MATH 425 A: Fundamental Concepts of Analysis

Introduction to metric spaces and multivariable differential calculus: Euclidean spaces, abstract metric spaces, compactness, Bolzano-Weierstrass property, sequences and their limits, Cauchy sequences and completeness, Heine-Borel Theorem, continuity, uniform continuity, connected sets and the intermediate value theorem. Derivatives of functions of several variables, chain rule, mean value theorem, inverse and implicit function theorems. Prerequisite: a minimum grade of 2.0 in either MATH 136 or MATH 208; and a minimum grade of 2.0 in either MATH 335 or MATH 424. Offered: WSp.