Complex Analysis

Reader's Comments

Many thanks to all the people around the world who have kindly shared their thoughts about this educational resource. If you want to share your thoughts, I'll be adding a link here soon. Thank you for your patience.

A book (site) that explains mathematical theory that is difficult to understand intuitively with tools that can create interactive content such as GeoGebra and p5.js. You can actually move the parameters and see how they change.
— piqcy

Ideal para mi curso de Análisis Complejo. Gracias por compartirlo.
— Ana María Lucca

Por si alguno está estudiando análisis complejo, esta introducción está fetén.
— ThePurpleSensation

A neat interactive approach to learning about complex analysis.
— Sean Walker

Las matemáticas viven en el razonamiento del ser humano y, dado su nivel de abstracción, una simple lectura no es suficiente para comprender y asimilar los conceptos. Todo resulta más fácil cuando dichos conceptos vienen acompañados por ilustraciones y explicaciones breves y sencillas. Pues bien, Juan Carlos consigue en este libro precisamente eso. Nadie como él para sacar partido a todos los recursos visuales posibles en forma de aplicaciones e ilustraciones interactivas para ilustrar la magia de los números imaginarios. Alégrense la vista y la mente con este fantástico libro.
— Julio Mulero

I like the way each page has careful and readable descriptions of the maths, while not shying away from the technical details. The particular strength here is that alongside the readable mathematics are regular interactive animations in Geogebra or p5.js (on every page!?). These really help the reader *literally* get to grips with the material. It's lovely stuff. I believe that making maths *move* in this way is the key for any of us trying to understand this subject better.
— Ben Sparks

I was just wanting to learn more about these holomorphic functions of the complex plane and conformal mapping and how this stuff relates to fluid flow myself, THANK YOU for making this!
— C010011012

Awesome work, thanks for sharing this! The maths is clearly written and - no surprise - the @geogebra applets are just perfect.
— Vincent Pantaloni

Brilliant work! It is a true honor to be included within it.
— GeoGebra

Complex Analysis: A visual and Interactive Introduction is like a virtual or imaginary candy-store for those interested in mathematical visualizations in general or complex numbers in particular. I have never seen so many mesmerizing applets in one place. The tools given to the user to explore the mathematics beyond the text and the attention to detail make a very captivating adventure.

Anyone interested in the Mandelbrot Set (which is probably just about everyone) should check out the chapter with the interactive Mandelbrot illustrations. I particularly like the applet that shows the changing character of the iterate orbitals as one moves among the various buds of the Mandelbrot set and another applet that connects the Mandelbrot set to the Julian sets.

After whetting one’s appetite on the Mandelbrot chapter, if you are like me, you will want to explore further. The colorful analytic landscapes and domain coloring apps are awesome. And don’t miss the cool conformal mapping applications in the last chapter!
— Ken Thele

Extraordinary....this will help a lot of guys.
— Azazaya

This is indeed one of the best educational content. Let's study. Thank you.
— ayush thakur

NEXT: Terminology and Notation