Chebfun is an open-source software system for numerical computing with functions. The mathematical basis of Chebfun is piecewise polynomial interpolation implemented with what we call “Chebyshev technology”. The foundations are described, with Chebfun examples, in the book _Approximation Theory and Approximation Practice_. Chebfun has extensive capabilities for dealing with linear and nonlinear differential and integral operators, and it also includes continuous analogues of linear algebra notions like QR and singular value decomposition. The Chebfun2 extension works with functions of two variables defined on a rectangle in the x-y plane. To get a sense of the breadth and power of Chebfun, a great place to start is by looking at our [Examples][1].

The mathematical basis of Chebfun is numerical algorithms involving piecewise polynomial interpolants and Chebyshev polynomials, and this is where the name "Cheb" comes from. The package aims to combine the feel of symbolic computing systems like Maple and Mathematica with the speed of floating-point numerics. The Chebfun project is based in the Mathematical Institute at the University of Oxford and was initiated in 2002 by Lloyd N. Trefethen and his student Zachary Battles. Its most recent version is on the web:
https://www.chebfun.org/download/
or from MathWorks web site.

To install, you can either clone the directory with Git or download a .zip file. Note that a call to `clear classes` is required if you had a previous version of Chebfun installed.

## Option 1: Download .zip file Download a .zip of Chebfun from - https://github.com/chebfun/chebfun/archive/master.zip

After unzipping, you will need to add Chebfun to the matlab path. You can do this either (a) by typing
```
addpath(chebfunroot), savepath

where `chebfunroot` is the path to the unzipped directory, (b) by selecting the `chebfun` directory with the `pathtool` command, or (c) though the File > Set Path... dialog from the matlab menubar.

## Option 2: Clone with Git
To clone the Chebfun repository, first navigate in a terminal to where you want the repository cloned, then type
```
git clone https://github.com/chebfun/chebfun.git
```
To use Chebfun in matlab, you will need to add the `chebfun` directory to the matlab path as above.

Most Chebfun commands are overloads of familiar matlab commands — for example sum(f) computes an integral, roots(f) finds zeros, and u = L\f solves a differential equation. To get a sense of the breadth and power of Chebfun, a good place to start is by looking at our Examples (http://www.chebfun.org/examples/) or the introductory Guide (http://www.chebfun.org/docs/guide/). Please contact us with any questions/comments at help@chebfun.org.

x = chebfun('x',[0,10]);

f = sin(x) + sin(x.^2);  plot(f)
r = roots(f); hold on, plot(r,f(r),'.r'), hold off

figure(1)
plot(x, y, 'Color', [1 0 0]) %blue line
hold on
plot(x, z, 'Color', [0 1 0]) %green line