Introductory physics textbook for a math student

[JonnyG]

Let's start off by assuming that I know no physics at all.

I am looking for an introductory physics book that is mathematically rigorous, but doesn't let formalism and rigor get in the way of intuition. My goal is to start from the "beginning" of physics and eventually reach general relativity and QFT. I have the mathematical background to handle any introductory physics textbook, so don't hold back.

What options do I have?

 

[BvU]

Don't let your 'handicap' be a hindrance. Any physics book (well, almost) is good enough: the rigour of math analysis is generally overkill for the functions we encounter in physics, so we skim over the math details. Until they become important, and by then they are at your level anyway.

 

[micromass]

Let's start off by assuming that I know no physics at all.

I am looking for an introductory physics book that is mathematically rigorous, but doesn't let formalism and rigor get in the way of intuition. My goal is to start from the "beginning" of physics and eventually reach general relativity and QFT. I have the mathematical background to handle any introductory physics textbook, so don't hold back.

What options do I have?

Drop the mathematical rigour. It's not helpful at all. Sure, once you know the relevant physics, you can think about how to rigorize it. And you can read very rigorous books on the topic that are really fun to read. But if you know NO physics at all, then mathematical rigour will just get in the way. Take it from somebody who loves mathematical rigor and is learning physics on the side.

That said, there are plenty of books that don't "botch" the math and treat it respectfully. Still, they will talk about infinitesimals, and do maybe questionable things. So I recommend such a book. If you want, I can provide many good reference I found very helpful as a mathematician.

Most important is to do as much problems as you can. This is essential. I thought I could get away with a good math knowledge. But I couldn't. You need to spend a lot of time thinking about problems.

 

[robphy]

Possibly interesting.. but maybe not precisely what you wanted...

https://www.amazon.com/dp/0521198119/?tag=pfamazon01-20 (standard "honors" intro text, usually followed by
https://www.amazon.com/dp/1107014026/?tag=pfamazon01-20 )

https://www.amazon.com/dp/0521406498/?tag=pfamazon01-20 (see also volume 2)
https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20 (draft: http://alpha.math.uga.edu/~shifrin/Spivak_physics.pdf )

 

[micromass]

Possibly interesting.. but maybe not precisely what you wanted...

https://www.amazon.com/dp/0521198119/?tag=pfamazon01-20 (standard "honors" intro text, usually followed by
https://www.amazon.com/dp/1107014026/?tag=pfamazon01-20 )

https://www.amazon.com/dp/0521406498/?tag=pfamazon01-20 (see also volume 2)
https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20 (draft: http://alpha.math.uga.edu/~shifrin/Spivak_physics.pdf )

Very good books, but if you NEVER saw physics before, I would not do those books just yet. I highly recommend the books from the mechanical universe, supplemented with the problem book from Morin and the Newtonian mechanics book from French. Those are very good starters.

Then I would go to Kleppner, and Gregory to do mechanics from a more advanced point of view.

 

[smodak]

Here are the books that I would start with (before moving to advanced texts)
1. https://www.amazon.com/dp/0300192207/?tag=pfamazon01-20
2. https://www.amazon.com/dp/0300212364/?tag=pfamazon01-20

Since you have the required math background, I am also tempted to suggest
https://www.amazon.com/dp/0679776311/?tag=pfamazon01-20
Beware that the book can get quite complicated quite fast.

 

[JonnyG]

Thanks for the replies everyone. I think I will go with the books written by Shankar. Is it suggested that I go through each book in a linear fashion?

 

[smodak]

Thanks for the replies everyone. I think I will go with the books written by Shankar. Is it suggested that I go through each book in a linear fashion?

Linear works. Be aware of the fact that these books do not have any problems. For practicing problems, you would need different books (covering much of the same topics as Shankar). The other two of my favorites are:
https://www.amazon.com/gp/product/8177091875/?tag=pfamazon01-20
https://www.amazon.com/dp/8177092324/?tag=pfamazon01-20

If money is not an issue (the books are not very expensive), see if you can get both Verma and Shankar. Shankar is very well written and explained and Verma covers the topics from problem-solving point of view.

 

[The Bill]

Linear works. Be aware of the fact that these books do not have any problems.

There are exercises for Shankar's Fundamentals of Physics books in the course materials zip files on the web pages for their Open Courses at Yale:

http://oyc.yale.edu/physics/phys-200
http://oyc.yale.edu/physics/phys-201

 

[smodak]

There are exercises for Shankar's Fundamentals of Physics books in the course materials zip files on the web pages for their Open Courses at Yale:

http://oyc.yale.edu/physics/phys-200
http://oyc.yale.edu/physics/phys-201

Cool.

 

[vela]

You might also check out Open Education Resources (OER) for free physics textbooks. Openstax is one resource. There are a bunch of others.

http://openstaxcollege.org