12/16/14: Final exam: 8:00-10:00 a.m. (Section 001) and
1:30-3:30 p.m. (Section 003) in your regular classroom. [Text:
Chapters 1-5]
12/16/14: Final exam: 8:00-10:00 a.m. (Section 001) and
1:30-3:30 p.m. (Section 003) in your regular classroom. [Text:
Chapters 1-5]
12/10/14: Last class meeting: discussion of the sample final
exam. [Text: Chapters 1-5]
12/8/14: Discussion of the actual second midterm. [Text: Chapters 3-5]
12/5/14: Midterm Exam II. [Text: Chapters 3-5]
12/3/14: Discussion of Sample Exam II. Student course
evaluations. [Text: Chapters 3-5]
12/1/14: Homework is due at the beginning of the Monday
class. Discussion of homework. [Text: Chapter 5: pages 109-113]
11/28/14: Thanksgiving Break: university closed. Happy holiday!
11/26/14: Differentiation of vector-valued functions. [Text: Chapter
5: pages 111-113]
11/24/14: L'Hôpital's rule. Derivatives of higher orders. Taylor's
theorem. [Text: Chapter 5: pages 109-111]
11/21/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapter 5: pages 103-109]
11/19/14: The derivative: examples. The mean value theorem. The
continuity of derivatives. [Text: Chapter 5: pages 106-109]
11/17/14: The derivative: definition and main theorems. [Text: Chapter
5: pages 103-105]
11/14/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapter 4: pages 89-98]
11/12/14: Continuity and connectedness. Discontinuities. Monotonic
functions. Limits with the extended real number system. [Text: Chapter
4: pages 93-98]
11/10/14: Continuity vs. compactness. [Text: Chapter
4: pages 89-93]
11/07/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapters 3-4: pages 75-89]
11/05/14: Limits of functions, continuity. [Text: Chapter 4: pages 83-89]
11/03/14: Series, continued: rearrangements. [Text: Chapter 3: pages
75-78]
10/31/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapter 3: pages 65-75]
10/29/14: Series, continued: power series, summation by parts,
addition and multiplication of series. [Text: Chapter 3: pages 69-75]
10/27/14: Series, continued: absolute convergence, the root and ratio
tests. [Text: Chapter 3: pages 65-69, 71-72]
10/24/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapter 3: pages 55-65]
10/22/14: Some special sequences. Series. Series of nonnegative
terms. The number e. [Text: Chapter 3: pages 57-65]
10/20/14: Sequences of real numbers: monotonic, upper and lower
limits. [Text: Chapter 3: pages 55-57]
10/17/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapter 3: pages 47-55]
10/15/14: Subsequences, Cauchy sequences. [Text: Chapter 3: pages
51-55]
10/13/14: Limits of sequences in metric spaces. [Text: Chapter 3:
pages 47-51]
10/10/14: Midterm Exam I. [Text: Chapters 1-2]
10/8/14: Nested intervals and rectangular solids (cells). The
Heine-Borel and Weierstrass theorems. Discussion of Sample Exam
I. [Text: Chapters 1-2]
10/6/14: Compactness is an absolute notion. Nested compact
sets. [Text: Chapter 2: pages 37-38]
10/3/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapter 2: pages 35-43]
10/1/14: Compactness: continued. The Heine-Borel theorem. The Cantor
set. Connectedness. [Text: Chapter 2: pages 37-43]
9/29/14: Some remarks on the closure and the
interior. Compactness: beginning. [Text: Chapter 2: pages 35-37]
9/26/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapter 2: pages 24-35]
9/24/14: Metric spaces (continued). Closed sets. Limit (accumulation)
points, isolated points. Boundary. [Text: Chapter 2: pages
33-35]
9/22/14: Metric spaces: introduction. Definition of a metric
space. Examples. Open balls. Open sets. Neighborhoods. [Text: Chapter
2: pages 30-32]
9/19/14: Homework is due at the beginning of the class. Discussion of
homework. Countability (finished): power sets, the hierarchy of
cardinals, the cardinality of the reals, the Continuum
Hypothesis. [Text: Chapters 1-2: pages 11-28, 29-30]
9/17/14: Countability (continued): the countability of the rationals
and the uncountability of the reals. [Text: Chapter 2: pages 26-28]
9/15/14: Euclidean spaces. Countability: basic notions. [Text: Chapter
1: pages 16-17, Chapter 2: pages 24-25]
9/12/14: Homework is due at the beginning of the class. Discussion of
homework. [Text: Chapter 1, pages 1-11, the Appendix to Chapter 1]
9/10/14: The extended real number system and the complex field. [Text:
Chapter 1, pages 11-16]
9/8/14: The real field. [Text: Chapter 1, pages 8-11, skim the
Appendix to Chapter 1]
9/5/14: Fields and ordered fields. [Text: Chapter 1, pages 5-8]
9/3/14: Introduction. The sum of all naturals. Ordered sets. The least
upper bound
property. [Syllabus. Text:
Chapter 1 through page 5]
Last modified: (2015-09-14 00:43:33 CDT)