Real Analysis II

Week 1:Metric spaces and normed linear spaces Week 2:Compactness and completeness in metric spaces Week 3:The Arzelà–Ascoli and Stone--Weierstrass theorems Week 4:The derivative in several variables as a linear map I Week 5:The derivative in several variables as a linear map II Week 6:The inverse and implicit function theorems Week 7:Manifolds, Tangent spaces and Lagrange multipliers Week 8:A precis of curves and surfaces Week 9:The definition of the Lebesgue integral Week 10:Convergence theorems for the Lebesgue integral Week 11:Multiple Lebesgue Integrals Week 12:The Jacobi transformation formula for Lebesgue integrals