**beautiful**... It read:

Assume thatProbably looks like nonsense to anybody except for Ste, but it basically gives me the easiest twenty marks in any exam I've taken so far. I utterly nailed it, because it's just a case of simple algebra. The other two questions were about calculating the derivatives of complex functions, after working out where they satisfy the conditions for complex differentiability, and integrating over contours in the complex plane. Simple....? ;o)

f: C -> C, f(z) = u(x,y) + iv(x,y), (z = x + iy) is an analytic function. Given that:

u_{x}= v_{y}

u_{y}= - v_{x}

(Cauchy-Riemann)

a) Find u(x,y) and f(z) if v(x,y) = xy [8]

b) Show that f(z) is constant if v(x,y) is constant [6]

c) Derive that the second partial derivative with respect to x (twice) of the real part of the function F, plus the second partial derivative with respect to y (twice) of the real part of the function F, is equal to zero. You may use the fact that Re f and Im f have continuous second partial derivatives. [6]

Anyhow, the important thing is that even though I did kinda crap, I actually think I passed it, which is quite something, considering :o)

thelostgirlnozza## Re:

unknownjAnyhow, it's good that they didn't state the equations themselves - I can always remember them, so I picked up a mark or two on that question, and on every other question where it asked you to use them - they

alwaysgive cheap marks for being able to remember the equations :o)## Re:

nozza## Re:

unknownjSee my latest post for how I did the problems - I got bored, so I wrote it all out :o)

## exams

dweezie(Anonymous)(Anonymous)