University of British Columbia
Vancouver, British Columbia, Canada
Mathematics offers engineers a vast array of sophisticated tools, but in practice these tools often outstrip the ability to use them. This occurs because mathematical power is seldom the barrier in solving problems faced by engineers. Rather, the barrier is one of defining a physical problem in mathematical terms, or extracting physical meaning from a mathematical expression. Once this link between physical phenomena and mathematics is established, often first or second year calculus is sufficient for an engineering solution.
Two examples illustrating these links will be described. First, the physical significance of imaginary components in the solution of simultaneous differential equations describing high speed paper making led to some new insights on pressure oscillations. Second, a simple empirical equation was inexplicably found to describe transient state plugging in pulp screens. A closer examination of this equation revealed that it was, in essence, the simple resistance equation with all terms dependent upon time.