Self-Teaching Physics: What Level Math Needed?

[CPL.Luke]

So, my present situation is that I dropped out of high school following the end of my junior year at the end of last year, got a GED, and am attending a community college this coming September. I took the AP calc and physics tests and did pretty well on them and I've been studying a linear algebra based multivariable book over the course of the past couple months.

In order to compensate for the lack of a major physics curriculum at the community college, and to satisfy my thirst for physics, I want to study the major modern books on classical theory. ie Jackson's electrodynamics and anouther major book for mechanics (I haven't heard what the cardinal one for this field is yet), and I need to know what level of mathematics I need in order to start tackling these.

I don't want to launch into them and have the experience soured by a fundamental lack of mathmatical knowledge.

Also just as a side note, what is the cardinal text for QM?
I figure I would like to tackle QM and GR as soon as I know that i have a solid footing in the classical theories.

 

[courtrigrad]

I heard Sakaurai is good for QM.

 

[jtbell]

Jackson's electrodynamics

Jackson is graduate-school level, and most current and former grad students will tell you that it is a difficult book (especially the homework problems!) for them. For the next step beyond the E&M you get in freshman physics, I suggest instead an intermediate-level undergraduate book like Griffiths, Purcell or Lorraine&Corson. The most important math used is multivariable calculus (gradient, divergence, curl, line integrals, surface integrals).

For classical mechanics, intermediate undergraduate books include Fowles&Cassiday, Symon and Marion. The standard graduate textbook is Goldstein/Safko/Poole (originally just Goldstein, but revised after his death by the other two). You need to know something about differential equations in order to get far in mechanics.

 

[leright]

Just a note, I have read through a decent portion of Jackson and it isn't necessarily hard because of a great deal of mathematical rigor, but it is hard because it is written in a very dry style and it will put you to sleep, even if you are genuinely interested in electromagnetics.

 

[ZapperZ]

Yikes! Don't even come close to texts such as Jackson or Sakurai until you have already had strong undergraduate knowledge of E&M and QM.

I would echo jtbell's suggestion of using Griffiths for both E&M (highly recommended) and QM, and using something like Marion for classical E&M.

Zz.

 

[robphy]

Mathematical Methods: Boas (You might find a deal on the recently-replaced 2nd edition)

For undergraduate GR, look at this current thread https://www.physicsforums.com/showthread.php?t=127327General: Feynman Lectures for supplementary reading.

 

[CPL.Luke]

well I'm going through a multivariable book right now that seems to be of pretty high quality, it covers everything including linear algebra, Fourier transforms, manifolds, and differential forms.

So maybe once I finish my work in that I can start in on the heavy stuff, from what I read on amazon using Griffith's and Jackson together was the best options.

I like challenges (ironic coming from a high school drop out I know) and so if a certain book presents the be all and end all of a certain subject, I don't see the need to dodge away from it. In amy sophmore year I got one of the AP physics books, and got through the E&M section before having taken any physics courses or having really bothered to learn mechanics properly.

and heck the worst that could happen is that I discover I can't penetrate the top stuff and I have to go and buy anouther book more suited for me and put the upper stuff on a shelf till I encounter later.

 

[JohnAdamnyc]

Jackson E&M book isn't hard. I love E&M and QM though =).

 

[ZapperZ]

Jackson E&M book isn't hard. I love E&M and QM though =).

That isn't the point. If you look closely, Jackson does practically all of undergraduate electrostatics in his INTRODUCTION! This is no way to learn E&M if you've never done anything that rigorous already.

A "good" book and a "pedagogically good" book can be two entirely different things.

Zz.

 

[CPL.Luke]

yeah after reading through Jackson's introduction on amazon.com I found that while I could keep up with the math, and quite possibly do all of the exercises it wouldn't be a good way to develop a deep understanding of electrodynamics. So I think I'm going to go with Griffiths book instead for electrodynamics and QM and then move on to Jackson, Sakurai and Gravitation.

First I'm now thinking I'm going to read Goldstein's mechanics. In order to get familiar with multivariable in a physical context.

Do you think that Goldstein's book could work for a self-study (ie there are exercises and solutions either directly in the text or in a solution manual etc.) or should I find a book with general problems and solutions in mechanics?