MA 472G 001
Advanced Calculus II
Spring 2015
Instructor: Prof.
Richard Carey
MWF 11:00 - 11:50 CB 347
Office POT 965
Office Hours: MWF 0300 - 0500 & by appt. Phone (859) 257-3745
E-MAIL: Richard.carey@.uky.edu
Text: Advanced Calculus 3h ed., 1978 by R. Creighton Buck & Ellen F. Buck ( Free -online)
References:
Principles of
Mathematical Analysis 3h ed., 1976 by Walter
Rudin
Elementary Differential Geometry, Revised second edition, 2006 by Barrett O’Neil [From the preface:
"This book is an elementary account of the geometry of curves and surfaces. It is written for students who
have completed standard courses in calculus and linear algebra, and its aim is to introduce some of the main
ideas of differential geometry.] [
Differential Forms with Applications to the Physical Sciences, 1989 by Harley Flanders [A
graduate-level text introducing the use of exterior differential forms as a powerful tool in the analysis of a
variety of mathematical problems in the physical and engineering sciences. Directed primarily to
graduate-level engineers and physical scientists, it has also been used successfully to introduce modern
differential geometry to graduate students in mathematics].
Prerequisites: For Ma 471G one needs MA 214 and Ma 322; for Ma 472G one needs Ma 471G or consent of instructor.
Background- Ma 471G : 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 the advanced calculus usually provides the
student's first experience with an abstract mathematical course.
Background- Ma 472G This course is a continuation of Ma 471G. The
following topics will be discussed: implicit function theorem, inverse function
theorem, multiple integrals, change of variables formula, vector analysis, line
and surface integral. The geometry of curves and surfaces in R^3, which is a
kind of extrinsic geometry. [The
intrinsic geometry of a surface that is seen by its inhabitants, with no assumption
that the surface can be found in ordinary three-dimensional space. This form is
studied in more advanced courses.]
Various versions of the fundamental theorem of calculus: Green's Theorem,
The divergence theorem, and Stokes' theorem.
Chapter 6 Uniform
Convergence (of functions)
Chapter 7
Differentiation of transformations
Chapter 8 Applications
to geometry and analysis
Chapter 9 Differential
geometry and vector calculus
Grading: Your grade will be calculated from the
following distribution of points:
Oral Presentations: (100 points) Everyone will be expected to present some
problem 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.
Homework problems: (100 points) From time to time I will ask for solutions 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: There will be three take-home exams given in
this course: two term exams and a final. The grading scale for the first two
exams will be as follows:
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
Your course score will be the sum of your test, homework, and presentation scores.
The grading scale for the course will be as follows:
Cumulative score grade
530-477 A
424-476 B
371-423 C
318-370 D
below 318 E
Exam, Quiz and Attendance Policy:
Students are
expected to attend each class meeting unless he or she has been excused by the instructor.
Failure to attend
class will result in a lower grade, and may result in failing the class. Absences
due to
illness or
emergencies must be reported within a week. You may call the instructor’s office
or email him at
the numbers/address listed on the first page of this syllabus. When there is an excused absence,
students will be
given the opportunity to make up missed work and/or exams.
The following are
typically accepted reasons for excused absences:
1. Serious illness.
2. Illness or death
of a family member.
3. Approved
University-related trips.
4. Major religious
holidays.
5. Other
circumstances found to be "reasonable cause for nonattendance.”
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. 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 Serge Ochanine.
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 the
religious liaison,
Mr. Jake Karnes (257-2754).
Unexcused Absences
A student who has
unexcused absences in excess of five 2 -hour classes will receive a failing
grade for
the course without regard
or points earned through completed assignments.Missing 5 classes results in a
penality of 1/2 a letter grade; and each subsequent miss produces another drop of 1/2 letter grade.
penality of 1/2 a letter grade; and each subsequent miss produces another drop of 1/2 letter grade.
No make-up
opportunities will be given for unexcused absences.
Make-up exam
Students are
expected to take exam at the times scheduled in the syllabus. Possible
exceptions include
verified serious
illness, serious family emergency, subpoenas, jury duty, military service,
religious
observances, or a
legitimate conflict with recognized University activities. If these apply, you
must contact
instructors to
request a makeup. Make these arrangements as soon as you know of the conflict
BEFORE
the exam. No
make-up for assignment is allowed.
Incompletes :
An incomplete grade
due to illness or other emergencies may be arranged. A request for an
incomplete
due to illness must
be accompanied by a letter from your doctor, the Student Health Service, or a
hospital. Lack of
time to complete assigned work, or other reasons not relating to unavoidable
excused
absences, will not
be accepted as a valid reason for petitioning for an incomplete. No incompletes
will be
given unless you
have a prior written agreement with the instructor BEFORE the end of classes.
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
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 (or a
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
January 14 (Wed.).................................................................... First day of classes
January
19 (Mon.) .........................................No classes – Martin Luther
King Day
January
21 (Wed.) ................................................................Last
day to add a class
February
4 (Wed.)………………………….Last day to drop a class without a grade
March
9 (Mon.)…………………………………….........................................Midterm
March
16-21 (Mon. –Sat.) ………........................... …No classes - Spring vacation
April
10 (Fri.)……………….. ................................Last day to withdraw from a
class
May1
(Fri.) …………………………………… …................... Last day of classes
May
4-8 ……………….... ……………………………………….Final examinations
May
6 (Wed.) 10:30-12:30……………….... ………………………Final examination
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