Would anyone be willing to check and comment on my work for finding the Laurent series of
f(z)=\frac{1+2z}{z^2+z^3} ?
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Well maybe since 1/(1-z) converges for |z|>1, with z=1/z, we get |1/z|<1 which is equivalent to |z|>1.
Is multiplying the fraction by 1/z a standard procedure for finding the series that converges for |z|>1 ?
I uploaded a scanned page from Schaum's Outline of Complex Variables. I have some questions on how they found the Laurent series in Example 27.
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In...
Ok, so it appears that I need to use the residue theorem in order to evaluate this integral. I was hoping I could just use the integral formula. I haven't got to study the residue theorem yet in my text. Thanks
Homework Statement
I am trying to determine if Cauchy's integral formula will work on the following integral, where the contour C is the unit circle traversed in the counterclockwise direction.
\oint_{C}^{}{\frac{z^2+1}{e^{iz}-1}}
Homework Equations
See Cauchy's Integral Formula -...
OK, I should have had |\gamma^{'}(t)|, instead of \gamma^{'}(t).
So the original integral becomes \int_{0}^{1}{\sqrt{1+4t^2}}dt or would I have
\int_{0}^{1}{\sqrt{1+4t^2} \cdot \sqrt{1+4t^2}dt} ?
Homework Statement
I want to compute \int_{C}^{}{|f(z)||dz|} along the contour C given by the curve y=x^2 using endpoints (0,0) and (1,1). I am to use f(z)=e^{i\cdot \texrm{arg}(z)}
Homework Equations
The Attempt at a Solution
I know that for all complex numbers z, |e^{i\cdot...
Well, I think this is true. Intuitively, I want to say that if there is a sequence {xn} with some points in both C and D that accumulate at x0, and we remove those points only in D, then we would still be able to find subsequences in C that converge to x0, and vice versa.
Regarding me not...
Does this look better?
Proof: Suppose x_0 is an accumulation point of C \bigcup D. Then either x_0 is an accumulation point of C or x_0 is an accumulation point of D or x_0 is an accumulation point of both C and D.
Case I: Without loss of generality, suppose that x_0 is an accumulation...
How does this proof look?
Proof: Suppose x_0 is an accumulation point of C \bigcup D. Then either x_0 is an accumulation point of C or x_0 is an accumulation point of D or x_0 is an accumulation point of both C and D.
Case I: Without loss of generality, suppose that x_0 is an accumulation...
I wish this was trivial for me. :) Well, I had the correct intuition on how to prove the statement. Let me see if I can write the proof correctly. Thanks.
Homework Statement
I want to show that if C and D and closed sets, then C \bigcup D is a closed set.
Homework Equations
A set is called closed iff the set contains all of its accumulation points.
The Attempt at a Solution
In order for me to prove this statement, I will be able...