mathematical-modeling

What I do

• Translate real-world problems into mathematical models
• Apply differential equations for dynamic systems
• Use statistical models for data analysis
• Optimize using linear and nonlinear programming
• Validate and calibrate models with data
• Analyze model sensitivity and uncertainty

When to use me

When predicting system behavior, optimizing processes, or understanding complex phenomena.

Key Concepts

• Differential Equations: Model continuous change over time
• Linear Programming: Maximize/minimize linear objective with constraints
• Statistical Models: Regression, ANOVA, time series
• Sensitivity Analysis: How output changes with input variations
• Dimensionless Numbers: Buckingham Pi theorem for scaling
• Model Validation: Compare predictions to observed data