Introductory Complex Analysis

Student Learning Outcomes, Goals, Objectives:

Upon successful completion of this course, the student will be able to:

• Represent, manipulate, and interpret complex numbers algebraically and geometrically, including polar and exponential forms, and apply basic topological concepts in the complex plane.

• Analyze complex functions using rigorous definitions and the Cauchy-Riemann equations.

• Investigate fundamental complex functions and mappings, including Möbius transformations, exponential, logarithmic, and trigonometric functions, and describe their geometric effects.

• Evaluate complex line integrals and apply major results of complex integration, including Cauchy’s Theorem and Cauchy’s Integral Formula, to solve mathematical problems.

• Construct rigorous mathematical arguments and proofs involving complex functions, mappings, and integration theorems, and communicate solutions using appropriate mathematical notation and reasoning.

Course Grading Information:

Activity	Percentage
Papers	35%
Tests	40%
Final Exam	25%

 

 

Attendance/Participation:

Unsatisfactory attendance and participation will result in lowering of the course grade by up to two full letter grades. 

 

# Absences	Grade Deduction
0-2	None
3-4	1/3 letter, e.g., B to B-
4-6	2/3 letter, e.g., B to C+
7-8	1 letter, e.g., B to C
Over 8	2 letters, e.g., B to D

 

Grading Scale:

Grade	Percentage
A	93-100
A-	90-92
B+	87-89
B	83-86
B-	80-82
C+	77-79
C	73-76
C-	70-72
D	60-69
F	0-59

 

Course Materials Purchased by the Students:

1. None.  The textbook is open-source and available online:  A First Course in Complex Analysis, by Beck, Marchesi, Pixton, and Sabalka