Course Log
Here you will find information about the material that was already covered or will be covered in the next few lectures.
| Covered | |
|---|---|
| Fri, Dec 9: | Review for Final Exam |
| Wed, Dec 7: | §37 Series of functions, Power Series |
| Mon, Dec 5: | §35 Ratio Test, §36 Dirichlet’s and Abel’s Tests, Alternating Series, §37 Series of Functions |
| Fri, Dec 2: | §35 Examples, Comparison Test, Limit Comparison Test, Root Test |
| Wed, Nov 30: | §31 Uniform Convergence and Integral, Bounded Convergence Theorem §34 Convergence of Infinite Series, Cauchy criterion, Absolute and conditional convergence, Rearrangement Theorem |
| Mon, Nov 28: | §30 Fundamental Theorem of Calculus, Integration by Parts, Change of Variables; §31 Convergence and Integral |
| Fri, Nov 25: | No class (Thanksgiving) |
| Wed, Nov 23: | No class (Thanksgiving) |
| Mon, Nov 21: | No class (cancelled because of evening exam) |
| Fri, Nov 18: | §30 Riemann Criterion for Integrability, Integrability Theorem, Differentiation Theorem |
| Wed, Nov 16: | Review for Midterm 2 |
| Mon, Nov 14: | §29 Examples, Properties of integral, Modification of the Integral |
| Fri, Nov 11: | §29 Riemann-Stieltjes Integral, Upper and lower integrals (Project 29.alpha) |
| Wed, Nov 9: | §28 L’Hopital’s rule, Taylor’s Theorem; §29 Partitions |
| Mon, Nov 7: | §27 Differentiation, Interior Max Theorem, Rolle’s Theorem, Mean Value Theorem, Cauchy Mean Value Theorem |
| Fri, Nov 4: | One-seded limits, monotone functions, §25 limsup and liminf at a point |
| Wed, Nov 2: | §24 Weierstrass Approximation Theorem (finish), §25 Limit at a point |
| Mon, Oct 31: | §24 Approximation by step and piecewise-linear functions, Weierstrass Approximation Theorem |
| Fri, Oct 28: | No class (cancelled because of evening exam) |
| Wed, Oct 26: | §24 Sequences of continuous functions, Uniform convergence theorem |
| Mon, Oct 24: | §22 Continuity of the inverse function; §23 Uniform continuity |
| Fri, Oct 21: | §22 Preservation of connectedness, compactness |
| Wed, Oct 19: | §20 Combinations of functions; §22 Global Continuity Theorem |
| Mon, Oct 17: | §20 Continuity at a point; Examples |
| Fri, Oct 14: | §18 limsup and liminf, unbounded sequences |
| Wed, Oct 12: | §18 limsup and liminf |
| Mon, Oct 10: | No class (October Break) |
| Fri, Oct 7: | §16 Examples; §18 limsup and liminf (start) |
| Wed, Oct 5: | Review for Midterm Exam 1 |
| Mon, Oct 3: | §16 Bolzano-Weierstrass for sequences; Cauchy sequences |
| Fri, Sep 30: | §15 Combination of sequences; §16 Monotone sequences; Number e |
| Wed, Sep 28: | §14 Examples; §15 Subsequences |
| Mon, Sep 26: | §14 Convergent sequences in in Rp |
| Fri, Sep 23: | §12 Connected open sets in Rp; §14 Sequences (start) |
| Wed, Sep 21: | §11 Cantor Intersection Theorem; §12 Connected sets; Connected sets in R |
| Mon, Sep 19: | §11 Compactness and Heine-Borel theorem |
| Fri, Sep 16: | §10 Nested Cells, Cluster points, Bolzano-Weierstrass theorem |
| Wed, Sep 14: | §9 Open and closed sets; §10 Nested Cells |
| Mon, Sep 12: | §9 Interior, exterior, boundary points; Open sets |
| Fri, Sep 9: | §8 Vector spaces, inner products, norms; the Cartesian space Rp |
| Wed, Sep 7: | §3 Finite, countable, and uncountable sets |
| Mon, Sep 5: | No class (Labor Day) |
| Fri, Aug 2: | §6 Cantor set; §3 Finite, countable, and uncountable sets |
| Wed, Aug 31: | §6 Existence of square roots (cont.); §7 Nested Intervals |
| Mon, Aug 29: | §6 Archimedean Property; Density of rational numbers; Existence of square roots |
| Fri, Aug 26: | §5 Absolute value; §6 Completeness property of R |
| Wed, Aug 24: | §5 Order properties of R |
| Mon, Aug 22: | §4 Algebraic properties of R |