Which manifolds books can help me with my class?

Question

Problem Set I

I'm looking for books that help me understand and solve these problems. The textbook that professor suggested is really deficient. Does anyone know any books on manifolds that cover these subjects?

Spivak's Calculus on Manifolds is one adopted in the course.

Answer 1

You should look into $\mathit{Calculus\ on\ Manifolds}$ by Michael Spivak. Another book you can look at is $\mathit{An\ Introduction\ to\ Differentiable\ Manifolds\ and\ Riemannian\ Geometry}$ by William Boothby