I have lecture notes on several variable calculus. But it omits many proofs as the subject is so large, and for example the Taylor's formula was given only in a special case. Is there a rigorous book to fill the details, or should a student just fill the details as he or she sees something that is omitted?
Lecture notes contains the euclidean space $\mathbb R^n$, real valued functions on $\mathbb R^n$, vector-valued functions, integrals in a plane and in higher dimensional spaces and integral formulas, like path integral, Green's formula in a plane, exact vector fields, surface integrals, Gauss's theorem, and Stokes's theorem.
