12/18/15, 10:30-12:30, regular classroom: Final Exam. [Chapters
1 through 6, skipping the starred sections, Theorem 3.1.11, the
material following 5.7.12 in Section 5.7 and Section 6.3]
12/18/15, 10:30-12:30, regular classroom: Final Exam. [Chapters
1 through 6, skipping the starred sections, Theorem 3.1.11, the
material following 5.7.12 in Section 5.7 and Section 6.3]
12/16/15: Review for the Final: discussion of the Sample Final
(selected problems). [Chapters 1 through 6, skipping the starred
sections, Theorem 3.1.11, the material following 5.7.12 in Section 5.7
and Section 6.3]
12/14/15: Discussion of Midterm II. [Text: Sections 3.5 through 6.4,
skipping the starred sections, the material following 5.7.12 in
Section 5.7 and Section 6.3]
12/11/15: Midterm II. [Text: Sections 3.5 through 6.4, skipping
the starred sections, the material following 5.7.12 in Section 5.7 and
Section 6.3]
12/9/15: Review for Midterm II: discussion of the sample test. [Text:
Sections 3.5 through 6.4, skipping the starred sections, the material
following 5.7.12 in Section 5.7 and Section 6.3]
12/7/15: More convergence tests. Absolute and conditional
convergence. [Sections 6.2 and 6.4 through the end]
12/4/15: Absolute convergence. Series with nonnegative terms:
convergence tests. [Sections 6.2 through 6.2.9 and 6.4 through 6.4.3]
12/2/15: Homework due at the beginning of class. Discussion of
homework: Problem 5.7.4. [Sections 5.5, 5.7-8]
11/30/15: Homecoming: A deeper look at Riemann integrability. Infinite
series. [Sections 5.8 and 6.1]
11/27/15: Thanksgiving break. Use the Analysis homework as an excuse
to leave that boring Thanksgiving dinner.
11/25/15: The gamma function. Further convergence tests for improper
integrals through the Root test. [Text: Section 5.7 through 5.7.12]
5.7-8]
11/23/15: Improper integration. The simple comparison test. [Text:
Section 5.7 through 5.7.7]
11/20/15: Homework is due at the beginning of class. Discussion of
homework: Problems 5.3.2 and 5.3.20(b). Improper integration:
definition. [Text: Sections 5.3; 5.7 through 5.7.2]
11/18/15: Integral mean value theorems. [Text: Section 5.5]
11/16/15: The Fundamental Theorem of Calculus. Change of
variables. Integration by parts. [Text: Section 5.3 through the end]
11/13/15: Homework is due at the beginning of the class. Discussion of
homework: Problem 5.1.8. [Text: Sections 5.1-2]
11/11/15: Riemann sums. The Fundamental Theorem of Calculus. [Text:
Sections 5.1 (through the end) and 5.3 (Theorem 5.3.1(a))]
11/9/15: Integrability of continuous and piecewise continuous
functions. Properties of the integral. [Text: Sections 5.1 (through
5.1.12) and 5.2]
11/6/15: Homework is due at the beginning of the class. Discussion of
homework: Problem 4.6.4. Integrability and proximity of upper and
lower Darboux sums. [Text: Sections 4.4-6; 5.1 through 5.1.9]
11/4/15: The Riemann integral: the lower and upper integrals, the
notion of an integrable function. [Text: Section 5.1 through
Proposition 5.1.7]
11/2/15: L'Hôpital's rule. Taylor's theorem. [Text: Sections
4.5-6]
10/30/15: Homework is due at the beginning of the class. Discussion of
homework: Problems 4.2.18 and 4.2.24. [Text: Sections 4.1-2]
10/28/15: The inverse function theorem. [Text: Section 4.4]
10/26/15: The mean value theorem. [Text: Section 4.2]
10/23/15: Homework is due at the beginning of the class. Discussion of
homework: Problem 3.5.12. Left and right derivatives. The theorem
about differentiability of a function f at x and the existence of a
function η, continuous at x, such that f(t) = f(x) +
η(t)(t-x). [Text: Sections 3.4-5; 4.1]
10/21/15: The derivative. [Text: Section 4.1]
10/19/15: Discussion of Midterm I. Uniform continuity of a function
with a bounded derivative. [Text: Chapters 1-3 through 3.5.6 and
Cardinality (class notes and page 508), skipping Theorem 3.1.11 and
Section 3.2; Section 3.5 through the end]
10/16/15: Midterm I. [Text: Chapters 1-3 through 3.5.6 and
Cardinality (class notes and page 508), skipping Theorem 3.1.11 and
Section 3.2]
10/14/15: Review for Midterm I: discussion of the sample test. [Text:
Chapters 1-3 through 3.5.6 and Cardinality (class notes and page 508),
skipping Theorem 3.1.11 and Section 3.2]
10/12/15: Properties of continuous functions. Uniform
continuity. [Text: Sections 3.4 and 3.5 through 3.5.6]
10/9/15: Homework is due at the beginning of the class. Discussion of
homework. [Text: Sections 3.1, 3.3]
10/7/15: Basic properties of continuous functions. Countable
sets. [Text: Page 508 and Section 3.3]
10/5/15: Continuous functions. [Text: Section 3.3]
10/2/15: Homework is due at the beginning of the class. Discussion of
homework. Limits of functions. [Text: Sections 2.1-4 and 3.1]
9/30/15: Proof of Corollary 2.4.3 (independent of Theorem
2.4.2). Neighborhoods and accumulation points of sets of real
numbers. [Text: Sections 2.4 and 3.1 up to, but not including, 3.1.3]
9/28/15: Cauchy sequences. Limit superior and limit inferior. [Text:
Sections 2.3-4]
9/25/15: Homework is due at the beginning of the class. Discussion of
homework. [Text: Sections 1.4-6]
9/23/15: Monotone sequences. Subsequences and cluster points. [Text:
Sections 2.2 and 2.3 through 2.3.5]
9/21/15: Euclidean space. Limits of sequences. [Text: Sections 1.6 and
2.1]
9/18/15: Homework is due at the beginning of the class. Discussion of
homework. [Text: Sections 1.1-4]
9/16/15: The existence and uniqueness of the nth root of a positive
real number. The extended real number system. Mathematical
Induction. [Text: Sections 1.4.9-14, 1.5]
9/14/15: Another introduction. Density of the rationals. [Text:
Section 1.4 through 1.4.8]
9/11/15 (Prof. Westerland substituting): The real number system as a
complete ordered field through the Well-Ordering
principle. [Text: Section 1.4 through 1.4.6]
9/9/15 (Prof. Westerland substituting): The syllabus is handed
out. The real number system as an ordered
field. [Syllabus. Text (Junghenn): Sections 1.1-3]
Last modified: (2018-10-07 23:13:32 CDT)