Math Prequisites: Landau's Course

[zonk]

I want to get a good survey book on physics and it seems like Landau's Course of Theoretical Physics might fit the bill. I enjoy Russian math books and do not mind the dryness at all. Which fields of mathematics must I master to get through the whole series without problems?

 

[Lavabug]

What do you mean by survey book? Are you a graduate looking for a text for review/fun?

I've only read Landau's mechanics volume, and that alone requires all of calculus, some DE's, linear algebra and probably beyond that to really understand the chapter on Hamilton-Jacobi theory. I've only skimmed through the fluid mechanics volume and I nearly had a heart attack.

I personally found Landau's mechanics pedagogically useless, but its the one we have to use along Goldstein's (even worse) for my sophomore course in analytical mechanics.

Calkin's "Lagrangian & Hamiltonian Mechanics" is really good for the theory bit and for its size it has a big collection of problems using both formalisms.

 

[zonk]

I would like to have a survey book that explains the fundamental principles of physics and their results for the undergraduate. Something similar to Mathematics: Its Content, Methods and Meaning. In that book they sum up most of undergraduate topics in mathematics and they also get technical (not afraid of proofs and equations). Someone recommended Landau's books. I want to understand the very basic laws of thermodynamics, basic fluid mechanics, derivation of lorentz equations and so forth. Most survey books are afraid of getting technical.

 

[Lavabug]

Then it sounds like you'd want to stay as far away as possible from Landau's IMO. They are brief yes, but I can't see myself picking up a "good foundation" on any subject from them because of their brevity and "arm-waving" discussion style.

Thermodynamics: methods of thermodynamics (Howard Reiss). I wouldn't know any specific book for fluid mechanics. Maybe try sifting through the classic Dover series books on the subjects and check their reviews, you might something you like that is straight to the point.

For classical mechanics, IMO it doesn't get any better than Morin's (Newtonian and some analytical mechanics) and Calkin's (purely analytical). E&M: Reitz or Griffith's.

 

[Clever-Name]

I think we should be asking the OP what his mathematical background is.

If you have completed an undergraduate degree worth of applied/pure mathematics then maybe Landau is exactly what you want because it approaches Physics from an extremely math-intensive point of view. It isn't 'basic' at all.

If not, stay far far away from it.

 

[zonk]

I am about to finish Apostol Volume II, then get down to a real linear algebra and differential equations book. I have a sizable collection of Dover math books I picked up in a campus bookstore that will cover most undergraduate topics in pure math. After this I want to brush up on physics so I understand most of the general principles: principles like least-action etc. I plan on getting into scientific computing and simulation programming and only know sophomore level physics. I do not mind a theoretical-mathematical level of physics, since I'll probably need to understand it like that to write useful programs, and math is always helpful.