Calculus Books for Math Competitions: Putnam & Beyond

[WiFO215]

Can anyone suggest any books that I can use to prepare for competitions like Putnam or any other math competition that gives problems in calculus? Single variable would be appreciated, but if it has multi-variable too, then I don't mind. I wouldn't want to get separate books later.

 

[WiFO215]

Oh c'mon! How'd you guys prepare for putnam without doing calculus?

 

[rasmhop]

Well I have never participated in Putnam or any other college-level competition, but since no one else has offered their advice I thought I might as well give you my thoughts.

You will probably be hard-pressed to find a book that deals exclusively with putnam-level single-variable calculus problems. A good preparation is any of the standard rigorous books (Apostol, Courant, Spivak) coupled with standard rigorous real-analysis books (I only have experience with Rudin's PMA, but that seems fine to me). If you truly understand all that stuff and have done some general problem-solving you should be able to tackle hard problems and with enough practice Putnam problems. As for actual books; I have Berkely Problems in Mathematics which is a pretty neat collection of problems. They are not all calculus and I guess most is below Putnam-level, but still good training. For high-school-level competitions I have good experience with the stuff by Titu Andreescu and Kiran Kedlaya and while I haven't read any of their college-level books I guess the books "Putnam and beyond" and "The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary" would be of use to you (again not exclusively calculus, but neither is the Putnam).

Oh c'mon! How'd you guys prepare for putnam without doing calculus?

Learn the theory and then practice a LOT of problems is my guess.