Web page at http://cas.bellarmine.edu/fenton
Section D meets 11:00-11:50 Mondays, Wednesdays, and Fridays in Pasteur 106.
A. INTRODUCTION
The discovery of complex numbers resulted from problems that could not be solved with real numbers. Thus the complex numbers are a more powerful system than the real numbers. Because of this, the theory of functions of a complex variable often simplifies problems encountered in the study of functions of one real variable.
In this course, we will study the complex number system and functions of a complex variable. Then we will explore the calculus of such functions, covering the major concepts of limit, derivative, integral, and series. There will be many similarities with standard calculus, but many important and interesting differences.
Every student in my mathematics classes has four freedoms:
I am serious about these. I believe that the best learning takes place when students have ideas, try those ideas, refine their ideas, and understand how these new ideas fit into what they already know. Most mathematics problems can be solved in more than one way, and I am happy to see new approaches; this shows real understanding.
Since this is a small class, I propose to run the course as a discussion seminar. At each class meeting, we will work together on the assignments. You will be expected to read the sections and prepare your questions before coming to class. I will not lecture on the material, but I will be happy to discuss it with you.
B. OFFICE HOURS
My office is Pasteur Hall 006-F, phone 452-8430. My office hours are 12:00-12:50 Mondays, Tuesdays, Wednesdays, and Fridays. Other times are possible, and you are welcome whenever I am there.
Messages may be left in my mailbox in Pasteur 006. You can contact me electronically either on the campus network or at wfenton@bellarmine.edu. Feel free to phone me at home at 454-7855 (but not after 9:00 p.m. please).
C. COURSE DESCRIPTION (from the College catalog)
“In this course we consider familiar concepts encountered in calculus in the new setting of functions of a complex variable. Topics covered include: the arithmetic, algebra, and geometry of the complex number system and complex plane; elementary functions of a complex variable; the derivative (analyticity and harmonicity); the integral (line and contour integrals); the topological aspects of the plane needed to develop the theory of differentiability and integrability (including Cauchy’s Theorem, Cauchy’s Integral Formula, and the Maximum Modulus Theorem); and series representations for functions.”
D. MATERIALS NEEDED
Fundamentals of Complex Analysis, 3rd ed., by Saff & Snider
This is available at the Campus Bookstore.
E. PREREQUISITE
MATH 216 Multivariable Calculus
F. LEARNING OUTCOMES
We will cover most of Chapters 1 through 5 from the text. At the conclusion of the course a successful student should be able to:
MATH 411 addresses the following goals of General Education (pages 47-50 of the 2003-2005 University catalog):
Goal 6, Item a: Students will understand the impact and pervasiveness of numeric and symbolic concepts.
Goal 6, Item b: Students will employ quantitative analysis as a method of problem solving.
Goal 6, Item c: Students will apply graphical, mathematical, and symbolic models.
Goal 6, Item d: Students will appreciate mathematics both as a creative endeavor and as a practical tool.
Goal 7, Item c: Students will employ analytic, logical, evaluative, and integrative thinking in processing information and in drawing conclusions.
As a senior-level course, MATH 411 addresses all five goals of the Mathematics Department. There is a significant component of problem-solving. Students will be expected to communicate mathematical ideas orally and in writing. The homework and class discussions will include proof problems. Applications will be discussed in the context of the techniques being presented. By presenting the concepts of calculus in a new setting, this course gives a deeper understanding of those concepts.
G. ATTENDANCE
(See also the Travel Policy in the section on University policies.) Attendance is up to you; I will not take attendance. However, you are responsible for all material discussed in class.
H. ACADEMIC HONESTY
(See also the more complete statement in the section on University policies.)
“Bellarmine students are expected to demonstrate a high standard of academic honesty in all aspects of their academic work and university life. Without intellectual integrity there can be no genuine learning. Academic dishonesty represents a direct attack on this integrity. In taking tests and examinations, completing assignments and laboratory work, writing papers, and using information technology, students are expected to perform honestly.” (from the 2003-2005 University catalog, pages 55-56.)
I. COURSE REQUIREMENTS
HOMEWORK: 300 points
Each section of the text ends with Exercise problems. There will be an assignment due about once a week, typically covering two sections. (See the attached schedule.) These assignments will be posted on the course Web page. These homework assignments will be 25 points. Late homework will not be accepted unless you contact me ahead of the due date.
I encourage you to work with others on the homework, and to ask me questions in and out of class. However, what you turn in must be your own work, in your own words.
TEST 1: 100 points, Chapters 1 and 2
This will be in two portions: a 50 point oral portion followed by a 50 point take-home portion.
TEST 2: 100 points, Chapters 3 and 4
This will also be a 50 point oral portion followed by a take-home portion.
FINAL EXAM: 150 points, Chapters 1-5
Monday December 6, 12:00 p.m. This will be a 50 point oral portion plus a 100 point in-class portion.
Make-up tests will be given only in extreme circumstances and only if I am contacted on or before the test date. You must take both tests and the final exam to pass the course.
For the oral components of these tests, I will provide in advance a list of items from which I will ask questions. These may include “true/false and why” questions and “give an example” questions.
J. GRADING
Grades will be assigned as follows:
A 90 – 100%
A- 85 – 89%
B+ 82 – 84%
B 78 – 81%
B- 75 – 77%
C+ 70 – 74%
C 60 – 69%
D 50 – 59%
F 0 – 49%
Homework 300 points
Test 1 100 points
Test 2 100 points
Final Exam 150 points
Your course grade will be your point total as a percentage of the 650 possible points.
K. UNIVERSITY POLICIES
University Mission Bellarmine University is an independent Catholic university serving the region, nation and world by educating talented, diverse students of all faiths and many ages, nations, and cultures, and with respect for each individual’s intrinsic value and dignity. We educate our students through undergraduate and graduate programs in the liberal arts and professional studies, within which students develop the intellectual, moral, ethical and professional competencies for successful living, work, leadership and service to others. We achieve these goals in an educational environment committed to excellence, academic freedom, and authentic conversations not dominated by particular political or other single perspective and thus to thoughtful, informed consideration of serious ideas, values, and issues, time-honored and contemporary, across a broad range of compelling regional, national and international matters. By these means, Bellarmine University seeks to benefit the public interest, to help create the future, and to improve the human condition.
Academic Honesty
I strongly endorse and will follow the academic honesty policy as published in Bellarmine’s Catalog 2005-2007 (pp. 55-56) and in the 2006-2007 Student Handbook (pp. 17-20); both documents are available online via the student portal on the University’s intranet. Students must be fully aware of what constitutes academic dishonesty; claims of ignorance cannot be used to justify or rationalize dishonest acts. Academic dishonesty can take a number of forms, including but not limited to cheating, plagiarism, fabrication, aiding and abetting, multiple submissions, obtaining unfair advantage, and unauthorized access to academic or administrative systems or information. Definitions of each of these forms of academic dishonesty are provided in the academic honesty section of the 2006-2007 Student Handbook. All detected instances of academic dishonesty will be reported to the Provost, and sanctions will be imposed as dictated by the policy. Penalties range from failing an assignment or test to dismissal from the University, depending, in part, on the student’s previous record of academic dishonesty. On the second offense during a student’s academic career, as a minimum additional penalty, the Provost will immediately suspend the student for the semester in which the most recent offense took place. On the third offense, the Provost will immediately dismiss the student from the University.
Disability Policy (from the Student Handbook)
“Students with disabilities who require accommodations (academic adjustments and/or auxiliary aids or services) for this course must contact the Disability Services Coordinator (Room 225 Horrigan Hall or 452-8150). Please do not request accommodations directly from the professor.”
Severe Weather
Refer to the current student handbook for details regarding changes in schedule due to bad weather. Faculty will arrange class schedules to meet learning outcomes in the event classes will be cancelled.
Travel Policy
The University requires students who will be absent from class while representing the University to inform their instructors in two steps. During the first week of the course, students must meet with each instructor to discuss the attendance policy and arrangements for absences related to University-sponsored events. Second, students must provide the instructor with a signed Student Absentee Notification Form, available via the student portal on the University intranet, at the earliest possible opportunity, but not later than the week prior to the anticipated absence. The Student Absentee Notification Form does not serve as an excused absence from class. Your instructor has the final say about excused and unexcused absences and it is the student’s responsibility to know and abide by the instructor’s policy.
L. TENTATIVE HOMEWORK AND EXAM SCHEDULE