This is the third module in the series Analysis 1, 2, 3 that covers rigorous Analysis. It covers convergence of functions and its applications to Integration, an introduction to multivariable calculus and Complex Analysis.
This course deals with the theories of differentiation and integration in higher dimensions, building a rigorous analytic framework for the multivariable calculus you saw in MA144 analogously to how MA139 provides a rigorous framework for the single variable calculus you learned at A level (or equivalent). The higher-dimensional setting also brings unique new challenges as well as useful theorems, such as the multivariate Taylor's Theorem and the Implicit Function Theorem, which will be essential to later courses in Analysis, Geometry and Differential Equations.
Further details are given on the module catalogue page: https://courses.warwick.ac.uk/modules/2025/MA263-10