorem 1.5 (Gauss' method). If a linear system is changed to another by one of these operations (1) an equation is swapped with another (2) an equation has both sides multiplied by a nonzero constant (3) an equation is replaced by the sum of itself and a...

So I'm taking my complex variables class and learning about these cool powerful theorems like the Cauchy Goursat theorem. I know this all has huge application in physics however I just don't know what they are. Currently I'm only taking freshmen E@M so I know I won't be using it there. But next...