Envelope viscosity solutions of first- and second-order PDEs with u-dependence

General envelope methods are introduced which may be used to embed equations with u-dependence into equations without solution dependence. Furthermore, these methods present a rigorous way to consider so-called nodal solutions. That is, if w(t,x,z) is the viscosity solution of some pde, the nodal solution of an associated pde is a function u(t,x) so that w(t,x,u(t,x))=0. Examples are given to first- and second-order pdes arising in optimal control, differential games, minimal time problems, scalar conservation laws, geometric-type equations, and forward backward stochastic control.