Newtons method in the complex plane

News

Staff

• Prof. Murat İbrahim Yazar (Erasmus guest lecturer)

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 CC BY-SA 3.0, Link

Julia set by Georg-Johann Lay - self-made, see Visualising Julia sets, Public Domain, Link

Topics:

• Newton’s Method as an iterated function
• Basic definitions and terms about fractals
• Examples of fractals in nature and mathematics.
• Basin portraits of polynomials in complex plain.

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