I'm looking for a text that covers roughly what's sometimes called "Calculus III" or multivariable calculus.* But this text must satisfy certain additional criteria: (1) It must be more in-depth (and consequently have harder exercises) than usual; (2) It must contain many solutions to the exercises; (3) It must not engage in the sort of unconvincing hand-waving common to "mathematical methods" texts.
Basically I'm looking for a difficult, thorough version of a calc 3 text. Bonus points if the book discusses differentials.
PS: I'm aware that a somewhat similar question has been asked here
Multivariable calculus: hard problems with solutions
but the problems in the books recommended were not hard enough.
*The sort of material in Stewart's Calculus.
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