Mathematics as an area of knowledge has several branches, such as geometry , algebra, probability and numerical analysis. The latter studies the most varied methods for solving problems, of which numbers are the fundamental reference. The purpose of this version of the mathematical world is to put itself at the service of other areas, such as programming, cybernetics and various engineering.
General scheme of all numerical analysis
The starting point is always some problem that needs to be solved. From that moment on, the moment of analysis begins, from which the initial problem, its variables, as well as its characteristics are studied. For this to be possible it is necessary to employ a determined explanatory model, for example, a system of linear equations. Once chosen the most suitable numerical method , it is possible to manipulate with the approximate solutions through the creation of an algorithm. Finally, with the use of a calculator and the presetting of functions, it is possible to solve the proposed problem. Numerical Analysis
Numerical methods are technical tools for solving mathematical problems and the principles of arithmetic are the pillar of this methodology.
Current computing and the use of advanced software allow arithmetic operations to be performed in a simplified manner
The thought mathematician is an addition to 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 resource of computation it is only possible to solve linear models or simple geometry problems. However, with computation techniques it is possible to solve the most complex problems (for example, the questions related to a larger number of data or the questions associated with the three spatial dimensions).
In numerical analysis with computer tools, machines need to be designed in such a way that the mathematical language is translated in an understandable way. In the origins of this discipline, several issues were addressed, such as the following: iterative methods to solve problems framed in linear systems or differential equation methods. Anyway, 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 a trace of numerical methods in the construction of the pyramids of Ancient Egypt, in the irrigation systems in Mesopotamia, or in the transport of water through aqueducts in Roman civilization.