D H Trollope Lecture: The Mathematics of Engineering

Dr Glen Peters, University of Newcastle

Boundary conditions are critical to the solution of most differential equations encountered in the physical sciences and engineering. In many mathematical models great lengths are taken to derive and explain the governing differential equations, the boundary conditions seem to be an optional extra!

It is an easy procedure to show how a small change in boundary conditions can lead to vastly different solutions to most equations. If the mathematical equations are so sensitive to changes in boundary conditions, shouldn’t we give them a little more attention?

This presentation takes us on a journey through the selection of boundary conditions for the advection-dispersion, equation regularly encountered in geoenvironmental engineering. Much of the discussion is quite general and is applicable to other areas of engineering.

A novel mathematical model is discussed that can circumvent the requirement for boundary conditions. In the limit the model converges to the standard techniques requiring boundary conditions. Thus giving an alternative approach to verifying the validity of certain boundary conditions.

An underlying theme of this talk is the relationship between mathematics and engineering. Should you have total trust in your mathematical model even if it does not agree with reality, or is it okay to “fudge” a few technicalities if it means it will fit to data?

The Mathematics of Engineering versus the Engineering of Mathematics…

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