of infinite mathematical series that
involves trigonomic functions. More sim-
ply put, it is essentially an infinite sum of
sine waves. The Fourier series is used in
applied mathematics. In engineering and
physics, it is used to split up a periodic
(or continuous) function into a group of
simpler terms; in electronics, it is used to
express the periodic functions seen in
waveforms of communications signals.
What is a finite element analysis?
A finite element analysis (also known as
FEA or finite element method) is a power-
ful tool to solve problems in engineering,
especially for heat transfer, fluid mechan-
ics, and mechanical system problems. The
FEA consists of a computer model of a
material or design that is stressed; the out-
come is then analyzed for specific results.
In reality, the computer is conducting a
numerical analysis technique used for
solving differential equations, and relating
it to stress in the engineering problem.
This technique was first developed in 1943 by Richard Courant (1888–1972), who
used a form of FEA to find approximate solutions to vibrational systems. Early in the
1970s, only companies that owned expensive mainframe computers were using FEA,
including the aeronautic, automotive, defense, and nuclear industries. Since the mid-
1990s, however, use of FEA has grown with the advent of faster and cheaper comput-
ers with more memory. The results are more accurate, too, allowing various industries
to analyze new product designs and refine existing products.
What types of analysesinterest engineers?
There are several types of analyses that interest engineers, all of which involve mathe-
matical modeling. Structural analysisdeals with linear and nonlinear models and
stresses on a material. The linear models assume the material does not plastically
deform (the remaining deformation after the load causing it is removed); nonlinear
models stress the material past its elastic capabilities. The stresses in the material
then vary with the amount of deformation. Vibrational analysisdeals with possible
resonance and subsequent failure. It is used to test a material that may experience 325
MATH IN ENGINEERING
When Napoleon Bonaparte led his army into Egypt,
French mathematician and physicist Baron Jean
Baptiste Joseph Fourier joined him and was a scien-
tific adviser. Fourier also worked for Napoleon when
he was involved in draining the Bourgoin swamps
and building a new highway. Library of Congress.