## Description

**Differentiation :** Differentiation of vector-valued functions.

**Functions of Several Variables** : The space of linear transformations on Rn to Rm as a metric space. Differentiation of a vector-valued function of several variables. The inverse function theorem. The implicit function theorem.

(**Lebesgue Measure :** Introduction, Outer measure, Measurable sets and Lebesgue measure. A non-measurable set, Measurable functions, Littlewood’s three principles.

**The Lebesgue Integral :** The Lebesgue integral of a bounded function over a set of finite measure. The integral of a non-negative function. The general Lebesgue integral, Convergence in measure.

**Differentiation and Integration :** Differentiation of monotone functions. Differentiation of an integral. Absolute continuity. Convex functions.