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.

Books

• Spivak, M., Calculus on Manifolds, W.A. Benjamin, Inc. 1965.

• Apostol, T.A., Mathematical Analysis, Narosa (Indian Ed.).

• Munkres, J., Analysis on Manifolds.

• Rudin, W., Principles of Mathematical Analysis, Mc-Graw Hill, 1976.