I am currently studying a course Real Analysis II(or Calculus II).
My Instructor gave me the reference to M. Spivak, Calculus on manifolds, fifth edition, Westview Press, 1971
But I find this has a very low number of examples and proofs are very concise and some of the topics are missing as per the course contents.
Can anyone please recommend me some good references for the following Contents(Specifically for Taylor's Theorem):
Vector-valued functions, continuity, linear transformations, differentiation, total derivative, chain rule, Taylor's Theorem for scalar and vector fields.
Determinants, Jacobian, implicit function theorem, inverse function theorem, rank theorem
Partition of unity, Derivatives of higher-order
Riemann integration in $\mathbb{R}^n$, differentiation of integrals, change of variables, Fubini’s theorem.
Exterior algebra, simplices, chains of simplices, Stokes theorem, vector fields, Divergence of a vector field, Divergence theorem, closed and exact forms, Poincare lemma