This text provides numerical algorithms and associated software for solving a spectrum on problems of ordinary differential equations (ODEs), differential algebraic equations (DAEs) and partial differential equations (PDES) that occur in science and engineering. Detailed examples are presented including, in each case, a complete analysis of a computer code written in transportable FORTRAN 77. Each example includes a discussion of the problem equations, the coding of the equations and the computed numerical solution. The benefits of using quality general-purpose library routines to solve ODE/DAE/PDE problems are illustrated as well.