Illustrating the Benefits of Embracing an Integrated Applied Mathematics Initiative: TRANSPORT PARAMETERS,LAPLACE TRANSFORMS,AND RESIDUE THEOREM

摘要

An example problem is presented here to illustrate the relative straightforwardness of a number of viable mathematical concepts often thought of as complex and unwieldy.These are concepts that engineering students often either shy away from-considering them too difficult to apply-or may just simply be unaware of.These knowledge gaps or confidence-level issues can be quite restrictive,and can lead to poor choices with respect to adequately and accurately representing system behavior.Ideally,when en route to obtaining robust solutions to relevant technological problems it is imperative to avoid undue oversimplifications and/or assumptions that can limit a solution's range of applicability,or sometimes even render it essentially useless.Unfortunately,too often systems are modelled using these restrictive approaches.Consequently,the opportunity to obtain the desired robustness is often lost.This can be extremely problematic(a)when evaluating model predictive control(MPC)strategies via simulation protocols and(b)in establishing evaluation criteria for the various design scenarios involved in both process systems and advanced materials development,as these rely upon characterization via transport property determinations(Cussler,[1] Bird,et.al.,|2] Deen,[3] and Incropera and DeWitt[4]).This latter issue is particularly relevant in the emerging area of nanotechnology,and specifically in its role in delivery platforms.Representative materials include:(i)smart membranes,as biomirnetic systems or as encapsulation materials/surfaces with unique barrier properties;(ii)novel chaperones for drag delivery and controlled release;and(iii)nano-scale entities that are entrapped in macro-scale matrices to produce unique physicochemical properties with enhanced performance characteristics(e.g.,Johnson,et.al.,[5] Sokolnicki,et.al.,[6] and Panagiotou and Fisher[7]).Topics such as these are of growing importance,and feature in both core and elective courses offered to support the student's multiple options with respect to concentration tracks.