Calculus & Analytic Geometry (B.A / B.Sc.)
Chapter:01 (Bounds, Limits and Continuity)
In this chapter, we will study the following topics:
- real numbers
- axioms of the real number system
- distributive operation over (+)
- lub or supremum
- bounds and bounded sets
- set of rational number
- bounded axioms
- the line and the real number system
- limit points of sets
- deleted nbhd
- limit points or points of accumulation
- limit superior or upper limit
- limit of the sequence
- the graph of the sequence
- graph on the line
- convergent sequence
- null sequence
- monotonic sequence
- bounded monotonic sequence
- divergent
- sets and sequences
- converging to s
- range of the values of the function
- the graph of a function f
- identity function and its graph
- addition, product and composition
- algebra of functions
- limits of functions
- mapping of onto function
- null sequence with negative terms
- range of values of the bounded function
- continuity and discontinuous of functions
- properties of the continuous function
- proofs of some continuity theorems
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