Python and MATLAB code to find the definite integral of a user-defined function within given limits and defined iterations.

There are in total 4 files in the repository, each following a different algorithms, namely Monte Carlo, Trapezoidal Rule and the two Simpson's Rules. Code for the Legendre-Gauss Quadrature formula will be added soon. Each folder contains MATLAB or .m and Python or .py. So you can use either syntax and program/language to numerically determine the roots of an equation/function using the given Methods or algorithms.

To access the files you can either Download the zip file or use the following command from your terminal

git clone https://github.com/adisen99/Numerical-Integration.git

then

cd Numerical-Integration

Then you can access the .py files or .m files depending on the program you wish to run. Please note than Simpson's3 is the Simpson's 1/3 and the Simpson's8 is the Simpson's 3/8 rule. The Simpson's3 folder contains two MATLAB files one of which has a much simpler algorithm as compared to the other more difficult one. Also the Trapezoidal_Rule folder contains two MATLAB and two Python files. One set is marked as easy and thus has a much easier algorithm, however the user can choose to run the more complex ones.

This program uses the following libraries as dependencies-

• Matplotlib
• NumPy
• SciPy
• Code2pdf (Optional, only to get your code as a pdf file)

• For Windows/Linux/Mac users

You can install these libraries using pip (if you have a virtual environment created and only want to install the libraries for that particular file/directory)

pip install <name of the library>

or Alternatively you can install using pip for your own user system-wide

python -m pip install --user <name of the libraries separated by a space>

or you could use conda (if you are using Anaconda IDE)

conda install <name of the library>

or (If you are using a Linux distribution) then you can simply use you distro's package manager to install the packages (but it will install the packages system wide)

• For Debian/Ubuntu users-

sudo apt install python-<name of the library>

• For Fedora users-

sudo dnf install numpy scipy python-matplotlib

• For Arch users-

sudo pacman -S python-<package name>

or

yay -S python-<package name>

Most python packages are in the ArchLinux repositories and the packages that are not are in AUR (ArchLinux User Repositories) - for these packages you have to download the PKGBUILD file and compile. After that, you have to use PACMAN to finish the installation

makepkg -s sudo pacman -U 'compiled-package'

• For Mac users-

Mac doesn’t have a preinstalled package manager, but there are a couple of popular package managers you can install. For Python 3.5 with Macports , execute this command in a terminal:

sudo port install py35-numpy py35-scipy py35-matplotlib

or Alternatively Homebrew has an incomplete coverage of the SciPy ecosystem, but does install these packages:

brew install numpy scipy matplotlib ipython jupyter