Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 200: Multivariable Calculus

Credits: 3:1

Prerequisite courses for Undergraduates: UM 204

Functions on \(\R^n\) , directional derivatives, total derivative, Contraction mapping principle, The inverse and implicit function theorem, Maxima, Minima, Saddle points, Lagrange’s Multipliers, higher order derivatives and Taylor series.

Integration on \(\R^n\) , differential forms on \(\R^n\) , closed and exact forms. Green’s theorem, Stokes’ theorem and the Divergence theorem.

Suggested books and references:

1. Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1986.
2. B. V. Limaye and S. Ghorpade, A course in Calculus and Real Analysis, Springer.
3. Spivak, M., Calculus on Manifolds, W.A. Benjamin, co., 1965.
4. Shifrin, Theodore, Multivariable Mathematics- Linear Algebra, Multivariable Calculus and Manifolds
5. Fleming, Wendell, Functions of Several Variables
6. Apostol, Tom M., Calculus, Vol-II

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