I'm a math student. I work with both Spivak's and Apostols calculus books. There is a solutions manual for Spivak and there is a blog for Apostol Vol I. However, I haven't been able to find any solutions manual for Vol II. Does anybody know where you can get it or if it doesn't exist?
Tom M Apostol Calculus Volume 2 Solution Manual
Moreover, if one is taking a class, then there is a ready-made structure for expanding upon and providing context for solutions to problems. This structure is not provided by a solutions manual, but can be found through conversation (e.g. on MSE). Such conversation is going to help one to understand the errors in their thinking or underlying assumptions much more readily than a solutions manual.
With regard to "checking one's work," I think it is worth pointing out that a solutions manual may not actually be all that useful. If you are really uncertain as to whether or not your proof is sound, a solutions manual may not help all that much, because the approach in the manual may be different from the approach of a given student. Again, the student is going to benefit more from conversation and interaction than from a solution written from a particular point of view at a particular point in time.
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