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The partial differential equation (Cole and Cook 1986, p. 34; Zwillinger 1997, p. 134).

The system of partial differential equations U_t = [V,W] (1) V_t = [W,U] (2) W_t = [U,V], (3) where [A,B] denotes the commutator.

Partial differential equation boundary conditions which give the normal derivative on a surface.

The partial differential equation u_(xx)=au_(tt)+bu_t+cu.

The partial differential equation u_(xy)+alphau_x+betau_y+gammau_xu_y=0.

The partial differential equation iu_t+[(1+|u|^2u)^(-1/2)u]_(xx)=0.

Anomalous cancellation is a "canceling" of digits of a and b in the numerator and denominator of a fraction a/b which results in a fraction equal to the original. Note that ...

The largest unit fraction, 1/2. 1/2 is a rational number with terminating decimal expansion 0.5.

The unit fraction 1/4, also called one-fourth. 1/4 is a rational number with terminating decimal expansion 0.25.

The partial differential equation partial/(partialx)(u_t+uu_x+1/2u_(xxx)+u/(2t))+(3alpha^2)/(2t^2)u_(yy)=0 which arises in the study of water waves.