This book explains the
following topics: Some Elementary Logic, The Real Number System, Set Theory,
Vector Space Properties of Rn, Metric Spaces, Sequences and Convergence, Cauchy
Sequences, Sequences and Compactness, Limits of Functions, Continuity, Uniform
Convergence of Functions, First Order Systems of Differential Equations
This note covers
Basic concepts in mathematical analysis and some complements,
Real numbers and ordered fields, Cardinality, Topologies, Construction of some
special functions.
The contents include:
The Real And Complex Number Systems, Sets And Functions, Basic Topology,
Sequences And Series, Continuity, Sequences And Series Of Functions,
Figures.
The contents include: Introduction,
Metric Spaces, Compactness, Cauchy Sequences in Metric Spaces, Sequences in
Rn, Continuous Functions on Metric Spaces, Sequences of Functions.
Author(s): Donald J. Estep, Department of
Mathematics, Colorado State University
Goal in this set
of lecture notes is to provide students with a strong foundation in mathematical
analysis. The lecture notes contain topics of real analysis usually covered in a
10-week course: the completeness axiom, sequences and convergence, continuity,
and differentiation. The lecture notes also contain many well-selected exercises
of various levels.
This text is an
outgrowth of lectures given at the University of Windsor, Canada. Topics covered
includes: Set Theory, Real Numbers. Fields, Vector Spaces, Metric Spaces,
Function Limits and Continuity, Differentiation and Anti differentiation.
This book explains the
following topics: Some Elementary Logic, The Real Number System, Set Theory,
Vector Space Properties of Rn, Metric Spaces, Sequences and Convergence, Cauchy
Sequences, Sequences and Compactness, Limits of Functions, Continuity, Uniform
Convergence of Functions, First Order Systems of Differential Equations