SYLLABUS

MATH 451 Complex Analysis Spring 2022

Instructor: Ivan C. Sterling, 177 SH, 240-431-8185, isterling@smcm.edu.

Office Hours: TBA & by appt

Book: Brown&Churchill: Complex Variables and Applications 7^th Ed

Course Outline: Chapters 1-? & Misc

Tests and Grades: There will be four exams (worth 80% of your course grade, 20% each). One of the four exams will be the non-comprehensive final. Homework will be part of your grade (worth 20%). The homework will be collected at the beginning of class on the day it’s due. Late homework will not be accepted. After it is collected some of the homework problems will be selected for grading. The exam problems will be the same or similar to those in the homework and the examples worked in class.

Dates for the exams:

Fridays 2/9, 3/9, 4/6; Final: M 5/6 9-11:15

Grading (roughly): 90-100% “A+”,A,A-; 80-90% B+,B,B-;

70-80% C+,C,C; 60-70% D+,D,“D-”; 0-60% F;

For Business Use Only: At the completion of MATH 451, students will be able to

• mathematical proofs and assessing whether or not these attempts constitute actual proofs.

• categorize complex numbers and functions as demonstrated by illustrating them with examples.

• illustrate differentiability and integration as demonstrated by knowing the basic properties of these operations.

• formulate convincing mathematical arguments in writing as demonstrated by providing solutions to problems involving complex variables.

• build cauchy theory as demonstrated by understanding the proofs of main theorems.

• compare power series and analytic continuation as demonstrated by articulating the similarities and differences between complex and real power series.