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 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 |