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    Prove not integrable. Is this correct?

    Well, what I was trying to say was that the upper sum cannot equal 0 because for any interval [a,b] M will not be 0 because there is always an irrational greater than 0 no matter how small the partition [Xo, X1] gets. Because M will never be 0 the inf of the Upper Darboux Sums will never be 0...
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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

    ^ If it does, I can't see it. I feel like I need to find an N in terms of e to show that this si continuous or something.
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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

    Okay so I get your method here and I am trying to apply it to this one (23)(13) but I am not getting the answer the book has which is (123) I set it up like this (23) (13) 123 123 132 321 then so 1 goes to 3 then 3 goes to 2, 2 goes to 2 then 2 goes to 3, 3 goes to 1 and 1 goes...
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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

    To give a bit more context. I was trying to solve the partial differential equation: 3U_{y}+U_{xy}=0 with the hint, let V=U_y substituting we have 3V+V_{x}=0 then -3=\frac{V_{x}}{V} I didn't really know how to continue from here so I just played around and figured out that V=e^{3x} and...
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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

    I see what you mean by the difference in functions, however I feel like they would have written it the way you did, {1, sin2x, cos2x}, if that's what they meant? They way I see it, the function in the question represents all functions of that form which is why they have function plural...
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    Show functions of this form are a vector space etc

    Well to be honest I have forgotten a lot of this stuff. I'm looking at the function (c_{1}+c_{2}sin^{2}x+c_{3}cos^2{x}) with c1, c2, and c3, as distinct constants and that all functions of this form can be combined to create another function this form. This seems to be the wrong way to think...
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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.

    To make it work for p_{1} I can just use p_{1} instead of p_{n}, I guess. I don't know if that helps me see what to do... I was thinking of writing something like what I had, but instead of p_{n} on the right I would have p_{x} where x\in{1,2,...,n}, but that seems weird.
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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

    I am having trouble understanding this. If it is even and 2-periodic are you saying that it would be basically the graph of |x| on (-1,1)? for odd just the graph of x on (-1,1)? What confuses me if this is right is that it says in the question that the interval is (0,1) Also can you confirm...
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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 dumber for not realizing this, and even more dumbest for this sentance. A little smarterest though for the learning... Thanks!
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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)