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.
Spivak, M., Calculus on Manifolds, W.A. Benjamin, Inc. 1965.
Apostol, T.A., Mathematical Analysis, Narosa (Indian Ed.).
Munkres, J., Analysis on Manifolds.
Principles of Mathematical Analysis, Mc-Graw Hill, 1976.