Covered

Dec 5: (planned) §37 Power series

Dec 2: § 35 Ratio test, §37 Series of functions

Nov 30: §34 Rearrangements of series, §35 Comparison and Limit Comparison tests, Root test

Nov 18: §31 Uniform Convergence and Integral (completed); Bounded Convergence Theorem, Dominated Convergence Theorem §34 Convergence of Infinite Series, Cauchy criterion, absolute and conditional convergence, nonnegative series.

Nov 14: §31 Uniform Convergence and Integral

Nov 11:§30 Differentiation Theorem, Fundamental Theorem of Calculus, Change of Variables

Nov 7: §30 Riemann Criterion of Integrability, First and Second Mean Value Theorems

Nov 2: §29 Properties of integral, Integration by parts, Modification of the integral

Oct 31: §29 RiemannSieltjes Integral, Examples.

Oct 28: §27 Mean Value Theorem, Cauchy Mean Value Theorem; §28 Taylor's Theorem.

Oct 26: §26 Limit of the function at a point, upper and lower limits; §27Differentiation, Rolle's Theorem.

Oct 24: §25 Weierstrass approxuamtion theorem (cont.), §26 Limit of the function at a point, upper and lower limits

Oct 21: §25 Weierstrass approximation theorem (Bernstein's proof)

Oct 19: §24 Pointwise and Uniform convergence of functions

Oct 17: §22 Preservation of compactness (cont), §23 Uniform continuity

Oct 14: §22 Preservation of connectedness, compactness

Oct 12: §20 Examples, §22 Global Continuity Theorem

Oct 7: Midterm 1 solutions

Oct 5: §20 Continuity at a point (topological, metric, and sequential definitions), examples

Oct 3: Review for Midterm Exam 1

Sep 30: §18 limsup and liminf

Sep 28: §18 limsup and liminf

Sep 26: §16 Cauchy sequnces; §18 limsup and liminf (started)

Sep 23: §16 Monotone sequences, BolzanoWeierstrass for sequences.

Sep 21: §14 Convergent sequences; §15 Subsequences and combinations, examples.

Sep 19: §12 Connected open sets in
R^{p} (finished); §14 Convergent sequences (started)

Sep 16: §12 Connected sets; Connected sets in
R; Connected open sets in
R^{p} (started)

Sep 14: §11 Compactness and HeineBorel theorem (finished), corollaries; §12 Connected sets (started)

Sep 12: §11 Compactness and HeineBorel theorem;

Sep 9: §10 Cluster points, Nested Cells and BolzanoWeierstrass

Sep 7: §9 Open and closed sets, interior, exterior, boundary points; §10 Cluster points (started)

Sep 2: §8 Vector spaces, inner products, norms, distance, §9 Open Sets

Aug 31: §3 Finite and Countable sets, §8 Vector spaces, inner products, norms (started)

Aug 29: §7 Nested Intervals, Cantor Set

Aug 26: §6 Completeness property of
R (continued)

Aug 24: §5 Order properties of
R; §6 Completeness property of
R (started)

Aug 22: §4 Algebraic properties of
R; §5 Order properties of
R (started)