I know that the answer is supposed to be that it hasnt changed but I am not sure how to prove it. The derivative is the rate of change, and its 0 no matter where you take it, so the function isn't changing. I find it really hard to get my head around this topic, in the real plane the function...
Oh i see, for some reason i was thinking f(z) = x + iy
So if we know that v(x,y)=0 and that the function is analytic then du/dx and du/dy have to equal 0 to satisfy CR.
So if the derivative is 0 then the function has to be a constant?
Okay, so u(x,y) = x and v(x,y) = 0
That means du/dx = 1 and all the others = 0 which means that the function isn't differentiable, but the question says its analytic so it is? So obviously I've done something wrong...
If v(x,y) = y then dv/dy =1 and it works. So I am assuming this is what I am...
You split the function into real and imaginary parts, u(x,y) and y(x,y) and then take the partial derivate of each with respect to x and y.
If du/dx = dv/dy and dv/dx=-du/dy for (xo, yo) then the equation is differentiable at zo.
And then the derivative is du/dx + i dv/y.
Thanks for replying winter85
Okay so i know that a function is analytic over a given open set if it is differentiable at every point in the set...thats about all I've picked up so far, the next thing that was covered in my lectures was the cauchy reimann equations which if i remember correctly...
Homework Statement
Suppose z0 = x0 + iy0 2 C, and r > 0. Further, suppose that f(z) is a real valued function that is analytic on the open box
B(z0; r) = { x + iy | x0 < x < x0 + r; y0 < y < y0 + r }.
Then show that f(z) must, in fact, be constant on the box B(z0; r).
The Attempt at...
oops yeah i did mean 1/(s+1) danago
and Pere i wouldn't have a clue about sinh(t) and cosh(t) a exponentials, maybe i should have paid more attention in first year maths
Hi all, 2 questions here
1) I've been doing some questions on laplace transforms and have been running into some trouble getting my answers into the same form as the answers given with the questions.
For example:
f(t) = 1 - e^(-t)
Using the linearity property i got 1/s - 1/(s-1) which is...
hey guys, I've got to make a voltage regulator for a uni project. it has to use hysterisis and produce 9v out from a 16Vrms AC powerpack over a 15 ohm load. It also needs overload protection, I've drawn up the attached circuit, i think it will work and filled in some of the values i know but I...
Thanks for the help guys i really appreciate it, i think ill definitely need this site to pass maths this semester, god i hope i don't have another maths subject next year
Just on a side note, I am doing electrical engineering and I am wondering when complex analysis would be used in a...
Evaluate the Line Integral (assume counterclockwise orientation)
\oint _{|z| = 2 } z^n \bar{z}^m dz for all m, n \in Z
I have no freaken clue about how to even attempt this...