Analytical Mathematical Model

A Analytical Mathematical Model is a mathematical model that has a closed form solution (expressed as a mathematical analytic function).

• AKA: Analytical Model, Analytical Function, Mathematical Analytic Model.
• Context:
  • It can typically represent System Change through analytical mathematical functions.
  • It can typically express Solution as a analytical mathematical closed form expression.
  • It can typically describe System Behavior using analytical mathematical equations with analytical mathematical exact solutions.
  • It can often enable Mathematical Analysis of analytical mathematical complex systems without requiring numerical methods.
  • It can often provide Exact Answer to analytical mathematical problems without approximation.
  • It can range from being a Simple Analytical Mathematical Model to being a Complex Analytical Mathematical Model, depending on its analytical mathematical equation complexity.
  • It can range from being a Domain-Specific Analytical Mathematical Model to being a General-Purpose Analytical Mathematical Model, depending on its analytical mathematical application scope.
  • ...
• Examples:
  • Analytical Mathematical Model Types, such as:
    • Differential Equation Analytical Mathematical Models, such as:
      • Linear Differential Equation Analytical Mathematical Model for analytical mathematical system dynamics modeling.
      • Partial Differential Equation Analytical Mathematical Model for analytical mathematical physics modeling.
    • Statistical Analytical Mathematical Models, such as:
      • Linear Regression Analytical Mathematical Model for analytical mathematical trend analysis.
      • Probability Distribution Analytical Mathematical Model for analytical mathematical uncertainty modeling.
    • Economic Analytical Mathematical Models, such as:
      • Supply-Demand Analytical Mathematical Model for analytical mathematical market equilibrium calculation.
      • Capital Asset Pricing Analytical Mathematical Model for analytical mathematical investment analysis.
  • ...
• Counter-Examples:
  • Numerical Models, which lack analytical mathematical closed form solutions and require computational approximation.
  • Simulation Models, which rely on iterative computation rather than analytical mathematical analytic functions.
  • Statistical Models, which focus on data-driven inference rather than analytical mathematical derivation.
• See: Analytical Function, Analytics, Mathematical Model, Computational Model, Mathematical Analysis Subject Area.

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References

2020

• (Serc, 2020) ⇒ https://serc.carleton.edu/introgeo/mathstatmodels/Analytical.html
  • QUOTE: Analytical models are mathematical models that have a closed form solution, i.e. the solution to the equations used to describe changes in a system can be expressed as a mathematical analytic function.

1999

• (Zaiane, 1999) ⇒ Osmar Zaiane. (1999). “Glossary of Data Mining Terms.” University of Alberta, Computing Science CMPUT-690: Principles of Knowledge Discovery in Databases.
  • QUOTE: Analytical Model: A structure and process for analyzing a dataset. For example, a decision tree is a model for the classification

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