MATH 4A03/6A03, Fall 2018
REAL ANALYSIS II
Analysis starts with the fundamental concept of distance: the properties of space are largely determined by how distances are measured, and different measures of distance give rise to very different worlds. From the notion of distance we may then extend the calculus tools of limits, continuity, and smoothness to new and different ``spaces". Much of what we will cover involves infinite dimensional spaces, whose ``points" are not numbers or vectors, but (for example) functions defined on a common domain. With these methods we may study approximation of functions (by polynomials or Fourier Series) and the solution of equations (integral, differential, or nonlinear.) Real analysis provides the foundation (and often the underlying toolbox) for many mathematical areas where limits and continuity play an important role, such as complex variables (3X03, 4X03), differential equations (3F03, 3FF3), differential geometry (3B03), dynamical systems (3DC3), Fourier series and transforms, numerical analysis (3NA3 and 4NA3), probability and stochastic processes (Stats 3U03), and topology (3T03, 4B03). The material of this course will be of interest to anyone desiring a deeper understanding of the underlying analysis related to the above areas. It is strongly recommended for any student who is considering graduate school.
INSTRUCTOR: L. Bronsard
3 UnitsMetric spaces, compactness. Spaces of continuous functions, functions of several variables, inverse and implicit function theorems. Lebesgue integration.
Three lectures; one term
Prerequisite(s): MATH 3A03
Antirequisite(s): MATH 3AA3
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