Math 407 Section 500
Complex Variables

Daily journal

Follow the above link for a record of class activities and homework assignments each day.

Course description

This three-credit course covers the elements of one-dimensional complex analysis: the complex numbers (their algebra, geometry, and topology); analytic functions of a complex variable (definition, examples, properties); integration in the complex plane, particularly Cauchy's integral formula and its consequences; infinite series of complex numbers and of complex variables, including Taylor series and Laurent series; the residue theorem and the computation of real integrals by complex methods; and conformal mapping.

Course objectives

By the end of the course, you should be able

• to analyze functions of a complex variable using series expansions, using line integrals, using geometry, and using partial differential equations;
• to explain the major theorems that distinguish complex analysis from real analysis; and
• to apply complex analysis to compute geometric mappings and real integrals.

Textbook

The required textbook is Schaum's Outline of Complex Variables, second edition, by Murray R. Spiegel, Seymour Lipschutz, John J. Schiller, and Dennis Spellman, McGraw-Hill, 2009, ISBN 9780071615693. The course covers Chapters 1–8. Some corrections to the textbook are posted.

Prerequisite

The official prerequisite for this course is Math 221 (Several Variable Calculus).

Venue

The course meets 9:35–10:50 in the morning on Tuesday and Thursday in room 148 of the Blocker building.

Exams and grades

Grades are based on the standard scale (60% is passing, 70% or higher earns a C, 80% or higher earns a B, 90% or higher earns an A).

• The two midterm exams are scheduled for February 16 (Thursday) and March 29 (Thursday). Each of these exams counts for 20% of the course grade.
• The cumulative final examination, which has been scheduled by the Registrar for 7:30–9:30 on the morning of Friday, May 4, counts for 20% of the course grade.
• Homework counts for 20% of the course grade.
• Quizzes count for 20% of the course grade.

Course website

http://www.math.tamu.edu/~boas/courses/407-2012a/

Office hours

During the Spring 2012 semester, my office hour in Milner 202 is 2:00–3:00 in the afternoon on Monday and Wednesday; I am available also by appointment. The best way to contact me is via email to boas@tamu.edu. Telephone messages can be left at the Milner office of the Department of Mathematics, 979-845-7554.

TAMU policy statements

Academic integrity

The Aggie Honor Code states: “An Aggie does not lie, cheat or steal, or tolerate those who do.” Information about the Honor Council Rules and Procedures can be found at the website of the Aggie Honor System Office.

Americans with Disabilities Act (ADA) 

This federal antidiscrimination statute provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services in Room B118 of Cain Hall, or call 979-845-1637. For additional information visit the website of Disability Services.

Attendance

See Student Rule 7.