Laplacian Differential Operator in Matrix Form

The Laplacian differential operator, so important in many investigations requiring the application of orthogonal curvilinear coordinates, is presented using a novel compacted matrix format. This alternative is easily memorized and can be converted, if necessary, to the standard final formulation with subindices regularly appearing in books. It therefore contrasts with the classical vector representation or the tedious chain rule mechanics. In the author’s opinion, matrix notation and their operational calculus, due to their recent preponderance in computer programming, appears to be more familiar to the majority of present-day college students pursuing a degree in engineering or physical science fields. Consequently, in this Technical Note some differential operators written in matrix form will be introduced as an alternative to other classical methodologies, perhaps, to be considered by some journal readers more versed with matrix operations and their practical implementation.