Recent content by eaglesmath15

Homework Statement Obtain the Taylor series ez=e Ʃ(z-1)n/n! for 0\leq(n)<\infty, (|z-1|<\infty) for the function f(z)=ez by (ii) writing ez=ez-1e. Homework Equations Taylor series: f(z) = Ʃ(1/2\pi/i ∫(f(z)/(z-z0)n+1dz)(z-z0)n The Attempt at a Solution The first part of this...

Homework Statement Prove Liouville's theorem directly using the Cauchy Integral formula by showing that f(z)-f(0)=0. Homework Equations f(a) = \frac{1}{2πi}\oint\frac{f(z)}{z-a}dz The Attempt at a Solution So the thing is, I know how to prove Liouville's theorem using CIF, but it...

Thanks! It looks like what I had tried before, but it hadn't worked, so I probably just missed something. I haven't really tried anything yet, I'm not entirely sure where to begin.

Homework Statement Show that if C is a positively oriented simple closed contour, then the area of the region enclosed by C can be written (1/2i)/∫C\bar{}zdz. Note that expression 4 Sec. 46 can be used here even though the function f(z)=\bar{}z is not analytic anywhere. FORMATTING NOTE: SHOULD...

Right, I should have clarified. Do you multiply v1 by the components of beta? So the column vector would be (v1v1 v1v2 ... v1vn) (except going down of course, not across)?

Do you multiply T(v1) by beta?

1. The question Let V be a vector space with the ordered basis β={v1, v2,...,vn}. Define v0=0. Then there exists a linear transformation T:V→V such that T(vj) = vj+vj-1 for j=1,2,...,n. Compute [T]β. Homework Equations [T]γβ = (aij), 1≤i≤m, 1≤j≤n (where m is dimension of γ and n is the...