News: You can download test 1 , test 2 and the FINAL TEST with my comments/solutions.

You are welcome to contact me if you want me to elaborate on those.

Here is the graph of the function in problem 4, hw 10.

Here is the proof of the Weierstrass approximation theorem.

This course is a first part of
what used to be an undegraduate
analysis sequence 411-412 and has been modified to become 4111-4112. It
presents
the theory of one and
several variable calculus followed by the introduction to Lebesgue
theory. This sequence is usually required for those wishing to
complete the so-called
"traditional"
math major, a group normally limited to students contemplating going on
to do graduate work in mathematics, physics, mathematical economics, or
some other highly quantitative discipline in which theory plays a large
role. Students who are not traditional math majors are welcome to
take the course provided they have an interest in understanding the
theoretical
basis for calculus.
Those interested in building up their prowess with techniques for doing
calculus problems and uninterested in understanding why the techniques
work are STRONGLY ADVISED NOT to take 4111-12. While it's true
that
occasionally techniques will be introduced in 4111-412 which aren't
covered
in other calculus courses, these will be few and far between; also,
most
of the lecture time will be devoted to the theory of why these methods
work rather than illustrations of the calculations. In brief,
there
is virtually nothing in common between the style of earlier math
courses
(nothing proven, hand-waving justifications, reliance on physical
intuition,
working out numerical exercises, developing computational skills) and
the
style of 4111-12 (nearly everything proven with a fairly high degree of
rigor, a large part of the homework and exam questions
theoretical
with only a few numerical problems tossed in for good measure, emphasis
on building up skills at proving theorems and developing mathematical
intuition).

Many 4111-12 students may have gotten a taste of theory in
Math 310;
others
may never have gone past the statements of unproved theorems in
Calculus
1-3. In any event, it will not be presumed that students have any
prior experience in proving theorems or working out well-reasoned
arguments
responsive to theoretical homework questions. To the contrary,
one
of the main goals of 4111-12 is to provide this kind of experience. **Location:
**Cupples I 111, -T-T---, 10:00AM - 11:30AM

Office: Cupples I, Room 202 (between the floors)

Office Hours: Tu,Th 11:40 - 12:40 or by appointment

Office Tel: 935-6785 (has voice-mail)

E-mail: krishtal @
math.wustl.edu

**Textbook:
**Rosenlicht, Maxwell. Introduction to analysis.

Dover
Publications, Inc., New York, 1986. viii+254 pp. ISBN 0-486-65038-3

**Topics: **The
real number system and the least upper bound property; metric spaces
(completeness, compactness, and connectedness); continuous functions
(in R^n; on compact spaces); pointwise and uniform convergence;
Weierstrass
approximation theorem; differentiation (mean value theorem;
Taylor's theorem); the contraction mapping theorem; the inverse and
implicit function theorems. Other topics will be tossed in if time
permits. Not all of the topics are covered in the textbook. For those
that are not other references or a handout will be provided.

**Exams:
**There
will be two in-class mid-term exams, on Oct 4 and OCT 27.
Each of these exams
will
ask for the proof of one or more theorems discussed in class. There
will also be questions asking for definions, examples, and
counter-examples
for the material covered by the exam. Finally, there will be some
problems
not previously covered in class but often analagous to homework
problems.
The final exam will likely be a take-home exam given out in early
December and due back in roughly a week. We will settle on the
exact
dates when everyone has a firm schedule for exam week. The final exam
will
consist entirely of problems not covered in class.

**Homework:
**There
will be weekly homework assignments to write up and hand in.
Usually
the homework will be due on Tuesday and the assignment handed out the
previous
Tuesday. The homework will consist of a mixture of selected
exercises
from the textbook and supplementary exercises made up by the
instructor. Click on current homework to get
it.

**Grading:**
Each of the two mid-term exams will count 20% toward the final grade,
the final exam will count 30%, and the final homework average the last
30%.

**Academic
Integrity:
**As
with all Washington University courses, cheating on exams will be taken
very seriously with evidence supporting a cheating allegation forwarded
to the Arts and Sciences Integrity Committee for adjudication.
When
the Committee concludes that a student cheated on an exam, it normally
directs the instructor to assign the student a failing grade for the
course.

**
**Cheating on homework consists of either blindly copying off someone
else's solutions or not acknowledging the receipt of assistance from
others
in completing the assignment. It's anticipated that students
will make a genuine effort
to solve the homework problems themselves. However, if the effort has
lead nowhere, discussing
problems with others is a way to avoid frustration and gain useful
insight. All students are expected to write up their own assignments
and to indicate in a short note at the top of the first page the names
of any people (other than the instructor) with whom they discussed the
problems or from whom they received some hints. Violation of
these
requests will result in an instructor-imposed penalty (e.g., something
like half credit for the assignment) but won't be treated as a
"hanging"
offense--in particular, won't be brought to the attention of the Arts
and
Sciences Integrity Committee.