MA 302: Advanced Calculus

Credits: 3:0

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:

  1. Rudin, W., Principles of Mathematical Analysis, McGraw-Hill, 1986.
  2. Apostol, T. M., Mathematical Analysis, Narosa Publishing House, New Delhi, 1992.
  3. Spivak, M., Calculus on Manifolds, The Benjamin Publishing Company, New York, 1965.
  4. Munkres, J., R., Analysis on Manifolds, Addison-Wesley Publishing Company, 1991.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 04 Aug 2020