CALCULUS ON MANIFOLDS
Functions of several real variables: Differnetiability, the total derivative and directional derivatives. The inverse and the implicit function theorems, Sard’s theorem. Integration on Euclidean spaces: Volume integrals and iterated integrals, Fubini’s theorem, the change-of-variables formula, partitions of unity. Manifolds: Definitions and examples, vector fields and differential forms on manifolds, Stokes theorem and applications.