4.1. Definition

Nonlinear equations are those that cannot be written in the form \(\vv{A}\vv{x} = \vv{b}\). Such equations come up in many places:

• Equations of state \(P(T, V)\)

• Second-order reactions \(2\,{\rm A} \to {\rm B}\), \(r_{\rm A} = -k c_{\rm A}^2\)

• Optimization/process design of full systems