Theoritical physics'/math textbook for self-study

[ZeroIQ]

Hello everyone,
I've been trying to study theoritical physics since a long time now. I've seen a bit of math(ODE, basics Algebra and analysis) and physics(Lagragian/Hamiltonian, Solid mechanics, optics) using free courses and youtubes videos. But i find it more hard now as there is no more courses (I've found at least) to keep goin'. So, I've been searching for some books and found many and I really don't what to choose.

So, if someone can advice some good books about all fields of Theoritical physics, i want the most complete/well-known/used books it doesn't matter for me if the book is hard,i think i can use Google to understand more, and also which book of Mathematics choose, I've found 3 that many people talked about(Mathematical method of boas/Arfken/Riley) Which one should i get or should i get all three?! Do I need more books about mathematics or these three are enough.
[URL='https://www.amazon.com/gp/product/9381269556/?tag=pfamazon01-20[/URL]
Thanks :).

 

[Orodruin]

First of all, let us get one thing straight. Neither of those books is a book on theoretical physics. They are all about the basic mathematical methods you will need to master when studying theoretical physics (or physics in general, or engineering). In order to delve deeper into any particular field in theoretical physics, you will need specialised textbooks.

In my experience, Arfken is not really well suited for self-study as it works way better as reference material than an actual book for study (this was also the view of my students when I tried using it as the main textbook for my course in mathematical methods). I also reviewed Boas and Riley when considering a change of textbook, but neither really covered the topics I needed in as much detail as I needed. All of these books are also quite broad and so includes a lot of material, usually starting from single variable calculus and moving up to partial differential equations and variational calculus.

 

[MidgetDwarf]

Hello everyone,
I've been trying to study theoritical physics since a long time now. I've seen a bit of math(ODE, basics Algebra and analysis) and physics(Lagragian/Hamiltonian, Solid mechanics, optics) using free courses and youtubes videos. But i find it more hard now as there is no more courses (I've found at least) to keep goin'. So, I've been searching for some books and found many and I really don't what to choose.

So, if someone can advice some good books about all fields of Theoritical physics, i want the most complete/well-known/used books it doesn't matter for me if the book is hard,i think i can use Google to understand more, and also which book of Mathematics choose, I've found 3 that many people talked about(Mathematical method of boas/Arfken/Riley) Which one should i get or should i get all three?! Do I need more books about mathematics or these three are enough.
Thanks :).

Seing videos of lectures is not enough. You have to get your hands dirty and go through actual text. Can you say you are good at Calculus, Linear Algebra, Ordinary and Partial Differential Equations?

 

[Orodruin]

Seing videos of lectures is not enough. You have to get your hands dirty and go through actual text. Can you say you are good at Calculus, Linear Algebra, Ordinary and Partial Differential Equations?

This is of course true. For self-study, I would strongly recommend to work out the steps yourself to make sure you follow what is going on or - at the very least - complete all of the problems provided in a text. Higher math and physics courses will require you to have mastered and remember what you did in earlier courses.

 

[ZeroIQ]

I'm not that good in fact but I've been working on Differential Equations last two weeks, I think I'm good at Calculus but I have very little knowledge of Linear Algebra. What book would you recommend about physics/math ? I was thinking about Feynman books and getting both Mathematical method of Boas/Arfken and use Google to help. Of course, I try to solve problems even though it's not always that easy.
Thanks for answers :)

 

[MidgetDwarf]

You need to go through actual textbooks. You are being hard of hearing.

For Linear Algebra:

Anton's textbook is good. It has theory, but does not get bogged down by it. If you have mathematical maturity, then Friedberg: Linear Algebra is a better option. It is meant for a second course. However, the author starts from the very basics.

For Differential Equations: I would buy a copy of Ross: Differential Equations and supplement it with Zill's : Differential Equations with Boundary Problems.

Ross is excellent, one of the best math books I have read. It lacks problems and the explanation for Laplace Transform is lacking. That is where Zill comes into. The Laplace and Annihilator Section, is the only reason I keep a copy of Zill on my bookshelf.

 

[Orodruin]

I'm not that good in fact but I've been working on Differential Equations last two weeks,

This is far from sufficient for learning differential equations properly - in particular when doing so exclusively by self-studies - unless you have an extreme affinity for learning maths. As an example, students at my university would typically spend something like 4-5 weeks of full-time studies to learn differential equations. This means 40 hours per week and many need to spend additional time (because people learn at different rates). Still, in many advanced courses there are often problems with students not having learned the subject on a deep enough level to remember the tools they were taught and that are relevant for further study.

If you do not find the problems you face easy, you should repeat the same type of problems until they are easy to you.

 

[spaghetti3451]

This is far from sufficient for learning differential equations properly - in particular when doing so exclusively by self-studies - unless you have an extreme affinity for learning maths. As an example, students at my university would typically spend something like 4-5 weeks of full-time studies to learn differential equations. This means 40 hours per week and many need to spend additional time (because people learn at different rates). Still, in many advanced courses there are often problems with students not having learned the subject on a deep enough level to remember the tools they were taught and that are relevant for further study.

There's of course the story of John Moffat who skipped formal training altogether and was famously the first person to be admitted into the PhD program at Cambridge without a Bachelor's degree. And then there's Lubos Motl who published groundbreaking papers on matrix string theory while still an undergraduate student at a university in Czech Republic where there were no theoretical physicists to begin with. In his blog of the review of Matthew Schwartz's QFT textbook, he talks about how he was learning QFT when he was a teenager. But, for mere mortals, this is a tall order to accomplish. Like Ashok Sen once told an outsider (to physics) who wanted to work with him - 'Spend one year learning Goldstein, one year on Jackson, one year on Sakurai, and then come back and we'll talk about research in string theory.' Of course, he skipped mentioning the required background preparation on quantum field theory, conformal field theory, supersymmetry, general relativity, supergravity and string theory.

Landau and Lifschitz do a good job of trying to compress the canonical theoretical physics stuff in a series of volumes, but they are not pedagogically useful. Feynman's three textbooks are a baby version of Landau and Lifschitz and suffer from the same problem. For one thing, the textbooks don't have exercises. Same with Greiner's or Weinberg's attempt with quantum field theory and Cohen-Tannoudji's attempt with quantum mechanics.

At the end of the day, textbooks are always too big to read cover to cover. That's why university courses always mention textbook names as references. In my view, the best way to learn the material is to read lecture notes and watch lecture videos, but then to spend the bulk of the time doing problem sets. It's all too common for student to read textbooks or lecture notes or watch lecture videos without making an attempt on problem sets. That's because problem sets require us to actively think about what we learned and most people are conditioned to avoid this active form of learning.

Unless of course we are talking about Ed Witten who happens to be able to develop his intuition about a problem and do all the computations in his head and then type everything up in LaTeX, without a single scratch mark on his paper. This is of course anecdotal, but is confirmed by professors who have been postdocs at IAS.

At the end of the day, I guess problem sets are the most part of learning. For this, I personally find it useful to download and use the problem sets from course webpages of professors who have kindly put their material on the Web.

 

[spaghetti3451]

You need to go through actual textbooks. You are being hard of hearing.

For Linear Algebra:

Anton's textbook is good. It has theory, but does not get bogged down by it. If you have mathematical maturity, then Friedberg: Linear Algebra is a better option. It is meant for a second course. However, the author starts from the very basics.

For Differential Equations: I would buy a copy of Ross: Differential Equations and supplement it with Zill's : Differential Equations with Boundary Problems.

Ross is excellent, one of the best math books I have read. It lacks problems and the explanation for Laplace Transform is lacking. That is where Zill comes into. The Laplace and Annihilator Section, is the only reason I keep a copy of Zill on my bookshelf.

Hassani Sadri is a good textbook in this respect, I think. It covers everything a beginning theoretical physicist needs in a graduate program. Of course, one can read a separate textbook for each maths topic, but then, this might be overkill.