[Math] solution manual for Apostol’s Calculus Vol. II

Question

I'm a math student. I work with both Spivak's and Apostol´s 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?

Thanks.

Answer 1

Since I think that this answers the question (though it is perhaps not the answer that was desired), and since it doesn't fit in a comment anyway, I am going to provide it as an answer.

When another MSE user asked for a solutions manual to Lee's Introduction to Smooth Manifolds, Lee himself responded with

Here's what I wrote in the preface to the second edition of Introduction to Smooth Manifolds:

I have deliberately not provided written solutions to any of the problems, either in the back of the book or on the Internet. In my experience, if written solutions to problems are available, even the most conscientious students find it very hard to resist the temptation to look at the solutions as soon as they get stuck. But it is exactly at that stage of being stuck that students learn most effectively, by struggling to get unstuck and eventually finding a path through the thicket. Reading someone else’s solution too early can give one a comforting, but ultimately misleading, sense of understanding. If you really feel you have run out of ideas, talk with an instructor, a fellow student, or one of the online mathematical discussion communities such as math.stackexchange.com. Even if someone else gives you a suggestion that turns out to be the key to getting unstuck, you will still learn much more from absorbing the suggestion and working out the details on your own than you would from reading someone else’s polished proof.

So if you have questions about specific problems, by all means ask them here. But posting a complete list of solutions will not be doing anyone a favor. Many instructors assign those problems as homework, and if complete solution sets become readily available, it makes the problems (and therefore the book) far less useful.

It's interesting to note that when I've written chapters with everything proved and few or no problems at the end, readers invariably ask me to provide some problems for them to work on. If you want problems with solutions already written down, they're already there -- the theorems and examples in the book! Just look at the statement of a theorem or the claims made in an example, close the book and try to prove the theorem on your own, and then go back and compare your work to the proof in the book. (And if you find a better proof that the one I wrote, please let me know about it!)

I think that this applies here as much as it did there.

In response to the counter-arugment "What about people who are self-studying, or for whom mathematics is just a hobby?", I think that the advice is even more relevant. If you are studying a subject for a class, you are rewarded and penalized for your work, hence there is a very strong incentive to get it done correctly under the pressure of a deadline. The hobbiest or self-studier is under no such pressure, and has the time to be "stuck" on difficult problems. There is no penalty for late work.

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.