# Scientific Modeling Concepts

## Mathematical models to represent reality

- Linear equations
- Non-linear equations
- Differential equations
- Integral/Integral-Differential equations

## Relationship Between Model and Empirical Data

- Model guides data acquisition and investigation
- Data may change parameters in model
- Data may cause model to be changed

## Approximation in Scientific Modeling

- Rigorously derive a model
- Make approximations until computationally tractable
- Make more realistic approximations when have:
- Faster machines
- Better algorithms

## Examples of Changing Approximations

### Computer Graphics

- Ambient light (Phong model)
- Radiosity

### Quantum Mechanics (Molecular Orbital Calculations)

- Huckel
- Semi-Empirical
- Ab Initio

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Last modified on February 11, 1999, G.
Scott Owen, owen@siggraph.org