# A Math Primer for Engineers

You start with a problem that spits out an answer. You feed the answer back into the problem and get another answer, which you put right back into the problem.

Most filmmakers don't have a favorite branch of math; but then most filmmakers don't have Mr. Carruth's career history, either.

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## Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds

Before he wrote "Primer," which won the grand jury prize this year at Sundance, he worked as a software engineer. In college he majored in math. Carruth doesn't see any contradiction. It's got to be aesthetically pleasing; it's got to have subtext; it's got to convey information. In school, when I got into upper-level math, there would be times when I would wake up from a dream and have -- not an answer, exactly, but a direction to pursue.

## [] A Primer on Differential Forms

My writing has always been like that. I wake up from dreams knowing which direction to go in.

So I find it hard to believe that there's a part of your brain for math and a separate part for art. Carruth , are building a mysterious machine in Aaron's garage. After many trials they get it to work.

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But what, exactly, does it do? Carruth said. The machine is supposed to use superconductors to degrade gravity.

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But like with a lot of inventions, what turns out to be the important thing is a side effect. In fact, time machines are theoretically possible, said Lisa Randall, a professor of physics at Harvard, in a telephone interview. Abe describes such a curve to Aaron in "Primer.

Randall said, physicists believe that our universe isn't the sort that can contain a closed, timelike curve, and nobody knows how you could connect such a universe to a garage.

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Abe builds a version of the time machine big enough to contain a person, then uses it to visit the past. At first he isolates himself carefully from any contact with his former self to avoid potential paradoxes, problems reminiscent of nonlinear dynamics and familiar from, say, the end of the most recent Harry Potter movie, in which the characters change their past and therefore their future.

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Illustrative applications are taken from a variety of engineering disciplines, and the choice of a suitable model is considered from the point of view of both the mathematician and the engineer. This book will be of interest to engineers and bioengineers looking for the mathematical means to help further their work, and it will offer readers a glimpse of many ideas which may spark their interest.

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