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- Mentor: Ricky Simanjuntak
- Faculty coordinator: Prof. Matt Bainbridge
One highlight of elementary complex analysis is the Riemann Mapping theorem: any simply connected domain not the entire plane can be conformally mapped to unit disk. It is a difficult task, however, to numerically compute the mapping.
One highlight of elementary complex analysis is the Riemann Mapping theorem: any simply connected domain not the entire plane can be conformally mapped to unit disk. It is a difficult task, however, to numerically compute the mapping.
A famous formula is given by Schwarz-Christoffel (SC) mapping describing the conformal map to a polygon as solution to differential equations (DE). See Figure 1. The goal of this project is to understand the theory behind SC and utilize some Matlab packages to:
A famous formula is given by Schwarz-Christoffel (SC) mapping describing the conformal map to a polygon as solution to differential equations (DE). See Figure 1. The goal of this project is to understand the theory behind SC and utilize some Matlab packages to:
1. Solve the DE numerically
1. Solve the DE numerically
2. Visualize how the map behave.
2. Visualize how the map behave.
This project will be of interest to anyone working in complex analysis or scientific computing. Given enough time we will explore some application towards engineering and fluid dynamics.
This project will be of interest to anyone working in complex analysis or scientific computing. Given enough time we will explore some application towards engineering and fluid dynamics.
Ideally, you would have basic knowledge of Real Analysis and differential equations, however this is not crucial. You will learn any background knowledge as you go.
Ideally, you would have basic knowledge of Real Analysis and differential equations, however this is not crucial. You will learn any background knowledge as you go.
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