MA 471G
002
Advanced
Calculus I
Fall 2014
Instructor: Prof. Richard Carey
MWF 1000-1050
CB 341 Office
POT 965
Office Hours: MW 0300-0500 & by appt. Phone
257-3745
richard.carey@ms.uky.edu
Text:
Advanced Calculus 3h ed.,
1978 by R. Creighton Buck & Ellen F. Buck
References: Principles of Mathematical Analysis 3h ed., 1976 by Walter Rudin
Real Functions, 1953 by Casper Goffman
Prerequisite: MA 214 and MA
322.
Background: It is assumed that the students have
learned to use elementary calculus, but are not experienced in the techniques
of proof and rigorous reasoning. After the
elementary calculus sequence advanced calculus usually provides the student's
first experience with an abstract analysis mathematical course.
This course, the first of a two course sequence, provides a rigorous foundational
introduction to the analysis of real-valued functions. Guiding principles of imagination
and intuition remain basic but are translated into more precise abstract language.
Course content includes theorems and proofs given in more or less complete form. In particular, the student becomes
acquainted with the principles of mathematical reasoning using patterns of number
sets and number valued functions. Aspects of set theory relevant to the study
of real-valued functions are considered while basic properties of the set R of
real numbers, such as ordering (not available with complex numbers), field (an
algebraic property) and completeness (a notion from mathematical logic) axioms are used. Concepts of continuity are introduced
via a topology on the real numbers. We reprise concepts of monotone and inverse
functions, define the derivative of a function and prove some mean value
theorems. The course also deals with Riemann integration theory both in one and
two variables. However, the fundamental theorem of calculus in several
variables awaits the second course in the sequence. The following topics from
the text are expected to be covered:
Appendix
1 Logic and Set theory
Appendix
2 Foundations of the Real Number System
Chapter 1
Sets and Functions
Chapter
2 Continuity
Chapter
3 Differentiation
Chapter
4 Integration
Chapter
5 Series
Chapter 6
Uniform Convergence (of
functions)
Grading:
Your grade will be calculated from the following distribution of points:
Oral Presentations: (100 points) Everyone will be expected to
present some number of problems in class. These presentations need to be both
clear and concise. Further, the rest of the class is responsible for monitoring
the presentation for accuracy. Details regarding the oral presentations will be
provided on a separate handout later on
Homework problems: (50 points) From
time to time I will ask for a complete solution to a particular homework
problem to be submitted. Your solution will be graded on the basis of accuracy,
exposition and neatness. Preparation of problems for presentation must be your
own, and submission of written
homework
problems must also be done on an individual basis.
Exams: Exams will be take-home and there will be
three of them. The grading scale for the
first two
will
be
90-100 A
80-89
B
70-79
C
60-69
D
Below 60 E
The grading scale for the final exam will be
as follows:
117-130
A
104-136
B
91-103 C
78-90 D
below 78 E
78-90 D
below 78 E
Your course score will be the sum of your
test scores and the instructor score.
The grading scale for the course will be as
follows:
Cumulative score
Grade
432-480 A
384-431 B
336-383 C
288-335 D
below 288 E
432-480 A
384-431 B
336-383 C
288-335 D
below 288 E
The
exams will be curved in the following way. The mean of all students who earn
40%
(55%
on the final exam) or more on an exam will be computed. Points will be added to
the scores so this mean is adjusted to a score of 75 (97.5 on the final). If
the mean is 75 or more, no points are added to the scores. You must bring a
photo ID to each exam and you may use a calculator on the exams.
Exam,
Quiz and Attendance Policy: It is very important to take each exam on
schedule. Missed work may be made up
only due to illness with medical documentation or for other unusual
(documented) circumstances. (See your
Student Rights and Responsibilities http://www.uky.edu/StudentAffairs/Code/). Students who have university excused absences
or who have university-scheduled class conflicts with uniform examinations may
arrange with their instructor to take the exam at an alternate time.
Work-related conflicts are neither university excused absences or
university-scheduled absences. If you miss an exam, you receive a zero. You will be eligible for a make-up only if
you present a valid excuse to me before the exam. If you cannot find a
reasonable arrangement for a make-up, contact the department DUS David Royster.
If you generate 5 (unexcused) recitation classes your cumulative score drops by
10%, i.e., from A to B. If you miss 6 (unexcused)
recitation classess your cumulative score drops 15%; if you miss 7 recitation
sections you lose 20%, e.g., A to C. If you miss 7 or more recitation classes
you get an E. This policy begins September 10, 2014.
Excused Absences: S.R. 5.2.4.2
defines the following as acceptable reasons for excused absences:
- serious illness;
- illness or death of family member;
- University-related trips;
- major religious holidays;
- other circumstances you find to be "reasonable cause for nonattendance."
Students
anticipating an absence for a major religious holiday are responsible for
notifying the instructor in writing of anticipated absences due to their
observance of such holidays no later than the last day for adding a class.
Information regarding dates of major religious holidays may be obtained through
the religious liaison, Mr. Jake Karnes (257-2754).
Cheating: Cheating will not
be tolerated, and you are responsible for knowing University policy on
cheating. The University’s minimum policy for cheating is failure in the
course. (Yes, the chair of the department does spend time each semester
prosecuting students who thought they’d never get caught!) Cheating can lead to
expulsion from the university. For a complete description of University
policies on excused absences, cheating, and student responsibilities see UK's
New Academic Offenses Policy can be found at
For
instance, Senate Rule 6.4.11 states:
The minimum penalty for an academic offense is an E
in the course in which the offense took place. The repeat option may not be
used to remove an E given for
an academic offense. If a prior academic offense
has been recorded in the Registrar’s Office, the minimum penalty shall be suspension
for one semester (ora minimum of four months in those colleges in the Medical
Center where the semester system is not in use. Penalties more severe than the
minimum may be imposed where warranted by the circumstances.
Our class is a cell phone-free zone. Cell phones must be off & out of sight for the entire class period.
Important
Dates
August 27 (Wed.)......................................... First
day of classes
September 1 (Mon.)............ …………………No classes – Labor
Day
September 3 (Wed.) .............................. Last day to add a class
September 17
(Wed.)….Last day to drop a class without a grade
October 3 (Fri.)………
……………………….………………… Examination 1
October 20 (Mon.)
……………………………………..................Midterm
November 7
(Fri.)……………….. .Last day to withdraw from a class
November 26-29
(Wed.-Sat.)……………… No classes-Thanksgiving
November 14 (Fri.)
………………………………………………Examination 2
December 12 (Fri.) …………………………………… … Last day of classes
December 17 (Wed) ……………… 0800 – 1000 am Final Examination
December 17 (Wed) ……………… 0800 – 1000 am Final Examination
Note: There is an official procedure for dropping a
course. You haven't withdrawn if you simply
quit attending. A student who drops a class before February 5 will receive no
grade. A student who withdraws after February 5 will receive a grade of W.
After March 7 no student will be allowed to withdraw unless his/her dean
determines that unusual circumstances merit the withdrawal.
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