## 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**R**^{p}(finish), §14 Convergent sequences (start)*Mon, Sep 16*: §12 Connected sets; Connected sets in**R**; Connected open sets in**R**^{p}(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)