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Modeling and simulation are important in research. Representing the real systems either via physical reproductions at smaller scale, or via mathematical models that allow representing the dynamics of the system via simulation, allows exploring system behavior in an articulated way which is often either not possible, or too risky in the real world.
The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social ...
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes.The shapes studied in geometric modeling are mostly two- or three-dimensional (solid figures), although many of its tools and principles can be applied to sets of any finite dimension.
Mathematical modeling is the use of mathematical language to describe the behaviour of a system. Subcategories. This category has the following 12 subcategories, out ...
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance).
The models in this chapter are constructed as the boundaries of solid objects, via two-dimensional paper cross-sections, and by string figures. [ 1 ] The fifth chapter, and the final one of the first edition, includes mechanical apparatus including harmonographs and mechanical linkages , [ 1 ] the bean machine and its demonstration of the ...
Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict.
In control engineering and system identification, a state-space representation is a mathematical model of a physical system specified as a set of input, output, and variables related by first-order differential equations or difference equations.