Mathematical modeling
Turn a physical question into a mathematical model before choosing a numerical method. This path assumes algebra, introductory calculus and basic programming. Read in order, or choose the lesson closest to your question.
Build a model
Section titled “Build a model”- Models are not simulations — separate the phenomenon, assumptions, mathematical meaning, realization and observation.
- Quantities, dimensions, and units — reject dimensionally inconsistent relations and recognize what unit checking cannot prove.
- Algebraic relations and networks — count unknowns, constraints and conservation relations in an acausal network.
- Ordinary differential equations — derive scalar decay, run the installed example and compare with the closed-form solution.
Extend it through space
Section titled “Extend it through space”- Fields and spatial domains — place scalar and vector quantities on supports and interpret their spatial operators.
- Conservation laws — connect local and integral statements of storage, flux and source.
- Constitutive laws — close a balance with material relations from transport and mechanics.
- Boundary and interface conditions — distinguish prescribed values, natural conditions, continuity and action–reaction.
Put it to use
Section titled “Put it to use”The ODE lesson includes an executable experiment using the named installed release. The other lessons retain their illustrative examples, derivations, deliberate failures and exercises; their labels state what can be reproduced.
Continue with a practical run-and-results guide, the Gallery investigations, or the Language reference.