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<title>Complex Analysis</title>

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<meta name="dc.creator" CONTENT="Juan Carlos Ponce Campuzano">

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<br>

<h1>COMPLEX ANALYSIS</h1>

<p class="w3-center" style="font-size: 28px">A Visual and Interactive Introduction</p>

<p class="w3-center w3-hide-small" style="font-size: 24px">Juan Carlos Ponce Campuzano <br>

<!--<a href="https://jcponce.com" target="_blank" style="font-size: 20px" >jcponce.com</a>-->

</p>

<p class="w3-center w3-hide-medium w3-hide-large" style="font-size: 20px">Juan Carlos <br>Ponce Campuzano <br></p>

<p class="w3-center" style="font-size: 20px"><span>2019-<script>document.write(new Date().getFullYear());</script></span></p>

<br>

<div><p class="w3-center" style="font-size:16px;"><a href="es.html" style="color:#666666;font-weight:normal"><em>- Español -</em></a></p></div>

<hr>

<p>The study of complex analysis is important for students in engineering and the

physical sciences and is a central subject in mathematics. In addition to being

mathematically elegant, complex analysis provides powerful tools for solving

problems that are either very difficult or virtually impossible to solve in any

other way.</p>

<p>In this book you will find examples, problems and applets that allow you to explore complex analysis by using

the visual interactive power of the computer (or tablet).</p>

<p class="callout" style="text-align:left"><strong>UPDATES!</strong>

This site has been getting lots of visits which is fantastic.

There are new sections about integration of complex functions and Laurent series.

The Spanish version is ready so more people around the world

can enjoy learning and playing with complex analysis.

Finally, this online book was recently included in the

<a href="https://www.acds.edu.au/teaching-learning/resource-repository/">Australian Council

of Deans of Science's repository</a>

as a teaching and assessment resource

to support online learning.

</p>

<p>Ready to get started? Skip ahead to the <a href="content/table_of_contents.html">Table of Contents.</a></p>

<h2>WHAT IT IS ABOUT</h2>

<p>This book is an interactive introduction to the theory and applications of complex functions

from a visual point of view. However, it <em>does not</em> cover all the topics of a

standard course. In fact, it is a collection of selected topics and interactive applets

that can be used as a supplementary learning resource by anyone interested in learning

this fascinating branch of mathematics.</p>

<p>Some of the topics covered here are basic arithmetic of complex numbers, complex functions,

Riemann surfaces, limits, derivatives, domain coloring, analytic landscapes and

some applications of conformal mappings.</p>

<p>What distinguishes this online book from other traditional texts in the first instance is the

use of interactive applets that allow you to explore properties of complex numbers

geometrically and analyze complex functions by using different techniques to visualize

them. For the design of applets I used the following open-source softwares:</p>

<div class="w3-row-padding w3-center">

<div id="ggb" class="w3-quarter w3-container w3-margin-bottom">

<div class="container">

<a href="https://geogebra.org/" target="_blank"><img class="w3-image" src="images/ggb.png" alt="GeoGebra"

title="GeoGebra" style="width:25%;">

</a>

</div>

</div>

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<div class="container">

<a href="https://p5js.org/" target="_blank"><img class="w3-image" src="images/p5js.png" alt="p5.js" title="p5.js"

style="width:25%;"></a>

</div>

</div>

<div id="cindyjs" class="w3-quarter w3-container w3-margin-bottom">

<div class="container">

<a href="https://cindyjs.org/" target="_blank"><img class="w3-image" src="images/cindyjs.png" alt="Cindy.js"

title="Cindy.js" style="width:25%;"></a>

</div>

</div>

<div id="cindyjs" class="w3-quarter w3-container w3-margin-bottom">

<div class="container">

<a href="http://mathcell.org/" target="_blank"><img class="w3-image" src="images/mathc.png" alt="MathCell"

title="MathCell" style="width:25%;"></a>

</div>

</div>

</div>

<br />

<p>Although I advocate for the use of computers as an aid to geometric reasoning,

I highly encourage you to practice your problem solving skills by solving

the suggested exercises, or filling the missing details, that you will

encounter throughout the sections.</p>

<p>Think of the computer as a physicist would his laboratory. It may be used

to check existing ideas about our world, or as a tool to discover new phenomena

which then poses new ideas or challenges for their explanation.

Throughout the sections I have provided detailed instructions (in some cases)

to explore concepts and relationships about complex numbers using specific softwares,

nevertheless you must still keep in mind that computer hardware and software

are ephemeral things in comparison with mathematical ideas, which are timeless.</p>

<p class="callout"><strong>NOTE!</strong> If you’re on a mobile device, some of the applets might not work super well for you.

They are designed for mouse input, so if you’re getting frustrated or your finger is in the way, try the site on a computer.</p>

<!--<p>Complex functions sometimes have the reputation of being mysterious entities;

<h2>ISSUES?</h2>

<p>Of course, no project such as this can be free from errors and incompleteness.

If you find applets that don't run correctly, or the examples that aren't explained

quite right, or a typo, please

<a href="https://github.com/complex-analysis/complex-analysis.github.io/issues">report them at this

project's GitHub repository</a>.

Thanks for your help!</p>

<h2>DESIGN CREDITS</h2>

<p>The design of this book is based upon the fantastic book

<a href="https://www.jeffreythompson.org/collision-detection/index.php" target="_blank">Collision Detection</a>

written by <a href="https://www.jeffreythompson.org/" target="_blank">Jeffrey Thompson</a>. If you

want to learn about the algorithms behind collisions using basic geometrical shapes,

you should check it!</p>

<h2 id="support">SUPPORT THIS PROJECT</h2>

<p>If you like this work and would like to support it with a donation, you can do it using the links below. Thank you for your support!</p>

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<div class="w3-center"><a class="w3-button w3-light-grey w3-round w3-hover-text-blue"

href="mailto:jcponcemath@gmail.com">Just want to say thanks</a></div>

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<h2>NAVIGATION</h2>

<p>OK, let's begin! Click the link at the bottom the page, or the arrows at the top, to

move to the next chapter. The <code>Complex Analysis</code> link at the top will

take you back to the <a href="content/table_of_contents.html">Table of Contents</a>.</p>

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