GNU Octave 

GNU Octave is numerical programming software featuring a high-level programming language, primarily intended for numerical computations. It uses matrix based computation, i.e. each input and output is considered as vector/matrix even if input is integer 1.  Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language. Since it is part of the GNU Project, it is free software under the terms of the GNU General Public License.

Octave is one of the major free alternatives to MATLAB, others being Scilab and FreeMat.  Scilab, however, puts less emphasis on (bidirectional) syntactic compatibility with MATLAB than Octave does; and FreeMat has not had an update since June 2013.

This software is helpful to:

1. Economically weak students who want MATLAB like experience and environment in their academic life without paying license fee.

2. Pre-university students being trained to understand in depth mathematics numerically.

3. Who wants to know how function are written by professional working in Software Industry. 

4. Engineers who wants to understand complex algorithm working behind the designing and fabrication software of 3D CAD, CAM and CNC machines.

This software helps in :

1. Understanding of algorithms.

2. Understanding complex theorems like SVD, Matrix Manipulation, Algorithm behind Calculus functions, ODEs etc.

3. Pre-school exposure of numerical software.

4. Easy and fast grasping of algebra, sets, matrix by matric level students.

Why should we use Octave :

1. Free of cost.

2. It is free but not worthless

3. Rich in functionality.

4. Can write own functions/algorithm related to Science, Engineering and Mathematics.

5. Long term support and rich documentation.

6. Compatible to MATLAB and easy to switch propriatory software.

7. It is better to start from scratch rather than from modules.