Multivariable calculus.

Engineering fields depend on position, time and several design variables.

Learning outcome: Use partial derivatives, gradients and flux as the language of changing fields.

Use partial derivatives, gradients and flux as the language of changing fields. Diagram is schematic and not to scale.

Core ideas

Build the model

partial derivatives.

gradients and directional change.

multiple integrals and flux.

Engineering bridge

Where it is used

thermodynamics
fluid mechanics
simulation and model verification

Original Lilerno structure and wording. Visuals are conceptual, inputs are not a design specification, and practical work requires appropriate supervision.