MATHEMATICS 470 Special Topics in Mathematics:  Complex Analysis – Spring 2006

 

INSTRUCTOR:   Dr. Christopher Swanson                   Office Phone:  419-289-5264               Office:  209 Patterson

                                E-mail:  cswanson@ashland.edu       Home Phone:  419-207-8818 BEFORE 10pm

                                Web Page:  http://personal.ashland.edu/~cswanson

OFFICE HOURS:                Mon. 1-2, 4-5; Tues. 12-1, 4-5; Wed. 10-11, 12-1; Thurs. 11-12, 3-4;

                                                Fri. 3-4, 4-5 OR by appointment OR almost any other time I am in my office.

CLASSES:            Tuesday  1:40 p.m.-2:30 p.m. in

 

TEXT:                    Complex Variables (2nd Edition) by Fisher.  Dover Publications, 1990.  BRING THIS TO EVERY CLASS!!!

 

COURSE DESCRIPTION: When you learned about subtraction in elementary school, you may have been initially told you couldn’t do problems like 3 – 8 = , and then later you were introduced to the negative integers.  When you learned about division, you may have been told you couldn’t do problems like 8 ÷ 3 = , and then you were introduced to fractions, and hence rational numbers.  When you learned about square roots, you began your study of irrational numbers, and may have been told you couldn’t do problems like .  You may also have been told in high school that polynomials like  have no real roots.  However, every polynomial has a root if we allow our domain to be all complex numbers.  In this course, we will study the properties of complex numbers and functions.  In particular, we will look at how to generalize results from calculus when we allow the domains of our functions to be complex numbers instead of being limited to real numbers.  This course should be of interest to anyone who has a love of mathematics and is looking to improve his/her understanding of calculus.  Anyone considering going to graduate school should definitely enroll in this course.

HOMEWORK:  Reading assignments and homework problems will be assigned during every class.  I will assume that you have completed the reading assignment for each class period, and thus comprehension of some of the material covered in class may depend upon this reading.  The reading assignments may cover material for which you are responsible to know for the course, although time constraints may result in this material not being covered in class.   Starting on Friday, January 21st, homework problems will be due in my office every Friday by 5pm.  If you are having difficulty with the reading or homework problems, please bring questions to my office or to class.  You may discuss the problems on the homework sets with other members of the class, but you should write up your solutions independently, and you should mention any classmates with whom you work.  Failure to do this will result in points being deducted from the assignment.  The homework set should be legible, written in correct English (including complete sentences when appropriate), and stapled.  Late homework will be accepted with a penalty of 10% of the point value of the assignment per weekday it is late. 

 

EXAMS:                All missed exams will be given a grade of “0” unless PRIOR arrangements are made, and you have a legitimate reason for missing class.  Personal travel plans will never be considered a legitimate reason for missing an exam.  Exams may include a take-home portion.

 

GRADING:           Homework problems            50%                        Midterm Exam                                       20%

                                                                                Comprehensive Final Exam 30%

 

Scaled course %                   Grade                      Scaled course %                   Grade

93 to 100                                   A                          73 to 77                                     C

90 to 93                                     A-                        70 to 73                                     C-

87 to 90                                     B+                        67 to 70                                     D+

83 to 87                                     B                          63 to 67                                     D

80 to 83                                     B-                         60 to 63                                     D-

77 to 80                                     C+                        below 60                                   F

 

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MATHEMATICS 470:  Complex Analysis – Spring 2006

The course will cover material from Chapters 1-2 of Complex Variables (2nd Edition) by Fisher. We will observe the following schedule as closely as possible:

 

Dates              Text Sections                         Comments

 

1/11                 Introduction

 

1/18                 1.1

 

1/25                 1.2

 

2/1                   1.3                              

 

2/8                   1.4                                          

 

2/15                 1.5

 

2/22                 1.6                                                                  

 

3/1                                                                   MIDTERM EXAM ON TUESDAY, MARCH 1st

 

J‰ { Ő Š  SPRING BREAK  ŠŐ { ‰ J

 

3/15                 2.1                              

                       

3/22                 2.2

 

3/29                 2.3                                          

 

4/5                   2.4                              

 

4/12                 2.4                                          

 

4/19                 2.5                                          

 

4/26                 2.6                              

 

COMPREHENSIVE FINAL EXAM IS 1:30 p.m. TO 3:30 p.m., TUESDAY, MAY 2nd

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Students with documented disabilities who require academic adjustments for this class are requested to contact me to discuss reasonable accommodations.  While not required, it is in the best interest of the student to have this conversation early in the semester.  Students must provide paperwork from Disability Services to document the need for academic adjustments.  Disability Services is located in 105 Amstutz, extension 5953.