Who uses Calculus?
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?
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 mathematics undergraduate or graduate student. 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. . ------------------------------------------------------------------- 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. -------------------------------------------------------------------- Hope this helps! -Doctor Jodi, The Math Forum
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