J. P. Ward

Assessment-driven learning of mathematics for engineering students

HELM (Helping Engineers Learn Mathematics) is a three-year curriculum development project undertaken by a consortium of five universities (Loughborough, Hull, Reading, Sunderland and UMIST) which aims to enhance the mathematical education of engineering undergraduates by the provision of flexible learning resources. HELM makes extensive use of a computer aided assessment (CAA) regime, available in web- and CD-based versions, to drive student learning. This paper first describes the HELM learning resources and outlines the projects assessment philosophy; the HELM assessment regime and how it can be successfully used for both formative and summative assessment are then described. Finally, the viability of the HELM assessment regime across the higher education sector is examined.

Position of Shelf Supports

Using the Euler–Bernoulli beam-bending differential equation we analyse the solution for a shelf deformed under gravity in two situations: (a) simple supports positioned at x = β and x = L – β and (b) Cantilever at one end with a simple support at x = β. We ask where the best position for the supports should be. A number of alternative positions are suggested though the eventual choice of support position is chosen to be that which minimizes the shelfs strain energy.

General Solutions Using the Castigliano Theorem

The Castigliano theorem of solid mechanics is normally used to obtain displacements at specific points on the surface of an elastic body. In this work it will be shown that by using fictitious forces placed in general positions the general solution for the displacement may be found without the need to solve a differential equation. The work also uses the technique to obtain an unusual derivation of the Euler-Bernoulli equation.