Electronic Design

Maxwell's Equations For Dummies?

By Daniel FleishISBN: 978-0-521-70147

I know an engineer who never bothered to memorize Ohm’s law. She says that when she needs it, she can always derive it from Maxwell’s equations. On the other hand, despite the fact that I aced my “fields” course as an undergraduate all those years ago, I can barely recognize Maxwell’s equations when I see them on a t-shirt.

That arises from my long-ago decision to pursue a career writing about engineering, rather than actually doing it. My undergraduate experience left me with the impression that practicing engineers spent all day, every day, solving differential equations. Of course, not even my friend who never memorized Ohm’s law—well, that’s what she said over pizzas one time—does that.

But who could blame a guy for forming that opinion after four years of engineering school? As a result, it has been a long time since I have had any real contact with the original Fab Four: Gauss, Ampere, Faraday, and Maxwell (not forgetting Heaviside and Gibbs, but including them would spoil the Fab Four reference). That changed recently.

One of the perks of being an Electronic Design editor is that we get lots of books that publishers would like us to review. The last time I went through the stack, A Student’s Guide to Maxwell’s Equations (ISBN: 978-0-521-70147-1) by Daniel Fleisch caught my eye. Published by Cambridge University Press, it goes for $28.99 in paperback.

I confess that the first thing that appealed to me about the book is that it isn’t very thick—130 pages. That seemed reviewable. The next thing was that it might be possible to reacquaint myself with the subject matter without an enormous time investment, so I settled down in the nearest chair and started to skim. Then I slowed down and started to read.

Professor Fleisch is a great scientific communicator. His students at Wittenberg University in Ohio agree. According to a post at ratemyprofessors.com, “The only thing hotter than brains is a great sense of humor. Dan’s got both. Easily the best and most dedicated prof I’ve ever met: could be 1/10 as good and still be outstanding.”

When I say “great scientific communicator,” here’s what I mean. Fleisch needs to explain four important equations to people who are nominally upper-division undergraduate engineering students, but he can’t count on them all having the same level of competence with the math concepts involved. He can’t simply decide, “Well, I’ll just spell everything out in monosyllables,” because then he’ll lose the attention of the best and brightest in his audience. But he doesn’t want to heartlessly wash out the students at the lower end of the curve, either.

One way to handle this dilemma is to provide the reader with cues in the writing that say “you can skip over the next few paragraphs if you think you already understand this concept,” where “this concept” might be as basic as the unit normal vector or as subtle as curl.

Still, Fleisch really doesn’t want to encourage readers to skip this material, because he expects that for some of them, their understanding is not as comprehensive as they think it is. So, he wants to make it attractive for the more savvy readers to just continue skimming the text at some level, if only for the sake of continuity. I believe that he carries this off brilliantly. I read everything, down to the explanation of the unit normal vector, and never felt patronized.

One thing more about Fleisch’s style—I don’t think it’s possible to lay out explanations of Maxwell’s equations in some purely linear fashion. The exegesis has to be somewhat recursive as it moves down through multiple levels of subtlety. I find that he also carries this off very well.

Is this book Maxwell’s Equations for Dummies? No. That headline was too appealing to pass up. But in my experience, the “Dummies” books are padded with secondary and tertiary trivia, and they generally aren’t as helpful as I’d have wished. A Student’s Guide to Maxwell’s Equations is far superior, though I confess that even after reading it, I still can’t use Maxwell’s equations to derive Ohm’s law.

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