The Right Physics Textbook (math)

[sassafrasaxe]

Hello. I have a bachelor's degree in both Applied Math, and Computer Science. But I would like to study physics on my own. I have flipped through the pages of a few physics textbooks, and I've noted that the math in these textbooks looks somewhat basic. I have not seen any double integrals, which I find odd.

I'd like to find a physics textbook that at least has some nested integrals, and that uses calculus to explain the derivation of all of the physical formulas. Is there any textbook that you recommend for this?
The two that I've looked at and haven't seen any double integrals in are Walker's Fundamentals of Physics, and Physics for Science and Engineers by Tipler and Mosca, versions 8th and 6th, respectively.

Am I looking for the wrong things? I just assumed that physics was more... mathematical... and would have more complex integrals than what I'm seeing in these textbooks. I just want to make sure that I'm building up as best an understanding of this subject in a mathematical perspective as I can. If I'm looking for the wrong things, please correct me and let me know.

Otherwise, please recommend some good... "mathy" physics textbooks, with deep explanations of derivation.

Thanks!

 

[The Bill]

There isn't a lot of need for double integrals when covering the basics in a typical three-semester introductory calculus based physics sequence.

That being said, you could start your study of classical mechanics with Kleppner and Kolenkow's An Introduction to Mechanics if you must have double integrals in your first book. It is quite a good intermediate mechanics text, often recommended here as a step between introductory calculus based physics and a text on Lagrangian and Hamiltonian mechanics.

 

[BvU]

There's a whole branch called mathematical physics !
And plenty tough integrals in electromagnetism, particle physics, quantum mechanics, etc. etc.

 

[sassafrasaxe]

The Bill, thank you so much! This looks great! I'll start digging in. I found a free PDF. Super :D

BvU, thanks! I thought that all physics was mathematical, at least to some extent. But maybe from now on whenever I'm searching for new physics literature, I'll keep that in mind, and search for mathematical physics

 

[JoePhysics]

And since you've already been recommended Kleppner and Kolenkow's excellent book, once you're ready to tackle electromagnetism, Purcell's Electricity and Magnetism would be a textbook at approximately the same level as K&K. Both books are routinely used as main textbooks for honors courses that are more rigorous than the standard sequence.

 

[sassafrasaxe]

Thank you! I'll keep that in mind for when I finish K&K :)

 

[jtbell]

The two that I've looked at and haven't seen any double integrals in are Walker's Fundamentals of Physics, and Physics for Science and Engineers by Tipler and Mosca, versions 8th and 6th, respectively.

In the electromagnetism chapters, the integrals that you see for (e.g.) Gauss's Law are surface integrals, which means that they can be written as double integrals in a suitable coordinate system. However, in a first-year intro course (at least in the US) we don't normally solve such integrals explicitly as double integrals. We set them up only for situations that are symmetric enough that the integrand is constant over the surface, so the integral reduces to constant * (area of surface) and it can be solved almost by inspection. I call them "Geico integrals" ... so easy a caveman can do them! For more sophisticated examples and exercises you need to look at an intermediate-level E&M textbook such as Griffiths.

 

[sassafrasaxe]

Haha so easy I could do it. I like. Thank you, you've all been so helpful! Purcell's and Griffith's. I hear Purcell's is better for stringing together the introductory concepts as you go along, but if Griffith's has more interesting math in it then maybe I'll go that route.

 

[JoePhysics]

Haha so easy I could do it. I like. Thank you, you've all been so helpful! Purcell's and Griffith's. I hear Purcell's is better for stringing together the introductory concepts as you go along, but if Griffith's has more interesting math in it then maybe I'll go that route.

Griffiths is the standard undergraduate E&M textbook in American universities; it's basically what is expected knowledge of someone with a degree in physics in the US, I guess.

 

[BvU]

I stumbled on Mathematical Methods in Quantum Mechanics - G. Teschl and immediately thought of you...

 

[Andreol263]

If you want to see some tough math, i recommend the Landau & Lifshitz Theorical Physics texts, especially the Classical Field Theory one, where he builds (basics)General Relativity and Eletromagnetism from the postulates of Special Relativity, really challenging and dense book, but beautiful. you may want to go with Jackson EM book for some really advanced calculus but with poor explanation of the physics behind it and a horrible manner of explaining Green Functions, that are really important on this textbook, go for Principles of Quantum Mechanics by Shankar for awesome linear algebra and calculus application on QM, really good book.

 

[Buffu]

"Geico integrals" ... so easy a caveman can do them!

Lol, I laughed so much at this.

 

[alan2]

I'm a little confused. How did you receive a degree in applied mathematics without a year of sophomore physics? I really think it's a bad idea to base your study of physics on your perception of the difficulty of the mathematics involved. Physics is much more than doing math and if you don't understand the basic concepts you won't understand more advanced material. Would you start your study of probability with Billingsley or your study of economics with Mas-Colell just because the math is harder? Certainly not, because it is assumed you understand the fundamentals. When I was a grad student we always had math students registering for physics classes without the requisite physics background because they assumed that if they could understand the math they could understand the physics. I don't recall a single one ever finishing the classes. It was exactly the same when pure math students registered for applied math classes because they somehow, in their arrogance, thought it would be easy. It wasn't, they usually struggled. If you want to understand physics you should start at the beginning noting that you at least won't have difficulty with the math which can be an obstacle for many freshmen and sophomores.

 

[MidgetDwarf]

If you find Kleppner and Kolenkow, or even Purcell to hard. A good supplementary book is Alonso and Fin: Fundamental University Physics. It is a 3 book series. It uses calculus to derive the results, is very condensed, and the way the material makes sense. Every new is well connected to a previous idea. That said, the book may not be as Mathematical as say, Goldstein: Mechanics, but it is a good supplement for Kleppner.

Please try not to be to snobbish about "Mathematical." Many would say, myself included ( I am a Pure Math Major), that Applied Math is not "Mathematical," by you're definition. The truth is, Rigor and Intuition, are both needed. One should not focus solely on the Theoretical side and neglect the application, and vise-versa.

 

[Dr Transport]

I'm a little confused. How did you receive a degree in applied mathematics without a year of sophomore physics? I really think it's a bad idea to base your study of physics on your perception of the difficulty of the mathematics involved. Physics is much more than doing math and if you don't understand the basic concepts you won't understand more advanced material. Would you start your study of probability with Billingsley or your study of economics with Mas-Colell just because the math is harder? Certainly not, because it is assumed you understand the fundamentals. When I was a grad student we always had math students registering for physics classes without the requisite physics background because they assumed that if they could understand the math they could understand the physics. I don't recall a single one ever finishing the classes. It was exactly the same when pure math students registered for applied math classes because they somehow, in their arrogance, thought it would be easy. It wasn't, they usually struggled. If you want to understand physics you should start at the beginning noting that you at least won't have difficulty with the math which can be an obstacle for many freshmen and sophomores.

https://catalog.buffalo.edu/academicprograms/mathematics_ba_-_computing_&_applied_math.html

No physics required to get a degree in applied math and computing...

 

[alan2]

Yes, that's what you said but I still don't know how they can call it applied math since there aren't any applied math courses required for the degree. It looks like a degree in computation. But my point was everything else, if you don't know anything about physics you need to start at the beginning.