Universidad Simón Bolívar Ingles para M atemáticos

1. Universidad Simón BolívarIngles para Matemáticos Mathematicalmodel Luis Augello 08-11280

2. Definition A mathematical model is a description of a system using mathematical concepts and language. Is one of the types of scientific models that used some kind of mathematical formalism to express relationships, substantive statements of facts, variables, parameters, entities and relationships between variables and / or entities or operations, to study behaviors of complex systems with difficult situations observe in reality. Application Los modelos matemáticos se utilizan no sólo en las ciencias naturales (tales como física, biología, ciencias de la tierra, la meteorología) y disciplinas de ingeniería (por ejemplo, la ciencia informática, inteligencia artificial), sino también en las ciencias sociales (como la economía, la psicología, la sociología y la política ciencia), físicos, ingenieros, estadísticos, analistas de investigación de operaciones y los economistas utilizan modelos matemáticos más ampliamente. Un modelo puede ayudar a explicar el sistema y para estudiar los efectos de los distintos componentes, y para hacer predicciones sobre el comportamiento.

3. Examples of mathematicalmodels • Many everyday activities carried out without a thought are uses of mathematical models. A geographical map projection of a region of the earth onto a small, plane surface is a model which can be used for many purposes such as planning travel. • Model of a particle in a potential-field. In this model we consider a particle as being a point of mass which describes a trajectory in space which is modeled by a function giving its coordinates in space as a function of time. The potential field is given by a function V : R3 → R and the trajectory is a solution of the differential equation • Computer Science: models in Computer Networks, data models, surface model

4. Classification of models • According to the information input     -Heuristics (Greek euriskein 'find, invent'). Are those based on the explanations of natural causes or mechanisms that lead to the phenomenon studied.-Empirical models (Greek empeirikos on the 'experience'). Are using direct observations or the results of experiments of the studied phenomenon. • Depending on the type of representation     -Qualitative or conceptual models, they can use pictures, graphics or causal descriptions generally are content to predict whether the system state in a certain direction will be increased or decreased or whether some extent, regardless of exactly how much concrete in most respects.     - Quantitative or numerical models, using numbers to represent aspects of the modeled system, and generally include mathematical formulas and algorithms more or less complex to relate the numerical values.