Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

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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