Mechanical Engineering
 Associate
Professor John Browne at Swinburne University of Technology
in Australia teaches an undergraduate-level engineering design course
as well as a Mathematica-based programming course for
second-year engineering students. A self-described "Mathematica
addict," he uses it not only as an all-purpose teaching tool in the
classroom but also exclusively for his research.
In addition, Browne and a colleague started Quantica Pty Ltd, a
Mathematica consulting company. Its mission is to specialize in
all things Mathematica-related, from training and consulting to
webMathematica and technical publishing.
Live Production
Browne uses Mathematica extensively in his engineering design
classes, composing and presenting the lessons to his students entirely as
Mathematica notebooks. The goal of the courses is to give students
a thorough introduction to all elements of engineering design from machine
elements to the design of products for mass production.
Mathematica is also ideal for developing formulas symbolically in class.
Says Browne, "We don't need to be satisfied with one-off calculations any
more. Now, Mathematica can develop many of the complex general
design formulas we need, live in front of the class."
In his programming class, students receive a project to create a
Mathematica package. For the last two years, this has
constituted predicting the top speed attainable by different types of
cars on different types of roads with various inclines, in various
gears, and in either two-wheel or four-wheel drive. The package is
constructed as a professional document that can be forwarded to
colleagues who could run the functions in the package to make their
own predictions.
Why Mathematica? Says Browne, "It provides a high-level
programming, computation, and graphics environment in which professionals can
prototype their ideas and computations, create packages encapsulating
their algorithms, and make them easily available to colleagues around the
world."
Developing Solutions
Probabilistic Design
Most of the variables that engineers deal with have "unsure" values. For
example, a civil engineer designing a building would calculate stresses in
the various structural members due to, among other things, the force
produced by the wind. But what value of wind velocity should be used?
Because wind velocity is a random variable, only the probability of the
wind reaching a certain velocity in the life of the building is known.
Probabilistic design is a method that takes into account this inherent
variability and produces designs that are predicted to work under all
probable circumstances that might arise.
Mathematica enables you to easily handle the laws of computing
with random variables. "For example," says Browne, "its powerful
differentiation capabilities allow you to determine any function of a
single random variable, while its graphic capabilities enable all
aspects of the computations to be visually presented."
Browne has written a Mathematica package called "The Random Variable
Explorer," which takes a random variable with any probability density
function (discrete, continuous, or mixed) and computes any function of it.
It can also take sums and products of independent random variables. Says
Browne, "If the results of the computations cannot be delivered in closed
form, the package uses Mathematica's ability to create an
expression that can still be tabulated, plotted, or used in subsequent computations."
Grassmann Algebra
Another long-time research interest for Browne has been Grassmann algebra, a
mathematical system that predates vector calculus. It is now emerging as a
potential mathematical system for describing such diverse applications as
engineering mechanics and fundamental theories of matter.
Why was he drawn to Grassmann algebra? Says Browne, "As an engineer, what
enticed me to distraction was that Grassmann algebra could represent a
force in such a way that Newton's law for rigid bodies reduced to just one
equation, instead of the standard two equations for the force and moment
vectors when using three-dimensional vector algebra."
Browne has been working on a Grassmann algebra package for Mathematica.
Using Mathematica to program meaning into mathematical symbols
significantly reduces the time needed for calculations. "Now I could do
all my theoretical computations, be assured of their correctness, do them
in orders-of-magnitude less time, and have the results nicely and legibly
presented," says Browne.
While working on the Grassmann algebra package, Browne has also been
writing a book entitled Grassmann Algebra: Exploring Applications of the
Extended Vector Algebra with Mathematica.
Contact Information
John Browne
Swinburne University of Technology, Australia
web: http://www.ses.swin.edu.au/homes/browne
Send email to John Browne
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