For questions involving analysis of complex functions (e.g. calculus with complex variables, residues, holomorphism). Should focus on particularities of evaluating complex functions/equations. For general questions about arithmetic on complex numbers, use the [complex-arithmetic] tag.
Questions tagged [complex-analysis]
25 questions
15
votes
1 answer
How to numerically calculate residues?
I need to calculate the following integral:
$$
{1\over 2\pi i} \int_C f(E) \, d E
$$
$$
f(E) = {\rm Tr}\,\left(({\bf h} + E)\,{\bf G}(E) \right)
$$
Where $\bf h$ is a matrix (one particle kinetic and potential energy expressed in a basis), $\bf G$…
Ondřej Čertík
- 2,930
- 18
- 40
1
vote
0 answers
Plot FDE Amplification Factor in Complex Plane
I am reviewing stability of finite difference methods. I am using the von Neumann method to study a linear PDE and an explicit finite difference scheme. The goal is to develop an expression for an amplification factor $G$.
I've read that if $G$ is a…
Nukesub
- 163
- 4
0
votes
1 answer
Calculating residue of a rational function
I have a function
$$
f(z) = \frac{1}{(z-z_1)(z-z_2)(z-z_3)(z-z_4)}
$$
All of $\{z_1,z_2,z_3,z_4\}$ are simple poles. The residues
for this function are given as
$$
\text{Res}(f(z),z_i)= \lim\limits_{z\to zi}…
Galilean
- 151
- 6