Definition of Numerical Analysis

Mathematics as an area of ​​knowledge has several branches, such as geometry, algebra, probability or numerical analysis. The latter focuses on the study of the different methods that allow solving problems in which numbers are the fundamental reference. The purpose of this version of the mathematical world is to serve other areas, such as programming, cybernetics or different engineering.

General scheme of all numerical analysis

The starting point is always some problem that needs to be solved. From there, the moment of analysis begins, in which the initial problem, its variables and characteristics are studied. For this to be possible, it is necessary to use a specific explanatory model, for example a system of linear equations. Once the most appropriate numerical method has been chosen, it is now possible to handle approximate solutions by creating a algorithm. Finally, with the use of a calculator and the predefinition of the functions, the resolution of the problem is already feasible.

Numerical methods are technical tools for solving mathematical problems and the principles of arithmetic constitute the pillar of this methodology

Current computing and the use of advanced software allow arithmetic operations to be carried out in a simplified way.

The Mathematical Thinking it is a complement for the resolution of any type of logical problems. With the models created in the numerical analysis equations related to a reference system are expressed. Every mathematical model has two parts: a dependent variable and an independent variable.

Without the recourse of the computing only linear models or simple geometry problems can be solved. However, with computer techniques it is possible to solve more complex problems (for example, questions related to a greater number of data or questions associated with the three dimensions space).

In numerical analysis with computer tools, it is necessary that the machines be designed so that the mathematical language is translated in an understandable way. At the origins of this discipline Issues such as the following were addressed: iterative methods to solve problems framed in linear systems or methods of differential equations. In any case, the most widespread numbering system is binary.

In the ancient world there was already a rudimentary numerical analysis

The numerical understanding of reality was present in the first civilizations. Thus, we find the trace of numerical methods in the building of the pyramids in Ancient Egypt, in the irrigation systems in Mesopotamia or in the transport of water by aqueducts in Roman civilization.

Fotolia photos: Janaka Dharmasena / Ilkercelik