MATH 2XX3, Winter 2019
ADVANCED CALCULUS II
As a last instalment of the calculus sequence we take a closer look at functions of several variables, adding a more geometrical flavor. An important part of the course will be to recognize the essential role of linear algebra in understanding higher dimensional calculus, and we will combine methods and ideas from calculus and linear algebra to better understand topics such as differentiability and critical points; curves and trajectories in space; and the solution of nonlinear equations. The course will conclude with an introduction to Fourier Series, a fundamental tool which again depends on the deep interaction between calculus and linear algebra. With this assortment of topics we look to your mathematical past (finding connections between areas you originally learned separately,) but also to your mathematical future, introducing you to analysis, topology, differential geometry, ordinary and partial differential equations, which you may want to study in 3rd year and beyond.
INSTRUCTOR: S. Alama
Theory of functions of several variables: limits, continuity, differentiability, Inverse Function Theorem, Taylor’s Theorem. Extreme values, optimization, introduction to Fourier series.
Three lectures, one tutorial; one term
Prerequisite(s): MATH 2X03; or credit or registration in ISCI 2A18 A/B
PLEASE REFER TO MOSAIC FOR THE MOST UP-TO-DATE INFORMATION ON TIMES AND ROOMS