Advanced calculus: theory and practice

Sequences and Their Limits Computing the LimitsDefinition of the Limit Properties of Limits Monotone Sequences The Number e Cauchy Sequences Limit Superior and Limit Inferior Computing the Limits-Part II Real Numbers The Axioms of the Set R Consequences of the Completeness Axiom Bolzano-Weierstrass Theorem Some Thoughts about RContinuity Computing Limits of Functions A Review of Functions Continuous Functions: A Geometric Viewpoint Limits of Functions Other Limits Properties of Continuous Functions The Continuity of Elementary Functions Uniform Continuity Two Properties of Continuous Functions