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