Simulations are used to understand the operation of real-world, practical systems;
for instance, the modeling of natural systems such as the human body. They can be
used to simulate a certain type of technology, such as a new type of airplane, or model
an engineering concern, such as the stability of a building during an earthquake. Sim-
ulators,interactive, physical devices that simulate reality, are also part of simulation.
For example, space shuttle simulators are used to help astronauts understand the
intricacies and various scenarios associated with flying the space shuttle.
OTHER AREAS
OF APPLIED MATHEMATICS
What is numerical analysis?
Numerical analysis is a branch of applied mathematics that studies certain specialized
techniques for solving mathematical problems. It employs mathematical axioms, the-
orems, and proofs, and often uses empirical results to further analyze or examine new
methods.
What are some characteristicsof numerical analysis methods?
Characteristics of numerical analysis methods include accuracy (the numerical
approximation should be as accurate as possible), robustness (the algorithm should be
able to solve many problems and should relate to the user when the results are inac-
curate), and speed (the faster the computation, the better the method).
What are some areasthat numerical analysis addresses?
Areas addressed by numerical analysis include computing the values of functions,
solving equations, optimizing functions, evaluating integrals, and solving for differen-
tial equations. (For more about these areas, see “Mathematical Analysis.”)
What is operations research?
Operations research, more commonly called optimization theory, is a form of applied
mathematics designed to determine the most efficient way of doing something by
using mathematical models, statistics, and algorithms in the decision-making
process. It is a branch of mathematics that entails the many diverse areas of optimiza-
tion and minimization, including the calculus of variations, control theory, decision
theory, game theory, linear programming, and many others. Operations research is
most often used to analyze complex, real-world systems, stressing the improvement in
or optimization of performance. 269