1. Software for scientific calculations

2. Software for Mathematics
Mathematica
Maple
Matlab
IDL
SciLab
Octave …

3. Mathematica - commercial system of symbolic and numerical calculations developed in 1988 by Stephen Wolfram. During more than 20 years of existence, Mathematica has become very popular among scientists and engineers.
Mathematica is split into two parts, the kernel and the front end. The kernel interprets expressions (Mathematica code) and returns result expressions.
The front end, designed by Theodore Gray, provides a GUI, which allows the creation and editing of Notebook documents containing program code with prettyprinting, formatted text together with results including typeset mathematics, graphics, GUI components, tables, and sounds. All contents and formatting can be generated algorithmically or interactively edited. Most standard word processing capabilities are supported, but there is only one level of "undo." It includes a spell-checker but does not spell check automatically as you type.
Documents can be structured using a hierarchy of cells, which allow for outlining and sectioning of a document and support automatic numbering index creation. Documents can be presented in a slideshow environment for presentations. Notebooks and their contents are represented as Mathematica expressions that can be created, modified or analysed by Mathematica programs. This allows conversion to other formats such as TeX or XML.
The front end includes development tools such as a debugger, input completion and automatic syntax coloring.

4. Maple – CAS-type computer program used to perform symbolic computation, created in 1981 by the Symbolic Computation Group at the University of Waterloo in Canada.
Users can enter mathematics in traditional mathematical notation. Custom user interfaces can also be created. There is support for numeric computations, to arbitrary precision, as well as symbolic computation and visualization. Examples of symbolic computations are given below.
Maple incorporates a dynamically typed imperative-style programming language which resembles Pascal.[1] The language permits variables of lexical scope. There are also interfaces to other languages (C, C#, Fortran, Java, MATLAB, and Visual Basic). There is also an interface with Excel.
Maple supports MathML 2.0, a W3C format for representing and interpreting mathematical expressions, including their display in Web pages.
Maple is based on a small kernel, written in C, which provides the Maple language. Most functionality is provided by libraries, which come from a variety of sources. Many numerical computations are performed by the NAG Numerical Libraries, ATLAS libraries, or GMP libraries. Most of the libraries are written in the Maple language; these have viewable source code.
Different functionality in Maple requires numerical data in different formats. Symbolic expressions are stored in memory as directed acyclic graphs. The standard interface and calculator interface are written in Java. The classic interface is written in C.

5. MATLAB - program komputerowy będący interaktywnym środowiskiem do wykonywania obliczeń naukowych i inżynierskich, oraz do tworzenia symulacji komputerowych.
MATLAB (matrix laboratory) is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran.
Although MATLAB is intended primarily for numerical computing, an optional toolbox uses the MuPAD symbolic engine, allowing access to symbolic computing capabilities. An additional package, Simulink, adds graphical multi-domain simulation and Model-Based Design for dynamic and embedded systems.

6. IDL (Interactive Data Language), is a programming language used for the numerical processing of large amounts of data.
IDL, short for Interactive Data Language, is a programming language used for data analysis. It is popular in particular areas of science, such as astronomy and medical imaging. IDL shares a common syntax with PV-Wave and originated from the same codebase, though the languages have subsequently diverged in detail. There is also a free implementation, GNU Data Language (GDL).
IDL is vectorized, numerical, and interactive, and is commonly used for interactive processing of large amounts of data (including image processing). The syntax includes many constructs from Fortran and some from C.

7. Scilab – software to perform scientific calculations, the program is based on the open source license

8. Octave – based on GNU license high level interpretive language to perform numerical calculations (very similar to MATLAB)

9. Arrays creation

10. Creation and displaying of the vector of data

11. Definition of vector variables

12. Definition of tables

13. Operations on vectors

14. 2D and 3D graphics

15. Integrate a function

16. Solving the equations

17. Solving systems of equations

18. Reading data from text files

19. The analysis by FFT

20. Loading images, filtering and presentation

21. Various forms of data presentation