Understanding Calculus – Course 1
Sequences, Limits, and Continuity of Functions
Limits of sequences
Sandwich principle
Completeness of the real numbers
Limit of a function at a point
Continuity of functions
Intermediate value theorem
Extremum theorem
Bolzano-Weierstrass theorem
This course is the first course of my “Understanding Calculus” course series. In this course, students will be introduced with
(1) Sequences and their limits
(2) Completeness of the real numbers
(3) Limit of a function at a point
(4) Continuity of functions
(5) Intermediate value theorem (IVT)
(6) Extremum theorem.
This course is very mathematically rigorous in the sense that we do manipulate the epsilon-N arguments for limit of a sequence and the epsilon-delta argument for limit of functions. These kinds of arguments are the gems of calculus and settle down the foundation for differentiation and integration that is to come in the next two courses in the series.
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