MA 229: Calculus on Manifolds

Credits: 3:0

Prerequisite courses: MA 221

Functions of several variables, Directional derivatives and continuity, total derivative, mean value theorem for differentiable functions, Taylor’s formula. The inverse function and implicit function theorems, extreme of functions of several variables and Lagrange multipliers. Sard’s theorem. Manifolds: Definitions and examples, vector fields and differential forms on manifolds, Stokes theorem.

Suggested books and references:

  1. Spivak, M., Calculus on Manifolds, W.A. Benjamin, co., 1965.
  2. Hirsh, M.W., Differential Topology, Springer-Verlag, 1997.

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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: 21 Jun 2024