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Who uses Calculus?

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Date: 12/13/95 at 14:13:40
From: Anonymous
Subject: Who uses calculus

I was wondering how calculus is used: what professions, in what
situations?  Since it deals with rates of change, it seems that
engineers would.  But more than that, I was wondering if the
calculus methods of differentiation and integration are actually
performed by the people in those professions.  How automated
are calculations?
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Date: 6/12/96 at 22:28:14
From: Doctor Jodi
Subject: Re: Who uses calculus

Hi there!  For some great ideas about using calculus in the real
world, check out

http://www.geom.uiuc.edu/apps/rainbow/

Calculus was originally developed to deal with several sorts of
problems, primarily sequences and series (including applications in
interest) and physics/motion. It is still used in financial and physics
calculations.

As for jobs involving calculus, you can also see biographies of several
mathematicians at

http://www.maa.org/careers/welcome.html

Here are some excerpts:

James L. Cooley
BS, Mathematics, University of Massachusetts
MA, Mathematics, The Pennsylvania State University

Aerospace Mathematician
NASA Goddard Space Flight Center

What does a math major do at NASA surrounded by engineers,
physicists, and astronomers?

Mathematics provides excellent background to model physical
systems. The physical systems can be related to a spacecraft (an
attitude system, a propulsion system, etc.), a spacecraft support
system (such as a ground or space tracking system) or a system
in nature (such as the Earth's gravity field or atmosphere).
Mathematics provides excellent background to model data (such
as noisy or biased data taken from an attitude system or a
tracking system) and determine the optimal information from the
data. Mathematics also provides excellent background to
understand geometric relationships and deal with changing
relationships over different time scales (predicting ahead, in
real-time, and after the fact).

After graduating from the Pennsylvania State University and
adding an additional year of graduate study in mathematics at
the University of Maryland, I joined the Goddard Space Flight
Center in 1963. Immediately there was the challenging problem
of modelling the tracking system for the Apollo program. There
continued to be many challenging problems in the area of Flight
Dynamics; the area encompassing orbits and orbit maneuvers,
attitude systems and attitude maneuvers, and spacecraft tracking.
Other challenges involved modelling tracking from spacecraft
(the Tracking and Data Relay system) instead of from ground
antennas, controlling spacecraft dipping low into the
atmosphere, and controlling spacecraft around a mathematical
point (the Sun-Earth L1 libration point). There continue to be
challenges in designing future missions; tracking and controlling
4 spacecraft in a tetrahedron formation, for example, and
designing missions allowing correlation of scientific data from 2
or more spacecraft. Mathematics and mathematical approaches
are used a great deal in modelling physical systems and
designing NASA missions.

Any spacecraft mission is a team effort involving engineers,
physicists, astronomers, and mathematicians. One rapidly
realizes it is necessary to have a background and learn the
language of engineering, physics, and astronomy. The
computer, and computer scientists, are also indispensable. Thus
I always recommend some minor courses in these fields as a

NASA Goddard Space Flight Center in Greenbelt, Maryland,
has formed a mathematics support group to enhance mathematics
and mathematics education. The group supports common areas
of concern, such as chaos theory (chaos theory may provide an
exciting breakthrough in modelling and predicting sunspots and
solar activity). This group also promotes to hiring officials the
concept that a mathematics major who is familiar with physical
science is as good, if not better, than an engineer, physicist or
astronomer who is familiar with mathematics.
.
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MATHEMATICIANS AT WORK

Bonita V. Saunders
PhD, Mathematics, Old Dominion University
MS, Mathematics, University of Virginia
BA, Mathematics, College of William and Mary

Mathematician, National Institute of Standards and Technology

Currently, I am doing research in a field called grid generation.
When an engineer designs an airplane wing, he (or she) has to
solve equations that model the air flow over the wing to
determine the best wing shape. Since these complicated
equations must be solved at many points around the wing, the
calculations must be done on a computer, and the points must be
chosen carefully so that the engineer receives an accurate picture
of how fast and smoothly the air flows. The points make up
what is called a grid, or mesh.  Grid generation is the
development of computer codes that automatically pick the mesh
points. It is used in any area of research, such as
aerodynamics, electromagnetics, and crystallization, where
equations must be solved on an oddly shaped region.  In my
work I use techniques from several areas of mathematics
including calculus, differential geometry, and numerical
analysis.
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Hope this helps!

-Doctor Jodi,  The Math Forum

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