Recent content by chocok

sr6622: sorry, I still haven't learned characteristic equation. so I can't use the technique yet.. but thanks! Defennder: Ohhhh. I mean it's a big question but each part has nothing to do with each other. They are just unrelated, like part i) is y' + y =0 and we are asked to do the same thing...

Thanks for replying! Actually this is one part of a big question where similar DE are given with the same solution(where others have y) so the solution y=exp(ax) seems irrelevant in this case. The question didn't state x" is being differentiated w.r.t. what variable, so I just assumed it's...

Question: I have to find the constant a such that y(x) = e^{ax} is a solution for x" = x My answer: I tried 2 ways of reasoning and they both led to my answer that a can be any number (but zero). Can anyone see if they are correct?? If not, pls give me some hint! 1. x= ln(y)/a but x"...

1. I need to reduce (a_{1}x + b_{1}y + c_{1})dx + (a_{2}x + b_{2}x +c_{2})dy = 0 to: \frac{dy}{dx} = F ( ax + by) with a_{1}b_{2} = a_{2}b_{1} i.e.: a_{1}b_{2}=a_{2}b_{1} \frac{a_{2}}{a_{1}} = k and \frac{b_{2}}{b_{1}} = k 2. First Try: I solved for dy/dx and tired to deal...

Hi, I have a BA II plus Prof. and there's no "pi" key, I tried using the trig functions to get the value but it always give me a something in degrees. I want to avoid using 22/7 as it's not close enough. Is there any way to get the number instead of memorizing it? THanks!

Question: If g(x)\in K[x] and 1< deg(g)=n. Given that G/K is a normal field ext., if g(x)=g1(x)*...*gk(x)\in G[x], then deg(g1)=...=deg(gk) My attempt: I let G = K adjoins the coefficients of gi's. Let \alpha be a root of g. Notice that K \subseteq G \subseteq K( \alpha) = G( \alpha)...

thanks~ pls tell me this is right for the 8 roots, eliminating the ones that can be expressed as multiples of others, i am left with e^{2\pi i/8} and e^{\pi i/2}=i where their orders are 4 and 2 respectively so i get a splitting field over Q of order 8 =>Gal( Q( e^{2\pi i/8} , e^{\pi i/2}) /...

thanks! can u tell me if I'm understanding correctly? so for Z \oplus Z -> Z (say Z is the integer field), can i have some maps like this (4 maps): map((a,b)) = \pm a \pm b i mean as long as the value on the right side stays in Z? and for Z \rightarrowZxZ, we are mapping from an elt...

can someone please explain what these mappings really means? like what is being mapped and mapped to..?? i get confused by the direct sum & product that gets mapped.. Z \oplus Z ->Z Z -> ZxZ

I was asked to find the Galois group of x^8-1 over Q, I first find all the roots to it : \pm i , \pm \sqrt{i} , \pm i \cdot \sqrt{i}, \pm 1. Then since i \cdot \sqrt{i} is just a multiple of i and sqrt(i) so I had Q(i, sqrt(i)) being the splitting field for the equation over Q. Next...

Thanks for replying! When I have 2 situations, how can i show that when L-tn>0 (L>tn) and L>x actually implies tn>x?? Can you give me some idea?

Then can i rephrase it as follows: As (t_n) converge, (t_n - x) converges too. And let lim(t_n - x) = k, for k in R, k>0. Then for some e>0, there's a number N s.t. n>N => 0<|(t_n-x)-k|< e |(t_n-x)-k|>0 implies t_n - k>x, since k is positive, it follows that t_n>x. does this sound right? (it...

Homework Statement The question asks to prove that if (t_n) is a convergent sequence and suppose that its limit is great than a number x. The prove that it exists a number N such that n>N => t_n>x The Attempt at a Solution I tried to say that as (t_n) converge, (t_n - x) converges too. And let...

<Inverse Laplace Transform> Hi, I was given this: F(z) = 1/(z^2)(z^2+1) and was asked to use its residues to compute f(t). [z is a complex number] The answer I got is -sin(t). But the answer on the book says t-sin(t). I double checked and the residue of z=0 is 0, I don't get where the t...

If S is a domain that is simply connected for S not equal to complex plane and z is in D. Assume g maps D into itself and f(z)=z. prove |f'(z)|<=1 how should I do this? nowhere near the desired result.. help!