A robust numerical method is presented for integration and parametric sensitivity analysis of nonlinear initial-boundary-value problems in a timelike dimension t and a space dimension x. Mixed systems of partial differential and algebraic equations can be treated. Parametric derivatives of the calculated states are obtained directly via the local Jacobian of the state equations. Initial and boundary conditions are efficiently reconciled. The method is able to handle jump conditions induced by changes of equation forms at given t-values, or at unknown t-values dependent on the solution. Transition points of the latter kind are computed via a Newton scheme coupled with the step selection strategy of the integrator. The method is implemented in a portable FORTRAN package PDASAC, and is illustrated with two examples from chemical and biochemical engineering. The acronym PDASAC stands for Partial-Differential-Algebraic Sensitivity Analysis Code.