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

Fri, Dec 11: Review for Final Exam
Wed, Dec 9: §37 Series of functions, Power Series
Mon, Dec 7: §36 Dirichlet’s Test, Alternating Series §37 Series of Functions
Fri, Dec 4: §35 Comparison Test, Limit Comparison Test, Root and Ratio Test
Wed, Dec 2: §34 Absolute and conditional convergence, Nonnegative Series, Examples, Rearrangement Theorem
Mon, Nov 30: Overview of Midterm 2, §34 Convergence of Infinite Series, Cauchy criterion,
Fri, Nov 27: No class (Thanksgiving)
Wed, Nov 25: No class (Thanksgiving)
Mon, Nov 23: No class (cancelled)
Fri, Nov 20: §31 Integral from of the Remainder, Uniform Convergence and Integral, Bounded Convergence Theorem
Wed, Nov 18: §30 Second Mean Value Theorem, Differentiation Theorem, Fundamental Theorem of Calculus, Change of Variables
Mon, Nov 16: Review for Midterm 2
Fri, Nov 13: §30 Riemann Criterion for Integrability, Integrability Theorem, First Mean Value Theorem
Wed, Nov 11: Integration by parts, Modification of the integral, Upper and lower integrals
Mon, Nov 9: §29 Properties of integral
Fri, Nov 6: §29 Riemann-Stieltjes Integral, Cauchy criterion, Examples
Wed, Nov 4: §28 Taylor’s Theorem, §29 Riemann-Stieltjes Integral (start)
Mon, Nov 2: §27 Rolle’s Theorem, Mean Value Theorem, Cauchy Mean Value Theorem; §28 L’Hopital’s rule
Fri, Oct 30: §25 limsup and liminf at a point, §27 Differentiation (start)
Wed, Oct 28: §24 Weierstrass Approximation Theorem (finish), §25 Limit at a point
Mon, Oct 26: §24 Approximation by piecewise-linear functions, Bernstein polynomials, Weierstrass Approximation Theorem (started)
Fri, Oct 23: §23 Uniform continuity (finish), §24 Sequences of continuous functions, Uniform convergence theorem, Approximation by step functions
Wed, Oct 21: §22 Preservation of compactness, Continuity of the inverse function, §23 Uniform continuity (start)
Mon, Oct 19: §22 Global Continuity Theorem, Preservation of connectedness, compactness
Fri, Oct 16: §20 Combinations of functions, examples
Wed, Oct 14: Midterm 1 discussion; §20 Continuity at a point
Mon, Oct 12: No class (October Break)
Fri, Oct 9: §18 limsup and liminf, unbounded sequences
Wed, Oct 7: Review for Midterm Exam 1
Mon, Oct 5: §18 limsup and liminf
Fri, Oct 2: §16 Cauchy sequences, examples
Wed, Sep 30: §15 Combinations of sequences, §16 Monotone sequences, Bolzano-Weierstrass for sequences
Mon, Sep 28: §14 Examples; §15 Subsequences
Fri, Sep 25: §14 Convergent sequences, examples
Wed, Sep 23: §12 Connected open sets in Rp (finish), §14 Convergent sequences (start)
Mon, Sep 21: §12 Connected sets; Connected sets in R; Connected open sets in Rp
Fri, Sep 18: §11 Compactness and Heine-Borel theorem
Wed, Sep 16: §10 Cluster points, Nested Cells and Bolzano-Weierstrass
Mon, Sep 14: §9 Open and closed sets; Interior, exterior, boundary points
Fri, Sep 11: No class (cancelled)
Wed, Sep 9: §8 Vector spaces, inner products, norms, distance
Mon, Sep 7: No class (Labor Day)
Fri, Sep 4: §3 Finite, countable, and uncounatble sets
Wed, Sep 2: §7 Nested Intervals, Cantor set
Mon, Aug 31: §6 Existence of square and k-th roots, §5 Absolute value
Fri, Aug 28: §6 The completeness property of R
Wed, Aug 26: §5 Order properties of R
Mon, Aug 24:  §4 Algebraic properties of R