# Tagged Questions

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### implicit non-linear equations with complex variables

I am trying to understand a methodology for solving implicit non-linear equations with complex variables. I would like to solve for z1 below where z2 is known. Also both z1 and z2 are complex ...
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### Solution of $\exp(z)=z$ in $\Bbb{C}$.

I have posted a related question here. I thinkg this one is more interesting: What about the solution of $\exp(z)=z$ in $\Bbb{C}$? My try : $z \mapsto e^z - z$ is entire non-constant. Perhaps ...
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### Accurate computation of arcsec near branch points

The direct numerical implementations of the usual definitions of the complex $\mathrm{arcsec}(z)=\arccos(1/z)$ and similar for $\mathrm{arccsc}(z), \mathrm{arcsech}(z),$ etc are not accurate near ...
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### How can I explicitly construct a *nice* conformal mapping from a triangle to a square in MATLAB?

I know the basics of the Riemann mapping theorem, SC maps, etc. I can look up formulae for the maps from the half-plane to a triangle or rectangle. But I want a particularly nice explicit map--easily ...
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### How to find an error estimate for integral of curvilinear surface triangle when using quadrature

I would like to find a way to estimate the error due to the calculation of the normal when one tries to find the volume of a volume composed of quadratic surface triangles using numerical gauss ...
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### Can I switch the order of integration and “Real(z)” operation?

Let $f(z,\eta)$ be an entire function. I need to calculate (numerically) the integral: $$\int\limits _{0}^{\pi}\mbox{Re}\left(\int\limits _{0}^{\pi}f\left(z,\eta\right)d\eta\right)dz$$ Can I switch ...
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### Techniques for removing removable singularities (without resorting to series expansion)?

Suppose $f: \mathbb{C} \supset U \to \mathbb{C}$ is a meromorphic function with a removable singularity at the point $z_0 \in U$. Then $f$ can be extended to a holomorphic function over all of $U$. ...
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### Analysis for Engineers: Where Do You Start?

Having taken none of the prerequisite rigorous treatments of mathematics during my undergrad years, I feel at a disadvantage to the people in my major what do have that analysis/abstract math ...