mathematically driven software—from
linked computers over a network to
supercomputers—many disciplines that
use applied mathematics have greatly
advanced. For example, the use of giant
wind tunnels to examine wind flow over
aircraft only a few decades ago has been
replaced by computer simulation. Now
the design and testing of aircraft is
accomplished by these simulations, mak-
ing the expense of building physical pro-
totypes a thing of the past because it is
now merely a matter of mathematically
“drawing” the aircraft on the computer in
order to test new designs.How do various disciplines use
applied mathematics?
Depending on the discipline, researchers use applied mathematics in various ways.
For example, some disciplines rely heavily on pure mathematics. Numerical analy-
sis—a form of applied mathematics—is a field that uses pure mathematics to decipher
partial differential equations and variational methods (for more information about
numerical analysis, see below; for partial differential equations, see “Mathematical
Analysis”). There are also areas of applied mathematics that overlap other fields of
study. For example, there are mathematicians who use applied mathematics to study
the structure of matter—especially the behavior of subatomic particles—a field that
also overlaps the same types of studies done by subatomic physicists.Why has the combinationof mathematical analysismethods and computers
been so important?
The combination of mathematical analysis and computers has been a strong alliance,
especially with regard to engineering, technology, and the sciences. In the past few
decades, researchers have used this combination to help predict the weather, describe
in great detail nuclear fusion in the sun, understand the movement of space bodies
around the solar system (orbital mechanics), and the flow of water in underground
aquifers (fluid dynamics). There are also the studies of chaos—the unpredictable
behavior of nonlinear systems—and quantum mechanics, or the physics of very small
particles, both of which entail the use of applied mathematics and computers.
In addition, in engineering (and almost all technology) the mathematical analy-
244 sis-computer combination has helped create structures that surround us every day.
Using mathematics and computers, engineers have
been able to create such technological advances as
factory robots. Taxi/Getty Images.