Subject Code: MA5L024 Subject Name:  Functions of Several Variables L-T-P: 3-0-0 Credit:3
Pre-requisite(s): Real Analysis (MA5L002)
Functions on Euclidean spaces, continuity, differentiability; partial and directional derivatives, Chain Rule, Inverse Function Theorem, Implicit Function Theorem. Riemann Integral of real-valued functions on Euclidean spaces, measure zero sets, Fubini's Theorem. Partition of unity, change of variables. Integration on chains, tensors, differential forms, Poincare Lemma, singular chains, integration on chains, Stokes' Theorem for integrals of differential forms on chains. (general version). Fundamental theorem of
calculus. Differentiable manifolds (as subspaces of Euclidean spaces), differentiable functions on manifolds, tangent spaces, vector fields, differential forms on manifolds, orientations, integration on manifolds, Stokes' Theorem on manifolds.
Text Books:
  1. Fleming W. Functions of Several Variables, Springer-Verlag
  2. Apostol  T. Calculus (Vol 2), John Wiley
Reference Books:
  1. Guillemin  V.  and Pollack  A. Differential Topolog , Prentice-Hall Inc., Englewood Cliffe, New Jersey.
  2. Munkre J.R. Analysis on Manifolds, Addison-Wesley
  3. Rudin  W. Principles of Mathematical Analysis, McGraw-Hill
  4. Courant  R. and John  F.  Introduction to Calculus and Analysis