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 lecture note
describes the following topics: Set Theory and Mathematical Induction, The Real
Numbers, Absolute value and real line, Sequences of Real Numbers, Open and
Closed Sets in R, Complex Numbers.
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