Semester 4

This module introduces the student to functions of many variables: Domains of definition, levels lines and surfaces, Limits and continuity; Partial derivatives, Schwartz theorem, chain rule; Total differentiation, directional derivative and gradient; Optimization: critical points given a formula, maxima and minima, second derivative test; Multiple integrals, curvilinear and surface integrals and their applications; Gradient, divergence and curl of vector valued functions and Green and Stokes theorems.