Self Study-Need books and outline recommendation

[perseid]

Hi all, hope to get the help I need here. I have basic calculus and physics knowledge. I'd like to study Physics starting with a basic Freshman level book like Resnick (Physics) and Apostol (Calculus) and end up to be able to fully comprehend modern physics (Quantum, Relativity, Field theories,etc) at the level of "The large scale structure of space time" by Hawking or "Gravitation" by Thorne. What would be a recommended course of study (books and in what order), both physics and math, that I would need to follow to achieve this? Thanks

 

[WannabeNewton]

There is a very expansive list of topics you will need to study if your goal is to ultimately go through a textbook like Hawking and Ellis. Hawking and Ellis requires a lot of mathematics: it contains PDE theory, differential geometry, topology, functional analysis, some measure theory and that's just off the top of my head. For now, just focus on learning calculus 1-3, ordinary differential equations, and (theoretical) linear algebra. As for physics, it is rather straightforward what you would need to study at the undergraduate level-just look at the recommended undergraduate physics course plans posted on various university websites (e.g. MIT). Once you have all that down you can start worrying about the more "advanced" stuff.

MTW is not nearly as advanced mathematically as Hawking and Ellis but the same suggestions stand.

 

[xatu]

Hi, welome to PF!

Woah that's GR, you have a long (but fun) way to go! I'll just recommend some starters, I'm sure others will chime in.

Most people on here will say that Halliday & Resnick problem are far too easy (especially the newer editions). Since you say you are familiar with calculus I'd recommend to you "An Introduction to Mechanics" by Kleppner & Kolenkow and "Electricity and Magnetism" by Purcell. These books are about as challenging as they come, but your hard work and perseverance will be rewarded with true understanding of the principles of physics. It might be useful to use Halliday & Resnick to clarify any concept or idea - it always helps to see something explained differently.

Apostol's is a fine book for calculus. Spivak and Courant\John have authored calculus books considered equivalent in reputation. Very roughly put: Spivak is considered the most "fun" with a pure emphasis (ie. very little application). Courant\John is considered the most application-oriented out of the bunch. Apostol can be considered a judicious middle ground, rigorous theory with interesting applications sprinkled throughout. I will note that Apostol does cover multivariable calculus, linear algebra, and differential equations.

Although what I've provided is surely rigorous and a great way to learn physics, keep in mind that you should use the material you find most helpful. If it you like Halliday & Resnick, then by all means use it. If you master these books then you'll be on a great path to success in physics.

Best wishes,

xatu

 

[perseid]

Thanks for the advice. Aside from books, are video learning materials (some commercial like TTC, some available on Youtube and some universities open courses) useful or should I focus on books? Also, how much time should I devote to problem solving? Or is the understanding of the concept more important? (as is implied in a book like The Feynman Lectures). I reckon that if I do all problems at the end of each chapter it will be a never ending endeavour.

 

[xatu]

It's easy to fool oneself into thinking that you understand something - especially in self-study. I advise that you actively read through the chapter of whatever book you are working (with pencil and paper) until you fully understand and are capable of deriving the key results. Once you've done this, do some difficult (ie. not a trivial plug n' chug) problems that you find particularly interesting. This is key, for it is in solving these challenging problems that you will develop true a understanding. If you can solve a decent amount of the problems (at least 70%), then I'd say move on to the next chapter. As you move on, be sure to frequently go back to previous chapters and solve different problems. The Feynman Lectures are a great resource to learn concepts, but most people will attest that solving problems is crucial to learning physics.

In regards to video lectures, if they help then I suggest that you incorporate them into your learning process. I personally don't find them that useful, but it's a matter of interest really.

 

[perseid]

Thanks Xatu, I agree with your remarks. I mentioned Resnick not because I particularly meant that book as a starting point, but rather to describe my starting level. I will look at the many references available to me and try to outline a course of study, starting from this basic level until Hawking's TVLSSU or MWT's Gravity. For each subject there are many good authors considered the "best", so the choice is sometimes not easy. I will post later this suggested course outline and see if you or someone can "approve" it.

 

[WannabeNewton]

May I ask, why Hawking and Ellis in particular? If you want to learn general relativity, this is not the book to do it from. MTW is also not a great book to learn general relativity from. Both of these books are better used as reference books once you have more or less learned the subject.

 

[perseid]

May I ask, why Hawking and Ellis in particular? If you want to learn general relativity, this is not the book to do it from. MTW is also not a great book to learn general relativity from. Both of these books are better used as reference books once you have more or less learned the subject.

Hi wannabe, yes I know. More suitable books at an introductory level would be "A 1st course in GR" by Schutz, Carroll's "Spacetime and Geometry", Hartle's GR, "einstein GR in a nutshell" by Zee or Laurent's "Intro to Spacetime".
The reason I mentioned Hawking's or MTW is because they are much more advanced and hence would be the ultimate target to achieve, or at least, I would consider myself very happy if I'll be able to reach that level. Of course that in the course outline I want to build I would start GR with one of these introductory level books before attempting Hawking or MTW (In fact, even before these "introductory" books I would refresh relativity with basic freshman level books like Resnick plus I would need to refresh calculus, differential equations, complex analysis, tensors, etc etc)

 

[WannabeNewton]

Hawking is definitely very advanced but MTW is not as far as mathematics goes (it is definitely advanced in terms of the physics). In fact even Carroll is more mathematically precise than MTW is. But MTW manages to cover an amazing breadth of topics and for that it is probably one of the best reference texts out there. Anyways, since you are just starting out with physics, these are things you won't have to worry about for a long time (although you don't need much to start Schutz-you can start it if you get through calc 1-3, ODEs, LA, and intermediate mechanics / EM). Regardless, Schutz -> Carroll -> Wald (once you learn some extra theoretical mathematics) + books like Poisson and Straumann -> Hawking and Ellis wouldn't be a bad progression. You won't need any complex analysis for general relativity but it is probably good to learn complex analysis anyways.

I agree with Xatu that you should start with Kleppner and Purcell. They are both difficult but very rewarding books. Honestly your best course of action, if you have yet to enter undergrad, would be to take an honors calculus sequence and honors physics sequence at your university because this will basically force you to use Kleppner / Purcell and Apostol or the equivalent. If you're doing it for self study then you can follow the same route but make sure you ask questions and post solutions on forums to make sure you're doing it right.

 

[perseid]

Thanks wannabe. Regarding electromagnetism, I read about Fleisch "A Student's Guide to Maxwell's Equations", I read very good reviews, do you have any feedback on that one? Seems to be more modern than Purcell's.
And regarding mechanics, does Kleppner replace Goldstein or Landau?

 

[WannabeNewton]

I have never heard of the Fleisch book but I would be hard pressed to find a freshman EM book more amazing than that of Purcell. The chapters on the fields of moving charges, on magnetism, and on induction are just absolutely amazing because Purcell derives many of the physical results using special relativity. He essentially captures the fact that classical electromagnetism is really described by a single Lorentz covariant entity (called the electromagnetic field strength tensor) even though he never explicitly mentions the entity. I don't think it can get much more modern than that as far as the exposition goes (the 2nd edition has Gaussian units which many would not find favorable). The 3rd edition is amazing for self study since Morin's revision added a bunch of appendices and answer solutions for a ton of problems (the revision itself added so many problems to the text that the sheer number of problems themselves are quite daunting not to mention a good number of them are crazy difficult).

And no, Kleppner does not replace Goldstein or Landau. Kleppner is meant as an introductory text for freshman whereas Goldstein and Landau are meant for advanced undergraduates and first year graduate students.

 

[perseid]

I had Purcell in my list for EM books as it's regarded as one of the top reference books for undergrad level. I always read that the problems are very challenging. Now that you mention that the 3rd Ed comes with solutions plus additional problems , I will definitely include it in the course and treat others (like Fleisch, I recommend that you take a look at it) as complementary.
Is Jackson's EM more advanced than Purcell?

 

[WannabeNewton]

Jackson is meant as a graduate level text. The natural progression would be like Purcell -> Griffiths -> Jackson.

 

[perseid]

Jackson is grad level? Some colleges in the USA include Jackson in their undergrad sophomore and Junior level courses, but just by browsing Jackson one can recognize that it's a step beyond Purcell
(If Purcell's problems are considered "very hard", I can't imagine Jackson's problems!)

 

[WannabeNewton]

What US universities use Jackson at the undergrad sophomore level? Could you provide the links? The only US university I personally know that does anything close to this is MIT (not that it's impossible to self study Jackson when you are a sophomore-if you can handle the book then all the power to you).

 

[perseid]

Caltech did for sure! But they offered a standard EM course with Marion/Heald (at least a few years ago) and a more advanced undergrad course with Jackson.

 

[WannabeNewton]

Alright well CalTech is not a normal US university. Their undergraduate courses might as well be graduate courses at many other US universities (a few years ago when I was browsing their course catalog they were offering topological field theory at the undergraduate level...lol). Also, I didn't mean a university that recommends Jackson as an optional text because many universities do this; usually this just means it is meant to be supplementary reading for the interested student. Most universities I know use Griffiths as the primary text for the sophomore level EM class.

Regardless, if you're self studying then do whatever it is you feel you are capable of doing. Whether or not a university uses a text at a certain undergraduate level or at the graduate level doesn't really matter if you're self studying. I have many friends who worked through (and are still working through) very advanced math and physics textbooks and they have yet to reach senior year of undergrad. Heck if I worried so much about whether or not I was using a book appropriate for my "school level" I would have never started working through Wald's "General Relativity" and looking back now I would have sincerely regretted it since it's one of my most favorite physics textbook ever.

 

[xatu]

Indeed Jackson's book is listed as an optional book. The required text is Griffith's.

http://www.astro.caltech.edu/~golwala/ph106bc/#mozTocId238853

Well said WannbeNewton.

 

[perseid]

Yes, I can see your love to Wald from your signature! (right?). Regarding jackson, yes, it was the primary required book for the first EM course after Feynman's Lectures! (as I said, at the sophomore level).
Anyway, going back to my self study course, I will probably NOT study Jackson after Purcell, but rather follow your advice with Griffiths

 

[perseid]

Indeed Jackson's book is listed as an optional book. The required text is Griffith's.

http://www.astro.caltech.edu/~golwala/ph106bc/#mozTocId238853

Well said WannbeNewton.

I mentioned that Jackson was a primary required textbook in Caltech's sophomore level A FEW YEARS AGO. I have no idea what they use now, but apparently you found the answer. Regards

 

[WannabeNewton]

Yes, I can see your love to Wald from your signature! (right?).

Haha yeah-Linearized Einstein equations in the Lorenz gauge vs. Maxwell equations in the Lorenz gauge. The similarity between them is absolutely beautiful.

Regarding jackson, yes, it was the primary required book for the first EM course after Feynman's Lectures! (as I said, at the sophomore level).

Speaking of which, the Feynman lectures are a great supplement to Purcell. Many universities (mine included) recommend this in the course description for honors introductory electromagnetism. Good luck with your studies!

 

[perseid]

Thanks Wannabe and Xatu! You definitely provided useful info and advice to build my self study course. I have no idea how long will it take or even if I will be able to reach the target, but the challenge itself is very encouraging!
I'll be back with updates or if I have any questions on problem solving.

 

[perseid]

I forgot another question. Would you advise to first master some math tools (Spivak/Apostol) and then continue with basic physics (Kleppner/Purcell) or to do both math and physics books simultaneously as is done in college?

 

[verty]

I forgot another question. Would you advise to first master some math tools (Spivak/Apostol) and then continue with basic physics (Kleppner/Purcell) or to do both math and physics books simultaneously as is done in college?

Personally, I advise doing the math first, for this reason: you will get a good understanding of the physics if you already know the math. But it may be more difficult this way.

 

[perseid]

But it may be more difficult this way.

Why?