## Wave Theory

I have a fair bit of academic writing as well, most of which is fairly dry, but a few pieces stand out as being of quite general interest: the *Water Waves* tutorial is regarded by some students I’ve taught as the Holy Grail of their uni experience, the reason they came to university in the first place, ie to better understand the surf.

I could not find a single text book that covered every aspect of wave theory; they all seemed to have different parts of it. So I sat down and wrote it out more or less completely, except for the bits on groyne construction. I will not take responsibility for those usually ill-advised controls on a shore line.

Waves, of course, are completely amazing, especially if you’re looking for the full mathematical theory with an accessible explanation. So here it is, river waves, ocean waves, the surf zone, rogue waves, flood waves, tsunami and all.

Another kind of wave theory, namely Einstein’s Relativity, has amazed me for a long time. So while writing some material for an astrophysics unit recently, I finally set out a complete set of derivations of *Relativity from Scratch*, mathematically exact but accessible to third year science students and of general interest to the public, so long as you don’t mind skipping a few equations. If you’ve read anything by Roger Penrose, a contemporary of Stephen Hawking, you’ll be OK with that. The gist of it is definitely there, and lots of illustrations.

This other one, *Vector Calculus for Fluid Mechanics*, is a refresher of some stuff they should get in first year but you never know how much of it they got or understood, and in any case needs to be re-understood in the fluid mechanics language, that is of flowing liquids and gases. It sounds like some boring stuff like hydraulic machinery theory but in fact it’s a very general description of all kind of fluid flows in a wonderfully consistent mathematical system which is graphically vivid with the directional, moving and changing quantities of flow velocity etc described as vectors, which are just mathematically directed arrows. So see if you like a glimpse of that kind of analysis.

These are of course, separate to the *Fragments of Invention* still to come, and in a different hall from *Quantum Cosmology.*

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