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I know this question has been asked so many times on this website but neither do the questions nor the answers satisfy my requirements accordingly.

I'm yet to go to a university with a keen interest in Mathematics. So, no wonder I would like to see no-nonsene math (not heavy either) in a Physics textbook.

I started reading R. Shankar's Fundamentals of physics and I have started to understand the physical phenomenon. I love this book.

But I don't like the way he gets all the $\mathrm{d}t$'s cancelling $\mathrm{d}x$ from both sides.

So, here is my requirements:

  1. An Introductory Physics Book having a good portion of Classical Mechanics
  2. The text should have fresh math. I would more than love to see a calculus-based approach.
  3. Not more than 500 pages, please!
user221153
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  • There's actually nothing wrong with "cancelling $dt$'s". It is a totally trivial shortcut for a chain-rule manipulation that is completely mathematically justified -- you should try to prove why this trick works. I don't think you should be choosing your textbooks based on such an unimportant thing. – knzhou Feb 20 '19 at 12:52
  • "But I don't like the way he gets all the $\mathrm{d}t$'s cancelling $\mathrm{d}x$ from both sides." huh? I don't quite understand that bit. Still, you could try this math SE post. –  Feb 20 '19 at 12:54
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    @knzhou Can you turn this comment into an answer, please? I would like to see the math. – user221153 Feb 20 '19 at 12:54
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    But it's not an answer to the question "which mechanics book should I study"? If you want an answer for that you can ask a new question. (But search before you do, because I bet this has come up before...) – knzhou Feb 20 '19 at 12:57
  • If you really want to understand how physicists "interpret" math, (and why they like "cancelling differentials") learn about hyperreal numbers and non-standard analysis. The limit-based approach to calculus taught in traditional math courses isn't a good match for physical intuition about "infinitesimal" quantities. – alephzero Feb 20 '19 at 13:00
  • @user221153 The math is in any calculus textbook. It doesn't have anything specifically to do with physics. – alephzero Feb 20 '19 at 13:04

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