This note is an activity-oriented
companion to the study of real analysis. It is intended as a pedagogical
companion for the beginner, an introduction to some of the main ideas in real
analysis, a compendium of problems, are useful in learning the subject, and an
annotated reading or reference list. Topics covered includes: Sets, Functions,
Cardinality, Groups, Vector Spaces, And Algebras, Partially Ordered Sets, The
Real Numbers, Sequences And Indexed Families, Categories, Ordered Vector Spaces,
Topological Spaces, Continuity And Weak Topologies, Normed Linear Spaces,
Differentiation, Complete Metric Spaces, Algebras And Lattices Of Continuous
Functions.
This note describes the following topics: preliminaries, The real numbers, Sequences, Limits of
functions, Continuity, Differentiation, Riemann integration, Sequences of
functions, Metric spaces, Multivariable differential calculus.
This
note covers the following topics: mathematical reasoning, The Real Number
System, Special classes of real numbers, Limits of sequences, Limits of
functions, Continuity, Differential calculus, Applications of differential
calculus, Integral calculus, Complex numbers and some of their applications, The
geometry and topology of Euclidean spaces, Continuity, Multi-variable
differential calculus, Applications of multi-variable differential calculus,
Multidimensional Riemann integration, Integration over submanifolds.
This note is an activity-oriented
companion to the study of real analysis. It is intended as a pedagogical
companion for the beginner, an introduction to some of the main ideas in real
analysis, a compendium of problems, are useful in learning the subject, and an
annotated reading or reference list. Topics covered includes: Sets, Functions,
Cardinality, Groups, Vector Spaces, And Algebras, Partially Ordered Sets, The
Real Numbers, Sequences And Indexed Families, Categories, Ordered Vector Spaces,
Topological Spaces, Continuity And Weak Topologies, Normed Linear Spaces,
Differentiation, Complete Metric Spaces, Algebras And Lattices Of Continuous
Functions.
This note explains
the following topics: Preliminaries: Proofs, Sets, and Functions, The Foundation
of Calculus, Metric Spaces, Spaces of Continuous Functions, Modes of continuity,
Applications to differential equations, Applications to power series.