Differentiation:Basic definitions and theorems, Partial derivatives,
Derivatives (as linear maps), Inverse and Implicit function theorems.
Integration:Basic definitions and theorems, Integrable functions, Partitions of
unity, Change of variables.
Manifolds:Basic definitions, forms on manifolds, Stokes theorem on manifolds,
Volume element, classical theorems (Green’s and divergence).
Suggested books and references:
Rudin, W., Principles of Mathematical Analysis, McGraw-Hill, 1986.
Apostol, T. M., Mathematical Analysis, Narosa Publishing House, New Delhi, 1992.
Spivak, M., Calculus on Manifolds, The Benjamin Publishing Company, New York, 1965.
Munkres, J., R., Analysis on Manifolds, Addison-Wesley Publishing Company, 1991.