### MA 229: Calculus on Manifolds

#### Credits: 3:0

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 :

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

#### All Courses

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265
E-mail: chairman.math[at]iisc[dot]ac[dot]in