Analysis II

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Author(s): N. Wickramasekera, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; calc; calculus; single variable; limits; differentiation; differential; integration; integral; continuity; differentiability; analysis; real; complex; multiple variables; multivariable; multivariate; several variables; many variables

Introduction
Uniform convergence
Series of functions
Convergence of series
Power series
Uniform continuity and integration
Uniform continuity
Applications to Riemann integrability
Non-examinable fun*
Rn as a normed space
Normed spaces
Cauchy sequences and completeness
Sequential compactness
Mappings between normed spaces
Metric spaces
Preliminary definitions
Topology of metric spaces
Cauchy sequences and completeness
Compactness
Continuous functions
The contraction mapping theorem
Differentiation from Rm to Rn
Differentiation from Rm to Rn
The operator norm
Mean value inequalities
Inverse function theorem
2nd order derivatives