We present a set of MATLAB functions developed for solving boundary-value problems using globally defined trial function expansions and weighted residual methods (MWR). The numerical techniques form a computational toolbox consisting of a common set of numerical tools for implementing the different MWR techniques used in the numerical solution: and analysis of process systems described by partial differential equation models. This paper presents the results of our initial efforts to create computational modules that have a one-to-one correspondence with each step of implementing eigenfunction expansion, Galerkin projection, collocation, and other weighted residual methods. Examples illustrating the use of the library of subprograms are provided, including discussions of the development and application of more advanced MWR numerical techniques.