Mathematical Methods/Classical Mechanics

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Hey,

I wanted some suggestions on a rigorous textbook for a Mathematical Methods course (which at my college) is taken after a one-semester (Differential Equations based) Modern Physics course in the sophomore year. Basically, I am looking for textbook suggestions that are considered "standard" and rigorous for a Mathematical Methods course for a physics major.

Additionally, I would also like suggestions for a "standard" and rigorous textbook for a junior level classical mehanics course. Personally, I'd like to find a textbook that is as rigorous for junior level Classical Mechanics as Griffith's Introduction to Electrodynamics is for junior level Classical Electricity & Magnetism.

Suggestions are appreciated.

Thanks,

-PFStudent
 

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George Jones
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Additionally, I would also like suggestions for a "standard" and rigorous textbook for a junior level classical mehanics course. Personally, I'd like to find a textbook that is as rigorous for junior level Classical Mechanics as Griffith's Introduction to Electrodynamics is for junior level Classical Electricity & Magnetism.
Greg Bernhardt posted a link to lecture notes that are freely available in the Advanced Physics Learning Materials forum. I'm not sure whether they fit your needs, but if not, you might use them to define what you are looking for, like "I'm missing treatment of ..... there" or "Its too rigorous / not rigorous enough". So here it is, about 3MB (pdf):

https://www.physicsforums.com/showthread.php?t=220908

If you have a slow internet connection, you might prefer to follow this link and have a look at the individual chapters of the lecture notes in HTML format to see if you like it:

http://farside.ph.utexas.edu/teaching/336k/lectures/

(it seems to be the same stuff, but I'm not sure whether the versions are really identical or whether they slightly differ)
 
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