This is a description of what was done in each class; there is a separate listing of the homework that was assigned.
Come to class ready to discuss any examples or problems that you were not sure of.References are to the textbook for this class, Introduction to Analysis, by M. Rosenlicht.
Classes are described in reverse time order.
Final exam, 7-10pm, M 12/10. (Solutions are here.)
Classes 42 and 43 (W 12/5 and F 12/7): R chap. 7, section 3; power
series.
Class 41 (M 12/3): 100-point exam on D-W pages
337-348 and R chap. 6, section 5, and chap. 7, sections 1 and
2. (Solutions are here.)
Class 40 (F 11/30): practice problems for upcoming exam. (The
practice problems are here.
Comments on solutions are here.)
Classes 38 and 39 (M 11/26 and W 11/28): R chap. 7, section 2;
convergence of series, especially series of functions.
Classes 36 and 37 (W 11/14 and F 11/16): R chap. 7, section 1;
limits of sequences of functions and relations to integration and
differentiation.
Class 35 (M 11/12): 50-point exam on the Riemann integral; D-W pages
337-348 and R chap. 6, section 5. (Solutions are here.)
Classes 33 and 34 (W 11/7 and F 11/9): R chap. 6, section 5;
logarithm and exponential functions.
Class 32 (M 11/5): D-W pages 345-348; Fundamental Theorem of
Calculus and its applications.
Classes 30 and 31 (W 10/31 and F 11/2): D-W pages
341-344; linearity and positivity of the integral.
Class 29 (M 10/29): D-W pages 344-345 and problem 17.14; monotone
and continuous functions are integrable.
Class 28 (F 10/26) continue defining the integral; included
discussion of problem 17.8.
Class 27 (W 10/24): pages 337-340 of D'Angelo-West; definition of
upper and lower sums and of the Riemann integral.
Next we treat the Riemann integral; rather than using Rosenlicht we
will use Chapter 17 of the D'Angelo-West text as the basis for our
treatment of integration. We'll return to Rosenlicht to introduce
the log and exp functions.
Class 26 (M 10/22): 100-point exam on chaps. 4 and 5. (Solutions are
here.)
Class 25 (F 10/19): practice problems for exam on chaps. 4 and
5. (The practice problems are here.
Comments on solutions are here.)
Problem session, Thurs. 10/18, 5:15pm.
Class 24 (W 10/17): chap. 5, section 4; Taylor's theorem.
Class 23 (M 10/15): chap. 5, section 3; mean
value theorem.
Class 22 (F 10/12): finish chap. 5, section 2; esp. the chain rule.
Class 21 (W 10/10): chap. 5, sections 1 and 2; differentiation of a
function on the reals.
Class 20 (M 10/8): finish chap. 4, section 6.
Class 19 (F 10/5): begin chap. 4, section 6; uniform convergence of
a sequence of functions.
Class 18 (W 10/3): finish chap. 4, section 4, and also discuss chap.
4, section 5.
Class 17 (M 10/1): begin chap. 4, section 4;
uniform continuity of functions between metric spaces.
Class 16 (F 9/28): chap. 4, sections 2-3.
Class 15 (W 9/26): chap. 4, sections 1-2; continuity of functions
between metric spaces.
Class 14 (M 9/24): 100-point exam on chaps. 2 and 3.
(Solutions are here.)
Class 13 (F 9/21): practice exam on chaps. 2 and 3. (The
practice problems are here.
Comments on solutions are here.)
Class 12 (W 9/19): chap. 3, section 6; connectedness of (a subset
of) a metric space.
Classes 8, 9, 10, and 11 (M 9/10, W 9/12, F 9/14, M 9/17): chap. 3,
section 5;
compactness of (a subset of) a metric space.
Class 7 (F 9/7): 50-point exam on chap. 2 and the first 3 sections
of chap. 3. (Solutions are here.))
Thurs. 9/6: problem session at 4:00 in the usual classroom.
Class 6 (W 9/5): chap. 3, section 4; completeness of a metric space.
Class 5 (F 8/31): chap. 3, section 3; convergence of sequences.
Class 4 (W 8/29): chap. 3, section 2; open and closed sets.
Class 3 (M 8/27): begin chap. 3; metric spaces.
Classes 1 and 2 (W 8/22 and F 8/24): review chap. 2; the real number
system.