The contents include: Introduction,
Axioms for arithmetic in R, Properties of arithmetic in R, Ordering the real
numbers, Inequalities and arithmetic, The modulus of a real number, The
complex numbers, Upper and lower bounds, Supremum, infimum and completeness,
Existence of roots, More consequences of completeness, Countability, More on
countability, Introduction to sequences, Convergence of a sequence, Bounded
and unbounded sequences, Complex sequences, Subsequences, Orders of
magnitude, Monotonic sequences, Convergent subsequences, Cauchy sequences,
Convergence for series, More on the Comparison Test, Ratio Test, Integral
Test, Power series, Radius of convergence, Differentiation Theorem.

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.

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 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 book covers the following topics: Calculus of
smooth mappings, Calculus of holomorphic and real analytic mappings, Partitions
of unity, Smoothly realcompact spaces, Extensions and liftings of mappings,
Infinite dimensional manifolds, Calculus on infinite dimensional manifolds,
Infinite dimensional differential geometry, Manifolds of mappings and Further
applications.