# Recent content by BustedBreaks

1. ### 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...
2. ### 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...
3. ### 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.
4. ### 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...
5. ### 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 ->...
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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...
10. ### 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...
11. ### 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...
12. ### 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)}...
13. ### 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...
14. ### 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?
15. ### 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...