Yes, and I'd take it further. What I'd like to see more of in physics texts is presenting a problem before offering the solution. Too often you get what amounts to a laundry list of techniques and ideas, which are the components to the answers to hard problems, but the student isn't motivated to learn them. If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill. For example, I think calculus is probably better learned after trying to write down some force laws, and perhaps doing some numerical analysis. Then when you learn them you realize those nice closed-form solutions aren't busywork, they are huge labor saving tools that eliminate ad hoc labor intensive analysis.
I would also deemphasize the more mathy parts of calculus - do you really need a deep dive into continuity or the fundamental theorem of calculus? Eventually, yes. But it's just like programming: you're not going to need to understand language theory or ADTs or category theory or lambda calculus to write your first program. Or your second. And, IMHO, you should only reach for this understanding when you realize you need it. Otherwise, it won't integrate well into your toolkit.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this!
I suffer from this. Sure, I'd like to learn physics, but what I don't want to do is learn all of it. Right now. Because what I'd rather learn is what I need to solve the problem I have. It's a silly problem, it's not real world, but it's my problem that I'd like solved.
As I've grabbed my horse and lance and rushed at this windmill from assorted directions, I quickly run into my limitations that prevent the problem being solved. I run into vocabulary problems with the math, the fact that I simply don't have the math to approach the problem (which appears to be some vector calculus -- I think. "No, you idiot, it's XYZ instead", but I don't know enough to know that it's not vector calculus, if, indeed, it isn't). I try to apply basic kinematics to the problem, but I don't know if that's enough. And, finally, it could be all of those things plus, oh, some optimization issues and, also, would you like to be introduced to the several different techniques for computing numeric integration and the differential equation solvers?
"Eeep!"
To quote the film "Addams Family Values":
Wednesday: Pugsley, the baby weighs 10 pounds, the cannonball weighs 20 pounds. Which will hit the stone walkway first?
Pugsley: I'm still on fractions.
So, yea, that's me, I'm Pugsley. It seems I need 2+ years of mechanics, calculus, and differential equations, and, probably, some time with computer based simulation all to chart the course for a spaceship to a planet for a 40 year old role playing game. Of course, I don't know what the, perhaps, abbreviated path I could take through those domains to get to be able to answer my question. That might knock a year off the study, but, unlikely. "Better to have all of the foundation" and all that. Which is true, but I'm kind of after the "reward" part here, not so much the "journey".
I don’t recommend the first book. At least in my edition the typesetting is just odd, which makes it harder to read than it should be. The front matter indicates it was typeset in Mathematica, which probably explains it. The later books in the series don’t suffer from this problem.
The videos that it was essentially transcribed from are great tho.
If it exists, you could probably replace most of the first book with just a really good explanation of the Lagrangian, with lots of examples, I think.
> What I'd like to see more of in physics texts is presenting a problem before offering the solution.
Yes.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill.
No.
If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
I never taught at the university level, but with middle and high school math students I taught them to how (re)discover the solutions, rather than teaching them the solutions directly.
As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution -- or tell us to learn it between classes and bring questions back.
> As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution
My calculus instructor in college was one of those where they'd go through the problem and on step 7 (or whatever) go "Oh, where did we make the error?" where we'd all flail until they pointed us back to step 3 and then had to redo everything all over again. It was, for me, the most maddening way to teach. I was struggling just to get everything copied from the board to experience it by rote, completely unprepared to even process what was going on, much less have to go back and redo everything all over again.
I dropped that class. I always felt it was a mistake not taking calculus in High School. I had a very good relationship with the math teacher there, and we could have done it, to some level, casually between classes. I just didn't take him up on it.
I don't think it breaks trust, if you tell them what's going on. "Hey kids, I'm going to give you a problem that went unsolved until Newton. I don't expect you to find his answer, which I'll teach you later, but I want you to try to solve it your own way."
> If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
This does not destroy trust, but gives the student an important lesson: we only have the techniques to solve, say, 0.0000001% of the problems. So you have to learn brutally hard for the next many years (or rather decades) to have the minimal qualifications to be able to invent whole new techniques that no person has ever come up in history before to increase this ratio from, say,to 0.000000100000000001% (even this would trigger a whole new aera in the history of science).
I would also deemphasize the more mathy parts of calculus - do you really need a deep dive into continuity or the fundamental theorem of calculus? Eventually, yes. But it's just like programming: you're not going to need to understand language theory or ADTs or category theory or lambda calculus to write your first program. Or your second. And, IMHO, you should only reach for this understanding when you realize you need it. Otherwise, it won't integrate well into your toolkit.