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.

The applets are beautiful! You found the right amount of interactivity: some sites have too much (overwhelming, or clunky), most have too little. It's also a great service to provide the source code on GitHub.
Marcus Berg

This looks fantastically useful for anyone who is teaching or taking a course in complex analysis. Thank you, Juan Carlos! Beautiful work! And very generous of you to share it with the world 👏
— Steven Strogatz @stevenstrogatz

I’m amazed at the availability and quality of such material. We live in such a wonderful time for learning.
— Matthew Mansfield @drunkengrass

Wow thank you @jcponcemath! I wish I had this when I took Complex Analysis ~20 years ago. Instead I treated a grad student friend to a meal so I could ask them 100 questions about how to visualize what we had to do for class.
— Federico Chialvo @FedericoChialvo

Complex analysis is imho perhaps the most “magical” corner of math, where the right amount of assumptions gives a counterintuitive amount of results... but for the same reason it is not easy to learn. This type of resources are really helpful!
— Fernando Rosas @_fernando_rosas

Te quería comentar nomas que estuve ojeando tu libro y me gustó mucho. Justamente este cuatrimestre estoy cursando una materia de análisis complejo y es un lindo complemento visual para muchas de las temáticas que vemos. En particular me fascinó el graficador interactivo de series de Taylor con domain coloring, resultó muy didáctico para entender el concepto de radio de convergencia!!!

Te quería agradecer por hacerlo material de libre acceso, lo compartiré con mis compañeros y docentes :)
— Agustín Brusco @fisplot

He leído tu libro de análisis complejo y me ha gustado mucho. Trata los contenidos de esta materia de una manera muy asequible que complementa visualmente con applets interactivos. Me parece idóneo para docentes, investigadores y estudiantes de ingenierías y matemáticas. Muchas gracias por esta aportación.
— Débora Pereiro @debora_pereiro

As Web-based open-access textbooks gain wider visibility, we need pioneers to demonstrate the possibilities of this emerging medium. In Complex Analysis: A Visual and Interactive Introduction, Juan Carlos Ponce Campuzano has already done something that was previously impossible: he’s seamlessly embedded beautiful, dynamic, interactive visualizations into the body of a math text.

Not only are these visualizations created with open-source software, but also the book itself is open to continual improvements. There is simply no need to wait for a new edition, and the contents are available to everyone with an internet connection. Authors, take note! This is how it’s done.
— Greg Stanton @HigherMathNotes

En mi opinión, este proyecto consigue el equilibrio perfecto entre el rigor matemático y la claridad. Está muy bien estructurado, pero lo que realmente le distingue de los libros al uso son sus applets interactivos, que permiten a los lectores ir jugando con distintos parámetros y ver el resultado que estos cambios provocan. De esta forma, es mucho más fácil para el lector entender la teoría que subyace y, sin duda, mucho más atractivo. Los gráficos interactivos se van haciendo cada vez más espectaculares a medida que avanza el libro y hacen justicia a lo fascinante que es esta rama de las matemáticas.

Mención especial merece también el hecho de que todas las animaciones hayan sido creadas con software libre, como GeoGebra, entre otros.

Lo recomiendo tanto para aquellos que vayan a impartir un curso en análisis complejo como para quienes quieran estudiarlo.
— Javier Arrospide Laborda

El tema de los números complejos es realmente apasionante y Juan Carlos Ponce nos organiza un recorrido por el mismo de manera clara, concisa y muy visual, incorporando aplicaciones con el programa GeoGebra para explicar los diferentes conceptos. El formato y la presentación hacen que la lectura sea muy amena, lejos de textos sobrecargados, densos y con demasiada información, muchas veces innecesaria. El lector puede ir descubriendo el mundo fascinante del análisis complejo interactuando con las aplicaciones del libro. Al final te acabas sintiendo como un viajero descubriendo un mundo nuevo... ¡y son matemáticas!
— Bernat Ancochea Millet

The applets and flow are a splendid way to get exposure to complex numbers and analysis. I have enjoyed reviewing a topic I haven’t played with in a long time. There are enthusiastic and eye-catching visuals throughout. Even if math is not your thing, I recommend that you take a look and play with the applets. This is a great book for anyone interested the complex plane, imaginary numbers, and jumping into some of the wonders of math.
— Sophia Wood @fractalkitty

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: A Brief History