A gamut of mathematical subjects and concepts are taught within a handful of courses formally required of the typical engineering student who so often questions the relevancy of being bound to certain lower-division prerequisites. Basic classes at the undergraduate level, in this context, include: Integral and Differential Calculus, Differential Equations, and Matrix (or Linear) Algebra. Focusing on but one sub-discipline within engineering, namely, Mechanics, the author attempts to expose the sheer pertinence of each of the aforementioned mathematical subjects as they unavoidably have materialized in various forms throughout his teaching experiences; specifically, an example is drawn from each of the following classes: Advanced Structural Analysis, Analysis of Plates and Shells, Fracture Mechanics and Fatigue, and Composite Materials. While comprehensiveness is not the aim of this article, the sampling of themes that are expounded upon--rudimentary to all disciplines of science and engineering--unearth such a commanding cross section of mathematical topics in their wake to warrant special consideration by every conscientious student. (Contains 4 figures.)