Mathematics for Scientific Modeling

Linear Transformations

Core step

Structure-preserving mappings of vectors represented by matrices, including area scaling and orientation behavior.

Derivative

Core step

Local rate of change represented as the limit of secant slopes and geometrically as tangent slope where differentiable.

Definite Integral

Core step

Accumulated signed quantity over an interval represented by a limiting sum.

First-Order Differential Equations

Core step

Equations relating an unknown function to its first derivative and therefore to a local rate of change.

Probability Density Functions

Optional branch

Continuous probability models represented by nonnegative normalized density functions.

A parallel modeling branch focused on continuous uncertainty and normalization.