# How often do engineers use calculus

Engineers are often math enthusiasts who got bored with the abstract. Even though number crunching is significant to engineers’ work, math is no more than a convenient means to arrive at a physical end. The type of math an engineer uses will depend on the type of engineer she is and the type of project in which she's involved.

## Basic Arithmetic

All math is based on the idea that 1 plus 1 equals 2, and 1 minus 1 equals 0. Multiplication and division –2 times 2 and 4 divided by 2 – are variations used to avoid multiple iterations of either subtraction or addition. One example of an engineer's use of basic arithmetic is the civil engineer's calculations for describing water flow across an open basin. The flow is reckoned in cubic feet per second, or Q, where Q equals the runoff coefficient times the intensity of the rain for a specified period, times the area of the basin. If the runoff coefficient is 2, the intensity, in inches of rain, is 4 and the basin – a specified area of land – is 1/2 acre, the engineer's formula resembles this: (2x4)/(.5x43,560), or 8/21,780. The result, 0.0003673, is the volume of water, in cubic feet per second, flowing across the land.

## Algebra and Geometry

When several of the factors of a problem are known and one or more are unknown, engineers use algebra, including differential equations in cases when there are several unknowns. Because engineers work to arrive at a solution to a physical problem, geometry – with its planes, circles and angles – determines such diverse things as the torque used to turn a wheel, and reduces the design of a roadway's curve to an accurate engineering or construction drawing.

## Trigonometry

Trigonometry is the science of measuring triangles. Engineers may use plane trigonometry to determine the size of an irregularly shaped parcel of land. It may also be used or to determine the height of an object based solely on the distance to the object and the angle, up or down, from the observer. Spherical trigonometry is used by naval engineers in ship design and by mechanical engineers working on such arcane projects as the design of mechanical hand for an underwater robot.

## Statistics

We all love statistics. They tell us where we stand in the world, among our peers and even in our family. They tell us who's winning. The engineer uses them for the same reasons – by statistical analysis of the design, the engineer can tell what percentage of a design will need armor or reinforcement or where any likely failures will occur. For the civil engineer, statistics appear as the concentration of rainfall, wind loads and bridge design. In many locations, engineers designing drainage systems must design for a 50- or 100-year storm in their calculations, a significant change from the normal rain concentration.

## Calculus

Calculus is used by engineers to determine rates of change or rates by which factors, such as acceleration or weight, change. It might tell NASA scientists at what point the change in a satellite's orbit will cause the satellite to strike an object in space. A more mundane task for calculus might be determining how large a box must be to accommodate a specific number of things. An engineer who designs packaging, for example, might know that a product of a certain weight must be packaged in groups of no more than 10 because of their weight. Using calculus, he can calculate both the optimum number of objects per box, plus the optimum size of the box.

#### About the Author

Will Charpentier is a writer who specializes in boating and maritime subjects. A retired ship captain, Charpentier holds a doctorate in applied ocean science and engineering. He is also a certified marine technician and the author of a popular text on writing local history.

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