Course Log

Here you will find information about the material which has already been covered or is going to be covered in the next few lectures

Covered

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