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    Prove not integrable. Is this correct?

    Let f:[0,1] be defined as f(x)= 0 for x rational, f(x)=x for x irrational Show f is not integrable m=inf(f(x) on [Xi-1, Xi]) M=sup(f(x) on [Xi-1, Xi]) Okay so my argument goes like this: I need to show that the Upper integral of f does not equal the lower integral of f Because...
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    Advanced Calc. Continuity problem

    So I've been trying to figure this out. The question is: If the limit x->infinity of Xn=Xo Show that, by definition, limit x->infinity sqrt(Xn)=sqrt(Xo) I'm pretty sure I need to use the epsilon definition. I worked on it with someone else and we think that what we have to show is the...
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    New at Mathematica, Need some help

    hi, I have two equations that I have used the Solve function in Mathematica to solve for A in both equations What I am having trouble with is trying to equate the results and solving for another variable J automatically Basically this is what I want to do: Solve[Eqn1, A] It gives {{A ->...
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    Direct Sum of Rings

    This may be a dumb question, but I jsut want to make sure I understand this correctly. For R_{1}, R_{2}, ..., R_{n} R_{1} \oplus R_{2} \oplus, ..., R_{n}=(a_{1},a_{2},...,a_{n})|a_{i} \in R_{i} does this mean that a ring which is a direct sum of other rings is composed of specific elements...
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    First order PDE help

    I'm trying to solve this equation: Ux + Uy + U = e^-(x+y) with the initial condition that U(x,0)=0 I played around and and quickly found that U = -e^-(x+y) solves the equation, but does not hold for the initial condition. For the initial condition to hold, I think there needs to be some...
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    Wave equation with Neumann BDC

    The problem statement is: Solve the Neumann problem for the wave equation on the half line 0<x<infinity. Here is what I have U_{tt}=c^{2}U_{xx} Initial conditions U(x,0)=\phi(x) U_{t}(x,0)=\psi(x) Neumann BC U_{x}(0,t)=0 So I extend \phi(x) and \psi(x) evenly and get...
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    Solve this PDE 2Ux-Uy+5U=10 with U(x,0)=0

    I'm following an algorithm my teacher gave us and I'm trying to understand it... I'm trying to solve this PDE 2Ux-Uy+5U=10 with U(x,0)=0 First I need to solve the homogeneous equation. So I set up the relation: V(y)=U(2y+c, y) to solve 2Ux-Uy=0 where the characteristic equation is y=1x/2...
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    Deriving a heat equation

    Consider heat flow in a long circular cylinder where the temperature depends only on t and on the distance r to the axis of the cylinder. Here r=\sqrt{x^{2}+y^{2}} is the cylindrical coordinate. From the three dimensional heat equation derive the equation u_{t}=k(u_{rr}+\frac{u_{r}}{r}). My...
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    Cosets of a subset of S_3

    I am having trouble understanding this example: Let G=S_3 and H={(1),(13)}. Then the left cosets of H in G are (1)H=H (12)H={(12), (12)(13)}={(12),(132)}=(132)H I cannot figure out how to produce this relation: (12)H={(12), (12)(13)}={(12),(132)}=(132)H I understand (12)H={(12), (12)(13)}...
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    Question of integration

    So in doing a homework problem I have convinced my self that \int\frac{V_{x}}{V}=ln(V) which I vaguely remember learning in class, but I'm having trouble deriving it. Can someone help me out?
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    Show functions of this form are a vector space etc

    Show that the functions (c_{1}+c_{2}sin^{2}x+c_{3}cos^2{x}) form a vector space. Find a basis of it. What is its dimension? My answer is that it's a vector space because: (c_{1}+c_{2}sin^{2}x+c_{3}cos^2{x})+(c'_{1}+c'_{2}sin^{2}x+c'_{3}cos^2{x})...
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    Linearity of Partial Differential Equations

    Is this linear homogeneous, linear inhomogeneous etc... u_{t}-u_{xx}+xu=0 From that first one I get this \frac{u_{t}-u_{xx}}{u}=-x which I'm not sure is linear. Edit: Similar questions involve the following equations: iu_{t}-u_{xx}+\frac{u}{x}=0 and u_{x}+e^{y}u_{y}=0 Another Edit: I...
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    Help Checking Some Proofs

    I have two proofs that I am uneasy about and one I'm having trouble with so hopefully I can figure out where I'm going wrong if I am. Ignore the weird numbers, its to help me organize the problems. 14) Let G be a group with the following property: Whenever a, b and c belong to G and ab=ca, then...
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    Uniqueness of integers question

    Find integers s and t such that 1 = 7*s + 11*t. Show that s and t are not unique. I can find numbers that satisfy this question, t=2, s=-3 and t=-5, s=8, that show s and t are not unique, but this doesn't seem to be rigorous and I'm not sure where to start with proving this.
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    Prime Number Proof Help.

    Let p_{1}, p_{2},...,p_{n} be primes. Show that p_{1} p_{2}...p_{n}+1 is divisible by none of these primes. Let p_{1}, p_{2},...,p_{n} be primes Let k \in N Assume p_{1}p_{2}...p_{n}+1=kp_{n} \frac{p_{1}p_{2}...p_{n}}{p_{n}}+\frac{1}{p_{n}}=k p_{1}p_{2}...p_{n-1}+\frac{1}{p_{n}}=k This is a...
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    Confusing Step - Euler's Formula?

    I'm following the answer to a problem and I see this step which I am unsure about: F[k]=\frac{1}{2}\int^{1}_{-1}|x|e^{-\pi i k x}dx F[k]=\frac{1}{2}\int^{1}_{-1}|x|cos(\pi k x)dx For k equal to all integers. Shouldn't the conversion from the exponential be cos(-\pi k x)
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    Severe Fourier Help

    Okay so I have the following problems to figure out by Monday morning. I'm very behind so I am going to spend some time trying to work them out on my own tonight and tomorrow so don't think I am asking for the specific answers, but I thought I would post this here so when I have some trouble...
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    Fourier Series

    Let f(x):= x when 0<x<1. Find the Fourier series for f if: a) f is 1 periodic b) f is even and 2 periodic c) f is odd and 2 periodic. I am very lost and behind. I'm reading through my notes and book and hopefully will be able to to this soon, but can anyone give me a hint or just explain how...
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    Reflection Rule of a Fourier Transform

    I feel a bit dumb, but could someone help me see this: G(s):= \int_{-\infty}^{\infty}f(-x)e^{-2\pi isx}dx = \int_{-\infty}^{\infty}f(u)e^{-2\pi i(-s)u}du = F(-s)
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    Work, A Charged Ring, etc

    A charge of 10 nC is uniformly distributed around a ring of radius 10 cm that has its center at the origin and its axis along the x axis. A point charge of 1 nC is located at x = 1.75 m. Find the work required to move the point charge to the origin. Give your answer in both joules and electron...
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    Two Spheres connected by a wire.

    Charge is placed on two conducting spheres that are very far apart and connected by a long thin wire. The radius of the smaller sphere is 5 cm and that of the larger sphere is 12 cm. The electric field at the surface of the larger sphere is 830 kV/m. Find the surface charge density on each...
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    Spherical Shell Capacitance

    What is the capacitance C of a capacitor that consists of two concentric spherical shells, the inner of radius r_{1} and the outer of radius r_{2}? What would the limit be if r_{2}-r_{1}<<r_{1}. What would happen if r_{2} goes to infinity (assume the potential there is zero)? Some equations...
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    Convolution Product

    I need to find the convolution product f*g when the functions f, g on P_{4} are given by: (a) f:=(1,2,3,4), g:=(1,0,0,0) (b) f:=(1,2,3,4), g:=(0,0,1,0) I know that (f*g)[n]=f[0]\cdot g[n]+f[1]\cdot g[n-1]+f[2]\cdot g[n-2]+...+f[N-1]\cdot g[n-(N-1)] and \sum_{m=0}^{N-1}f[m]g[n-m] when f...
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    What does this notation mean?

    u := -v specifically the " := " Here is the context. When f, g are suitably regular functions on R we can use the change of variable u:=-v etc.. I should add that I came across this in a Fourier Transform book.. Thanks!
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    Two Analysis questions

    1) By writing a = (a+b) + (-b) use the Triangle Inequality to obtain |a| - |b| \leq |a+b|. Then interchange a and b to show that ||a| - |b|| \leq |a+b|. The replace b by -b to obtain ||a| - |b|| \leq |a - b|. Okay. I am a bit lost. I started out by plugging in what they give me for...
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    I feel a bit stupid

    So my mother mentioned to a co-worker, who is a "math guy," that I was interested in math. The co-worker subsequently gave her a piece of paper with the following written on it to give me to to "solve" or "prove" in my mother's words, yet I am unsure what to do. Here is what was on the paper...
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    New to Comp. Programming

    Hello everyone. I want to start learning some sort of computer programming. ...Where do I start?... Yes. That is all I have. I don't know what kind, cause I don't know what kind does what. I don't even know what kinds there are, or if there are kinds. I am blissfully ignorant...
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    Development of Complex Numbers

    I was wondering if someone could recommend a good text that explains the construction of complex from real, real from rational, rational from integers, and integers from natural numbers. Thanks
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    Analysis Questions-Thanks for helping me!

    Analysis Questions--Thanks for helping me! I have a final in an introductory analysis class that covers mostly sequences and series on Friday and I'm a bit behind in the course work. I have a bunch of questions so instead of making a different thread for each one I figured I would just use this...
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    Question on graphing in the complex plane

    Okay, I need to graph the following set in the complex plane: M={z\inC:[(1<|z-i|\leq2) and (z\neq2+i)] or [z = 1 + \pii]} I got the last two constraints, but the first one is what's giving me trouble. is z-i just x+yi that is (1,1) on the complex plane lowered by 1? Thanks
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