Taketechease - Mathematics Computational Physics - Free Software And Courses
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The main scope of interest considers scientific computer programs and mobile applications together with the educational path, however, another piece of work is also developed. The latter one includes
Scientific applications are based on the following mathematical methods: the finite element method, genetic algorithms and the machine learning.
The first above-mentioned method, the Finite Element Method, allows to solve multi-dimensional differential equations. Differential equations are used to describe a huge amount of phenomena in various different scientific areas ranging from physic, chemistry, biology to economics. The Finite Element Method is a mathematical technique used to find a discrete approximation to the exact continuum solution. As every approximate technique, this approach can be easily translated into computer procedures. Among a large variety of approximate methods, the Finite Element Method has considerable better numerical accuracy than other standard discrete approaches.
Genetic algorithms are one of numerical methods for finding 'the best' fitted individuals within a population of organisms. In biology, the fitness of organism refers to its ability to 'survive' and 'reproduce' in given environment. In contrary, the genetic algorithms are a numerical method where an individual object can represent not real organism but some numerical attribute (just a number). And therefore, its goodness is considered in relation to some mathematical condition. For example, if one can find the minimum of a mathematical problem then an individual (i. e. number) fitness reflects how close to the minimum value our number is. Thus genetic algorithms work as function 'optimisers'.
The third numerical method is the machine learning. Machine learning approach is aimed at finding such a system configuration that allows to cooperate with environment in the most efficient way.
Free Scientific Software
At that moment the following numerical packages are available:
Metfem2d - FEM Solver for time-dependent two-dimensional (spatially) linear differential problems based on the Finite Element Method (FEM);
OptFinder for genetic algorithms simulation.
and in preparation:
Metfem3d - FEM Solver for time-dependent three-dimensional (spatially) linear differential problems based on the Finite Element Method (FEM)
OptFinderML for a genetic-based machine learning systems. This package contains modules for stochastic and chaotic analysis.
Free Online Courses
Together with the above-mentioned mathematically advanced applications few free online courses are also provided:
I hope that they both will be recognised as a good announcement for much more complicated software in preparation. To learn more use topics presented below (i. e. The Scope Of Goods On Offer).
Last update: August 31, 2023
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