Newtons method in the complex plane

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Times and Place


Lecture:
Tuesday 10th October 12:30-14:00 in 5A
Wednesday 11th October 14:30-16:00 in 5G


Exercise/Lab:
Wednesday 11th October 16:30-18:00 in 25.42 2542.00.41 and
Thursday 12th October 14:30-16:00 in 25.42 2542.00.41

Aim

This short course mainly is about bringing students together with mathematical beauty of fractals. You will learn about fractals, Mandelbrot sets and Julia sets. In the computer lab sessions we will develope basin portraits of polynomials.

Mandelbrot set
Mandelbrot set CC BY-SA 3.0, Link
Julia set
Julia set by Georg-Johann Lay - self-made, see Visualising Julia sets, Public Domain, Link


Topics:

Prerequisite

Some basic knowledge of complex numbers.

Material

  1. Berkey D.D., Blanchard P.P. , Calculus (third edition), Saunders college publishing, New York (1992) Pages 182-187 and Appendix-IV
  2. Aaron Burton, Newton's method and fractals PDF
  3. Lily Yau and Adi Ben-Israel, The Newton and Halley Methods for Complex Roots PDF
  4. Carmen Q. Artino, The Complex Roots of a Quadratic Equation: A Visualization PDF

last modified on: 11 October 2017 at 10:05am.