Recent content by semithinking

Have you thought about using mathematical induction? Set up your base case: n = 3 You will show that 2^3-1 = 8 - 1 = 7 is prime and 2^3 + 1 = 9 is not since 9 = 3 \cdot 3. Assume that it's true for n. Then prove the case for n + 1.

Homework Statement Use separation of variables to find a general series solution of u_t + 4tu = u_{xx} for 0 < x < 1, t> 0 and u(0,t) = u(1,t)=0. Homework Equations The Attempt at a Solution Looking for a solution of the form u(x,t) = X(x)T(t) implies that \frac{T'}{kt} - \frac{X''}{X} = 0...

We also know that f,g are biholomophic which implies that it's a conformal map, thus it is angle preserving. Is this a way to two conformal mapping to each other?

Homework Statement Let f and g be bijective holomorphic maps from an open set A to the unit circle. Let a \in A and c=f(a) and d=g(a). Find a relation between f and g that involves a,c,d,f'(a),g'(a).Homework Equations The Attempt at a Solution If we also assumed that the open set is...

GmailTeX works if both parties who are emailing each other have it...

So I would substitute zz* into |phi_w(z)| to see if it's 1?

Homework Statement For each w \in \mathbb{C} define the function \phi_w on the open set \mathbb{C}\backslash \{\bar{w}^{-1}\} by \phi_w (z) = \frac{w - z}{1 - \bar{w}z}, for z \in \mathbb{C}\backslash \{\bar{w}^{-1}\} \back. Prove that \phi_w : \bar{D} \mapsto \bar{D} is a...