Over the last two years, we have been developing a library of Matlab subprograms integrated with on-line lecture notes in the form of WWW documents which are used in both undergraduate and graduate-level Chemical Engineering Applied Mathematics classes. The goal has been to make as transparent as possible the relationships between model development, solution, and analysis of systems described by partial differential equation models. This paper presents the results of our initial efforts to create computational modules which have a one-to-one correspondence with each step of implementing eigenfunction expansion, Galerkin's, and other weighted residual methods. Examples representing heat transfer in a cylinder, and gas flow and heat transfer in a chemical vapor deposition reactor are presented.