The Theoretical Minimum: What You Need to Know to Start Doing Physics by Leonard Susskind and George Hrabovsky
For several years now, the physicist Leonard Susskind has been teaching continuing education courses at Stanford that were (and are) being recorded and put online for free, a real education boon. The reason is that the physics isn’t a toned-down cereal box version, but is in essence the “real thing” with differential equations, the lot. It’s not the equivalent of getting a physics degree or reading actual textbooks, though, since a great deal of fat and arguably some muscle has been removed such that only the really essential bits required to do “real” physics remain. He calls it The Theoretical Minimum (and Physics for Old People). Wikipedia has a nice listing with links to these courses.
The problem is that a 2 hour recorded lecture can be a bit exhausting to work through, despite Susskind being a capable lecturer. I know, as I’ve watched more than a few. I believe numerous other people agreed and while they found the resource particularly intriguing, they would rather have the lectures put down on paper for more personal perusal. Working with George Hrabovsky from the non-profit Madison Area Science and Technology (MAST) organization, the result is also called The Theoretical Minimum, though I think it’s missing a subtitle –Classical Mechanics. They refer to it as such in the preface and it’s blindingly obvious that it’s only going to be the first in series (with the next book probably on quantum mechanics). One, since there are just more courses ready for transcription, and two, because the book has been among the top sellers on Amazon since its release.
This isn’t your usual popular science (ie. not a textbook) work, as equations abound throughout. Rather, it’s more like a low-cost classical mechanics textbook for educated/willing-to-put-in-an-effort laypeople. It introduces things gently enough, with really general discussions on states of a system and reviews of coordinates, vectors, and calculus. In fact, I’d be interested in an experiment where this book was given to a bright high schooler who did not have experience with derivatives or vector algebra and see what they could make out of it. Probably the more you know, the more of the book you can breeze through (some prior knowledge of calculus would no doubt be fairly advantageous, though they really do start at the beginning with limits).
It does ramp up as you approach the end, though. About half the book is spent on shoring up the basics until around the midpoint we get to the Principle of Least Action which is the start of so-called higher mechanics and from there to symmetries and conservation laws (ie. Noether’s Theorem, though they don’t use that name), Hamiltonians, phase space, Poisson Brackets, and the Lagrangian formulation of magnetic fields. There’s a final appendix on central forces and a derivation of Kepler’s Laws (or at least Laws 2 and 3).
To be clear, this is not a substitute for a more in-depth and complete textbook like, say, Classical Mechanics by Taylor. Rather, it’s for a popular audience that doesn’t mind getting it’s hands dirty with some (not even that bad) equations who are tired of reading about the elegance and beauty of physical theories without getting to witness first-hand the genuine article. If all you’ve had is high-school math and physics, I think you could make it through the book with some effort (it being highly advisable to do the exercises, solutions for which are being provided at the book’s MAST site). If you’ve had two years of college math, like what an engineering student or a non-physics/math science student would take, I think the book is at a very comfortable level, even if you’ve forgotten most of introductory calculus.
My two minor gripes are that I found the typesetting to be a bit weird, with things like vector arrows and time derivative dots seeming to be placed too highly, etc, and that my own teaching prejudice is always in favor or more and more examples (I thought the discussion jumped from particles to systems like springs and pendulums without much elaboration on how the Lagrangian deals with constraints, which a few more examples could have cleared up). Those aside, I highly recommend The Theoretical Minimum and look forward to future books in the series.