Math skills needed to tackle Goldstein/Jackson

[Saketh]

I'm teaching myself mechanics from Goldstein (2nd edition), and electromagnetism from Jackson (2nd edition). I have an undergraduate-level grounding in both subjects, although completely self-taught.

As with all self-taught students, I am sure I have holes and gaps in my education. I have gone through the first chapter of Goldstein, and have done most of the problems for that chapter. I have not yet tackled Jackson, however, because I have heard that it is a difficult text to self-study. I also have Merzbacher's text on QM, but I'm holding off on that until I've mastered mechanics and EM (or is this a bad idea, and I should start with it instead of EM?).

Anyway, I have a thorough understanding of variational calculus (at least, I have mastered the content in the Arfken chapter on the subject). So you can deduce from that my current level of math - I don't know where I'm standing. I also have absolutely no background in linear algebra, matrices, tensors - that sort of thing.

My question is, what topics in mathematics do I need to master before I can confidently tackle these graduate physics books (especially Jackson)? I have a copy of Arfken's Mathematical Methods for Physicists (2nd edition), and Hildebrant's Methods of Applied Mathematics (both of the books I have taken from people who were throwing them away, so selection was limited), so anyone who has had experience with those books can help me more easily.

I realize how open-ended this question is, but if someone could give me the mathematical path to graduate physics, I would be extremely thankful. It would focus my pathless study of mathematics.

 

[cristo]

My advice is to learn Linear Algebra, sooner rather than later. If you have not come across matrices yet, then you will definitely come to a point where you will become unstuck because of this. There are hundreds of books on Linear Algebra around. The one that I used, and can recommend, is called "Elementary Linear Algebra" by Howard Anton. https://www.amazon.com/dp/0471170550/?tag=pfamazon01-20 Although it is quite pricy, I found it very useful when studyin the topic for the first time.

With regard to your other questions; you should definitely learn Classical Mechanics thoroughly before moving onto Quantum Mechanics. Goldstein is a good book for CM, and working through that would be a good start (especially since you say you have a thorough understanding of variational calculus).

I don't think it matters which order you learn EM and QM. I studied them more or less simultaneously. However, like I say above, both will involve Linear Algebra, so learn that first!

 

[Saketh]

Thank you for your advice! I will begin to learn linear algebra as soon as possible, before it becomes an issue.

I forgot to say that I also have Landau & Lif****z Volume 1: Mechanics in their Course of Theoretical Physics. Should I go through that instead of Goldstein? Before Goldstein? From your advice, I should study mechanics first - now it's a matter of which book to focus on!

EDIT: It appears that Landau's associate has been censored by PhysicsForums.

 

[cristo]

I've never used L&L Vol 1, and so can't really comment. That said, given that you already have it, you could use it simultaneously with Goldstein. It is generally better to learn from different books (different writing styles, and content, etc.)

 

[dextercioby]

Thank you for your advice! I will begin to learn linear algebra as soon as possible, before it becomes an issue.

I forgot to say that I also have Landau & Lif****z Volume 1: Mechanics in their Course of Theoretical Physics. Should I go through that instead of Goldstein? Before Goldstein? From your advice, I should study mechanics first - now it's a matter of which book to focus on!

EDIT: It appears that Landau's associate has been censored by PhysicsForums.

Well, Landau is very concise. It tells what it has to tell without using many words which could be quite a good thing sometimes. I'd rather use both simultaneously.

Use the German spelling: Lifschitz.

Daniel.

 

[Dr Transport]

The mathematics taught in Arfkins' entire text should be sufficient to be able to learn from Jackson. The only chapter you can skip is the one on group theory because it is not needed for anything in Jackson's book.

 

[Daverz]

This is an area where Dover is strong on helpful books. Chapter 3 & 4 of Byron & Fuller would probably give you what you need.

I think you will find Landau and Lifschitz very helpful for mechanics. And Goldstein is reasonably suited for self study.

However, Jackson is a book that cries out for guidance from an experienced instructor. A great reference, and very good on some subjects, but I don't think I'd recommend it for a program of self study. See previous threads on E&M books here, here, and here.

Have you thought about studying QM at the undergrad level before moving on to mechanics and E&M at the graduate level? That would give you a good linear algebra workout. I love the book by Shankar, it's actually fun to read.

 

[Saketh]

Okay, based on the replies I think I'll spend my years before university studying mathematical methods in physics, and save the physics for later. Then I won't stumble as much, and if I do it will be a physics issue, not a math issue.

Is it helpful for physicists to know calculus on manifolds? I've found the subject intriguing, and I want to know if there are direct physical applications for it.

 

[dextercioby]

Is it helpful for physicists to know calculus on manifolds? I've found the subject intriguing, and I want to know if there are direct physical applications for it.

Of course it is. Using exterior calculus gives a new insight on the equations of classical electrodynamics and general relativity. Not to mention Lagrangian and Hamiltonian dynamics.

Daniel.