Foundations

Graphs represent pairwise connections; trees impose acyclicity.

An interface defines operations; an implementation determines costs.

An invariant establishes correctness only with its proof obligations.

Distinct-key comparisons need enough branches to distinguish orders.

Graph searches visit reachable vertices using different orders.

Edge weights determine which shortest-path method applies.

Finite instructions can act on an unbounded writable tape.

A relation is a set of tuples from declared domains.

External force controls the mass-weighted centre's acceleration.

A tensor relates rotation to angular momentum.

Body-axis angular acceleration includes rotation of the axes.

Stationary action supplies coordinate equations of motion.

Canonical coordinates and momenta evolve from the Hamiltonian.

Density change balances mass flux through a region.

An ideal steady flow balances pressure, motion and height.

Fluid inertia balances pressure, viscosity and gravity.

Compare inertial and viscous scales of a flow.

A linear restoring force, damping and periodic drive determine response.

A local differential equation determines small string disturbances.

Linear disturbances add; their relative phase determines reinforcement.

Boundary conditions select standing-wave frequencies.

Angles at an interface depend on refractive indices.

A paraxial lens relates object and image distances.

An aperture's finite width selects dark far-field directions.

An ideal analyzer transmits the field component along its axis.

Scalar and vector potentials encode electric and magnetic fields.

A linear two-conductor arrangement stores separated charge.

Changing current changes linked magnetic flux and induced emf.

The rate of field-energy change balances outward energy flow and power transferred to charges.

Lumped circuit models balance node currents and loop voltages.