MATLAB contains mathematical, statistical, and engineering functions to support all common engineering and science operations. These functions, developed by experts in mathematics, are the foundation of the MATLAB language. The core math functions use the LAPACK and BLAS linear algebra subroutine libraries and the FFTW Discrete Fourier Transform library. Because these processor-dependent libraries are optimized to the different platforms that MATLAB supports, they execute faster than the equivalent C or C++ code.

MATLAB provides the following types of functions for performing mathematical operations and analyzing data:

Matrix manipulation and linear algebra
Polynomials and interpolation
Fourier analysis and filtering
Data analysis and statistics
Optimization and numerical integration
Ordinary differential equations (ODEs)
Partial differential equations (PDEs)
Sparse matrix operations

MATLAB can perform arithmetic on a wide range of data types, including doubles, singles, and integers.

Add-on toolboxes provide specialized mathematical computing functions for areas including signal processing, optimization, statistics, symbolic math, partial differential equation solving, and curve fitting.

Plot showing the complex valued gamma function on the complex plane, where the height of the surface is the modulus, or absolute value, and the contour lines are modulus and phase.