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...
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...
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 ->...
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...
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...
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...
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...
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...
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)}...
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?
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})...
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...
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...
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.
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...
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)
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...
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...
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)
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...
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...
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...
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...
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!
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...
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...
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...
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
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...
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