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Automated dimensional analysis — Buckingham Pi theorem, non-dimensionalization, unit validation with pint, and characteristic scale estimation. Use before any physics computation to verify consistency and reduce parameter space.
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Mathematical verification for physical calculations: unit tracking algebra (exponent maps), PhysicalQuantity pattern for compound units, SI/Imperial mixed-unit handling, Buckingham pi theorem for dimensionless groups, and common engineering dimensionless numbers. Activates for unit verification, dimensional consistency checks, scaling analysis, and calculation validation across all infrastructure domains.
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Real-world problem formulation, mathematical abstraction, and applied mathematics for translating between practical problems and mathematical frameworks. Covers the modeling cycle (problem identification, assumptions, formulation, analysis, validation, interpretation), Polya's framework adapted for modeling, common model types (linear, exponential, logistic, periodic, power-law), dimensional analysis (Buckingham Pi theorem), optimization (linear programming, gradient descent, constraint satisfaction), probability models (Markov chains, queuing theory, Monte Carlo simulation), statistical modeling (regression, hypothesis testing, model selection), model criticism (overfitting, underfitting, sensitivity analysis), and real-world case studies. Use when formulating mathematical models, performing dimensional analysis, optimizing systems, running simulations, or evaluating model validity.
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