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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