To the Instructor xx ixSection(s) Description Number of Days
(Core) (Optional)
1.1-1.4 Fields; ordered fields; natural and rational nos. 1.5 2.5
1.5 Archimedean fields; density of rationals. 1
1.6 Suprema/infima;. completeness property. 1.5 .5
1.7 Existence and uniqueness of the real number field. 0 1
2.1 Limits of sequences; the basics. 1.5
2.2 Algebra of limits of sequences. 2 .5
2.3 Inequalities and limits. 1
2.4 Divergence to oo. .5 .5
2.5 Monotone sequences. 3
2.6 Subsequences; cluster points of sequences. 1 12.7 Cauchy sequences. (^1 1)
2.8 Countable and uncountable sets. 0 2
2.9 Upper and lower limits. 0 2
3.1 Neighborhoods; open sets. 1.5
3.2 Closed sets; cluster points; closure of a set. 1.5
3.3 Compact sets. 0 2- 3
3.4 The Cantor set; Cantor-like sets. 0 2
4.1 Limits of functions: definition and c:-0 proofs. 1.5
4.2 Algebra of limits of functions.^2 .5
4.3 One-sided limits. .5 .5
4.4 Infinity in limits.^1 1
5.1 Continuity: definition and c:-8 proofs. 1.5
5.2 Discontinuities; monotone functions. .5 1.5
5.3 Continuity on compact sets and intervals. 2 .5
5.4 Uniform continuity (can be postponed to Sect 7.2). 1 1
5.5 Monotonicity, continuity, inverses; Cantor function. 0 2-3
5.6 Exponential, powers, and logarithms 0 2
5.7 Sets of points of discontinuity. 0 2
6.1 The derivative; differentiability. 1
6.2 Rules for differentiation. 1 1
6.3 Relative extrema; monotone functions. 1 1
6.4 Mean value-type theorems. 1.5 1
6.5 Taylor's theorem. 1.5^1
6.6 L'Hopital's rules. 0 2