Here are the solutions to the exercises in Volume 2 of "Calculus" by Tom Apostol:
While many standard calculus courses treat multivariable calculus as a collection of computational techniques, Apostol’s Volume 2 integrates as the foundational language for multivariable analysis. Go to product viewer dialog for this item. Calculus, Volume 2 tom apostol calculus vol 2 solutions pdf
Because Apostol emphasizes theory over rote computation, relying on a solutions manual can sometimes be less effective than discussing problems on forums like . Community members there often provide the intuition behind a proof rather than just the final answer. Here are the solutions to the exercises in
: Offers digital explanations and "verified" answers for various editions of Apostol's Multi-Variable Calculus and Linear Algebra . Community members there often provide the intuition behind
In the last five years, a movement of math graduate students has begun creating open-source solution sets. Search for rather than just "PDF." Several repositories offer step-by-step TeX'd solutions to every problem in Chapters 1 through 12 (Linear Algebra) and 13 through 17 (Multivariable Calculus). Because these are student-created and under open licenses (like GPL or Creative Commons), they are perfectly legal.
So begin your quest. But remember: the best "solution" is the one you work out yourself after a long, arduous, and ultimately rewarding battle with the material.
Several educational platforms host worked-out solutions for specific chapters and exercises: