Good Book to Learn the Math Behind the Theory

[Fig Neutron]

I have read about general relativity, quantum mechanics, and physics is general, but I'm looking for a book that goes a little bit more in depth with the math behind the theories (I understand a lot of those equations are going to be complicated). I'm in 10th grade so I'm doing Algebra II this year. I've also done a little bit a precalculus on my own. I'm guessing most books are going to require a certain level of proficiency in calculus, so I guess I'm looking for a book that will introduce me to the concepts while I work my way up to calculus.

Most of what I have read has been in books that don't really give a mathematical explanation or on Wikipedia where some of the math is a bit over my head (I know Wikipedia is not always the most reliable source).

 

[Wrichik Basu]

Reading about the theories and understanding the theories has a great difference.

You want to study QM and Relativity. But with your level of math, you'll simply be unable to go into even the shallows in the subject, and you might even grow a bad taste for the subject when you find that you're not understanding anything.

Relativity and QM require a thorough understanding of Linear Algebra (not equal to Algebra 2) and Multivariable calculus (which means precalculus won't help you in the least).

I would advise you to put up these topics for now. You can, of course, read books on QM that are a little bit less rigorous, but for that you need to complete full single variable calculus.

For general physics, you can refer to Resnick and Halliday's book Fundamentals of Physics.

 

[PeroK]

I have read about general relativity, quantum mechanics, and physics is general, but I'm looking for a book that goes a little bit more in depth with the math behind the theories (I understand a lot of those equations are going to be complicated). I'm in 10th grade so I'm doing Algebra II this year. I've also done a little bit a precalculus on my own. I'm guessing most books are going to require a certain level of proficiency in calculus, so I guess I'm looking for a book that will introduce me to the concepts while I work my way up to calculus.

Most of what I have read has been in books that don't really give a mathematical explanation or on Wikipedia where some of the math is a bit over my head (I know Wikipedia is not always the most reliable source).

Special Relativity is a subject that you can start to learn properly without very much maths. A bit of calculus helps, though. There is a free pdf text here:

http://www.lightandmatter.com/sr/

I would also recommend Helliwell's book:

https://www.amazon.com/dp/1891389610/?tag=pfamazon01-20

You'll have to leave QM and General Relativity for a little while yet, as they are both highly mathematical.

Of course, you need to focus on your schoolwork, but SR is certainly your best bet if you want to learn something more advanced.

 

[jtbell]

You can, of course, read books on QM that are a little bit less rigorous, but for that you need to complete full single variable calculus.

Right, the textbooks for an "introductory modern physics" course which is often taught in the US right after the first-year calculus-based intro physics course that focuses on classical mechanics, E&M, and thermodynamics. I learned my first bits of QM from such a course when I was an undergraduate. Later I taught that course for many years to students who usually had not yet finished Calculus III (multivariable).

It focused mainly on one-dimensional systems: particle in a box, potential barrier (tunneling), etc., so we needed partial derivatives only at the beginning when discussing the time-dependent Schrödinger equation for $\Psi(x,t)$ and separating the variables to get two single-variable equations. For that, all you need is the concept of a partial derivative and how to calculate it, which took up half a lecture or less.

After getting the solutions (energy eigenstates) for the particle in a box, these courses used them to introduce some concepts from linear algebra: orthogonality, etc.

One doesn't get very far into QM, but I found it to be a useful start.

 

[Fig Neutron]

Thanks everyone, I wasn't expecting there to be much of a chance on QM or GR. I'm not expecting to get to that level any time soon. I just meant something to introduce me to the basics of physics in general, maybe with that goal in the future. Again, thank you for your suggestions.

 

[Wrichik Basu]

@jtbell thanks for reminding me of something.

@Fig Neutron if you can learn at least single variable calculus, then you can surely look into this course on Introductory QM by Prof. Manoj Harbola of Indian Institute of Technology (IIT), Kanpur. I can guarantee that the lectures are authentic, but I'm not sure on the level of math it needs, as I've never attended it. I think single variable calculus and a bit of linear algebra will be helpful.

I also have a very good book by Dr. H. C. Verma named "Quantum Physics". But it's not sold online. I like the book because it is a good balance between mathematical rigour and theory. Don't buy the one available at Amazon. If you want it, I can give you the number of the publisher, and you can contact them directly.

 

[Fig Neutron]

@Wrichik Basu thanks for the suggestion. It sounds interesting, could you pm me the number?

 

[Wrichik Basu]

@Wrichik Basu thanks for the suggestion. It sounds interesting, could you pm me the number?

I've sent it to you.

 

[smodak]

Op. Don't skip steps. You have enough background to start right. Your next step is to learn precalculus properly and learn calculus and mechanics.
If I were you, here is the path I would follow..

Start with Axler's Precalc
Then read Savov
At that point, start with Susskind's Theroretical minimum series.
Mechanics
Quantum Mechanics
Special Relativity and Field Theory in that order
- You can also follow lectures on youtube by susskind on which the books are based.

At that point Susskind might be coming up with his Gavitation book...

Just remember that susskind's books are not very deep and there will be a lot of hand waving but gives a very good non trivial overview of the subject. After you learn calculus and mechanics, you will be well equipped to tackle other physics books.

 

[RedDelicious]

Unfortunately, reading more in depth versions of the theories is a complete waste of time unless you actually understand the math and basic physics principles behind it all. While there are obviously watered down semi-quantitative treatments of certain topics available, even the most elementary ones I can recommend require single variable calculus.

My suggestion is to really buckle down on the math and to master precalculus so that you can get a good grasp of calculus when you take it. After you take calculus, you can start building a foundation in physics, and for that purpose, pretty much any of the big named intro textbooks will do (e.g., Halliday and Resnick, Tipler, Serway). They are all huge books with 5+ sections that give you an intro to all the major topics in general physics. It is only required that you first work through the section on mechanics in its entirety, as it forms the basis for all of the other subjects. After that, you can start to explore the other sections, such as fluids, thermodynamics, E&M, and modern physics, in pretty much whichever order you want.

 

[Buffu]

I also have a very good book by Dr. H. C. Verma named "Quantum Physics". But it's not sold online. I like the book because it is a good balance between mathematical rigour and theory. Don't buy the one available at Amazon. If you want it, I can give you the number of the publisher, and you can contact them directly.

1. What is wrong with the Amazon version ?

2. Why I choose this over something like Griffiths ?

 

[Daverz]

Here's a short informal book about calculus available on archive.org, W. W. Sawyer's What is Calculus About:

https://archive.org/details/W.W.SawyerWhatIsCalculusAbout

A good introduction to special relativity is N. David Mermin, It's About Time:

https://www.amazon.com/dp/0691122016/?tag=pfamazon01-20

 

[Fig Neutron]

So many choices. Thank you everyone.

 

[Wrichik Basu]

1. What is wrong with the Amazon version ?

2. Why I choose this over something like Griffiths ?

1. It's overpriced. It's costs about 300 INR hen bought from publisher, with shipping extra.

2. Of course you can, but this is like a starter I recommended for the OP, who doesn't have a proper level of math to start with QM. Once he has that, Ramamurti Shankar or Griffiths would be good books.

 

[PhysicsMarco]

My first recommendation would by "Road to Reality" by R. Penrose. It covers a lot topics and always dives into the mathematical aspects.

 

[smodak]

My first recommendation would by "Road to Reality" by R. Penrose. It covers a lot topics and always dives into the mathematical aspects.

I will recommend against it give OP's background. It gets extremely hard pretty fast (say chapter 7). Awesome book but very hard to read and comprehend. Have you finished reading the book?