| Wed, Nov 28: |
§34 Absolute and conditional convergence, Examples, Rearrangement Theorem |
| Mon, Nov 26: |
Overview of Midterm 2, §34 Convergence of Infinite Series, Cauchy criterion, Nonnegative Series |
| Fri, Nov 23: |
No class (Thanksgiving) |
| Wed, Nov 21: |
No class (Thanksgiving) |
| Mon, Nov 19: |
No class (cancelled because of evening exam) |
| Fri, Nov 16: |
§31 Uniform Convergence and Integral, Bounded Convergence Theorem |
| Wed, Nov 14: |
Review for Midterm 2 |
| Mon, Nov 12: |
§30 First and Second Mean Value Theorems, Differentiation Theorem, Fundamental Theorem of Calculus, Change of Variables |
| Fri, Nov 9: |
§30 Riemann Criterion for Integrability, Integrability Theorem, §29 Integration by parts |
| Wed, Nov 7: |
§29 Properties of integral, Upper and lower integrals (Project 29.alpha) |
| Mon, Nov 5: |
§29 Riemann-Stieltjes Integral, Cauchy criterion, Examples |
| Fri, Nov 2: |
§28 Mean Value Theorem, Cauchy Mean Value Theorem; Taylor’s Theorem |
| Wed, Oct 31: |
§27 Differentiation, Interior Max Theorem, Rolle’s Theorem |
| Mon, Oct 29: |
Monotone functions, §25 limsup and liminf at a point |
| Fri, Oct 26: |
§24 Weierstrass Approximation Theorem (finish), §25 Limit at a point |
| Wed, Oct 24: |
§24 Approximation by step and piecewise-linear functions, Bernstein polynomials, Weierstrass Approximation Theorem (started) |
| Mon, Oct 22: |
§23 Uniform continuity (finish), §24 Sequences of continuous functions, Uniform convergence theorem, Approximation by step functions |
| Fri, Oct 19: |
§22 Preservation of compactness, Continuity of the inverse function, §23 Uniform continuity (start) |
| Wed, Oct 17: |
§22 Global Continuity Theorem, Preservation of connectedness, compactness |
| Mon, Oct 15: |
§20 Continuity at a point, Combinations of functions |
| Fri, Oct 12: |
§18 limsup and liminf, unbounded sequences |
| Wed, Oct 10: |
Midterm 1 discussion; §18 limsup and liminf (cont.) |
| Mon, Oct 8: |
No class (October Break) |
| Fri, Oct 5: |
No class (cancelled because of evening exam) |
| Wed, Oct 3: |
§16 Examples, §18 limsup and liminf (start) |
| Mon, Oct 1: |
Review for Midterm Exam 1 |
| Fri, Sep 28: |
§16 Cauchy sequences |
| Wed, Sep 26: |
§16 Monotone sequences; Bolzano-Weierstrass for sequences |
| Mon, Sep 24: |
§14 Examples; §15 Subsequences, combinations of sequences |
| Fri, Sep 21: |
§14 Convergent sequences; Examples |
| Wed, Sep 19: |
§12 Connected sets in R; Connected open sets in Rp |
| Mon, Sep 17: |
§11 Heine-Borel (cont.); §12 Connected sets |
| Fri, Sep 14: |
§10 Bolzano-Weierstrass (cont.); §11 Compactness and Heine-Borel theorem |
| Wed, Sep 12: |
§9 Boundary points (cont.); §10 Cluster points; Nested Cells and Bolzano-Weierstrass |
| Mon, Sep 10: |
§9 Open and closed sets; Interior, exterior, boundary points |
| Fri, Sep 7: |
§8 Inner products, norms; the Cartesian space Rp |
| Wed, Sep 5: |
§3 Uncountability of Cantor set and R; §8 Vector spaces |
| Mon, Sep 3: |
No class (Labor Day) |
| Fri, Aug 31: |
§3 Finite, countable, and uncountable sets |
| Wed, Aug 29: |
§6 Existence of square roots (cont.); §7 Nested Intervals; Cantor set |
| Mon, Aug 27: |
§6 Archimedean Property; Density of rational numbers; Existence of square roots |
| Fri, Aug 24: |
§5 Absolute value; §6 Completeness property of R |
| Wed, Aug 22: |
§5 Order properties of R |
| Mon, Aug 20: |
§4 Algebraic properties of R |