ADVANCED CALCULUS
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).
Books
- Rudin, W., Principles of Mathematical Analysis, Third Edition, International Editions, McGraw Hill Book Co., Singapore, 1976.
- 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.