Here you will find information about the material that was already covered or will be covered in the next few lectures.

Unless indicated otherwise, the sections numbers are from the textbook [B].

Projected  
   
Thur, Dec 5: §36 Dirichlet’s and Abel’s Tests, Alternating Series, §37 Series of functions, Power Series
Tue, Dec 3: §34 Convergence of Infinite Series, Cauchy criterion, Absolute and conditional convergence, Rearrangement Theorem; §35 Examples, Comparison Test, Limit Comparison Test, Root Test, Ratio Test
Thur, Nov 28: No class (Thanksgiving)
Tue, Nov 26: No class (canceled because of evening exam)
Thur, Nov 21: §29 Properties of integral, Modification of the Integral; §30 Fundamental Theorem of Calculus, Integration by Parts, Change of Variables; §31 Convergence and Integral
Tue, Nov 19: Review for Midterm Exam 2
Covered  
Thur, Nov 14: §29 Upper and lower integrals (Project 29.alpha), §30 Riemann Criterion for Integrability, Integrability Theorem, Examples
Tue, Nov 12: §27 Cauchy Mean Value Theorem §28 L’Hopital’s rule, Taylor’s Theorem; §29 Partitions, Riemann-Stieltjes Integral, Upper and lower integrals (Project 29.alpha)
Thur, Nov 7: Monotone functions (finish), §25 limsup and liminf at a point; §27 Differentiation, Interior Max Theorem, Rolle’s Theorem, Mean Value Theorem,
Tue, Nov 5: §24 Weierstrass Approximation Theorem (finish) §25 Limit at a point; One-sided limits, monotone functions
Thur, Oct 31: §24 Approximation by step and piecewise-linear functions; Weierstrass Approximation Theorem; Bernstein polynomials
Tue, Oct 29: §23 Uniform continuity; §24 Sequences of continuous functions, Uniform convergence theorem
Thur, Oct 24: §22 Relative topology; Preservation of connectedness, compactness; Continuity of the inverse function;
Tue, Oct 22: §20 Continuity at a point; Examples; Combinations of functions; §22 Global Continuity Theorem
Thur, Oct 17: §18 Unbounded sequences; §20 Continuity at a point
Tue, Oct 15: §18 limsup and liminf
Thur, Oct 10: §16 Monotone sequences; Number e; Cauchy sequences;
Tue, Oct 8: No class: October break
Thur, Oct 3: §15 Subsequences, Combination of sequences; §16 Bolzano-Weierstrass for sequences
Tue, Oct 1: Review for Midterm Exam 1
Thur, Sep 26: §14 Sequences, Convergent sequences in in Rp; Examples
Tue, Sep 24: §12 Connected sets in R (cont); Connected open sets in Rp; §14 Convergence (start)
Thur, Sep 19: §11 Heine-Borel theorem; Cantor Intersection Theorem; Nearest Point Theorem; §12 Connected sets; Connected sets in R
Tue, Sep 17: §10 Bolzano-Weierstrass theorem; §11 Compactness and Heine-Borel theorem.
Thur, Sep 12: §9 Closed sets in Rp; Open sets in R; §10 Nested Cells, Cluster points
Tue, Sep 10: §8 Cauchy-Schwarz and Triangle inequalities; §9 Interior, exterior, boundary points; Open sets in Rp
Thur, Sep 5: §6 Cantor set revisited; §8 Vector spaces, inner products, norms; the Cartesian space Rp
Tue, Sep 3: §3 Finite, countable, and uncountable sets
Thur, Aug 29: §6 Existence of square roots; §7 Nested Intervals, Cantor set
Tue, Aug 27: §6 Completeness property of R, Archimedean Property, Density of rational numbers
Thur, Aug 22: §5 Order properties of R, Absolute value
Tue, Aug 20: §4 Algebraic properties of R; §5 Order properties of R (started)