Math 3574: Applied Complex Variables

Course Description

On line delivery

This class will be delivered on-line. As far as possible, the course will be self-paced. Students taking this class will need well-developed independent learning skills to succeed. Students wishing to learn the same material in a more traditional setting should take MATH 4574 or MATH 4234

Prerequisites

Multivariable calculus

Material covered

The course is intended to cover most of the material on complex variables usually covered in MATH 4574. There are four "modules" covered.

1. Basics of Complex Numbers
• Basic Components of Complex Numbers
• Arithmetic of Complex Numbers
• Complex Conjugate
• Modulus
2. The Geometry of Complex Numbers
• The representation of complex numbers in polar coordinates
• Geometry of the basic arithmetic operations of complex numbers
• Geometry of exponentiation
• Geometry of roots
3. Elementary Functions of a Complex Variable
• Complex exponentials
• Complex trig functions
• Complex hyperbolic functions
• Logarithmic functions
• Powers of complex numbers
4. Properties of Complex Functions
• Sets in the Complex Plane
• Limits and Continuiuty
• Differentiability
• Analytic and Harmonic Functions

Texts

The text for the course is available as a .pdf file. Please download it and print it out.

Students may find that a text such as Advanced Engineering Mathematics by P.V. O'Niel is helpful in supplementing on-line materials. (This text is often used in Virginia Tech's Math 4574 course. It contains a great deal of material in addition to the sections on complex variables.)

On line quizzes and tests

• Some general advice on using the online testing system can be found here. These are general instructions for using the testing system. Not all items mentioned apply to this class.
• There is a collection of short Practice Quizzes that can be taken from any computer. The practice quizzes are available here. (Click the Quiz and Test System button near the bottom of that page.) The questions in these quizzes will be randomly selected from the question database for the appropriate module. By taking thes Practice Quizzes several times, you should be able to get an idea of all of the types of questions to appear on the module tests.
• The Module tests (which are used to determine your grade) are refered to as Poctored Exams in the on line testing system. These must be taken at the Math Emporium. See the Emporium web page for hours when testing is available. You will need your Hokie passport and must know your PID and password.
• You will be able to review any previously taken test at any time. Feel free to discuss previously taken test with other students or with me.

WARNING: While the on line testing system has been working well, but there still may be technical glitches or errors in the question database. If you are unable to read a question or feel that the question is in error, please write down the time, the number of the question, and problem. Point this out to the proctor, note the name of the proctor and send me an email with the information.

The course grade will be based on the four proctored online module tests. Each test will be given equal weight. Each test has 20 points for a total of 80 points for the course. Grades will be assigned as follows

 A 75-80 A- 72-74 B+ 69-71 B 66-68 B- 64-65 C+ 61-63 C 58-60 C- 55-57 D+ 53-54 D 48-52 F 0-47

Testing Procedures

Students may take each proctored test as many times as they wish (versions will be generated on line) and will receive credit for the highest grade received. Tests may be taken whenever the student is ready, subject to availability.

Note: It is our intention that you teach yourself this material by taking the tests repeatedly. You are encouraged to take the test often. In particular, it is good practice to take the online quizzes or even a proctored test before reading the section.

Honor Policy

• The Undergraduate Honor Code pledge that each member of the university community agrees to abide by states:
• As a Hokie, I will conduct myself with honor and integrity at all times. I will not lie, cheat, or steal, nor will I accept the actions of those who do.
Students enrolled in this course are responsible for abiding by the Honor Code. A student who has doubts about how the Honor Code applies to any assignment is responsible for obtaining specific guidance from the course instructor before submitting the assignment for evaluation. Ignorance of the rules does not exclude any member of the University community from the requirements and expectations of the Honor Code.