MAT 342: Applied Complex Analysis

Spring 2024

Department of Mathematics
Stony Brook University

Course Description: This is a mathematically rigorous course, and most statements will come with complete proofs. Topics covered will include properties of complex numbers, analytic functions with examples, contour integrals, the Cauchy integral formula, the fundamental theorem of algebra, power series and Laurant series, residues and poles with applications, conformal mappings with applications and other topics if time permits.

Textbook: Complex Variables and Applications, by James W. Brown and Ruel V. Churchill, 9th Edition, McGraw-Hill, 2014.

Prerequisite: In order to take this course, you must have passed MAT 203 or MAT 220 or MAT 307 or AMS 261 (Calculus III) with a grade of C or better. Also, it is recommended that you have passed MAT 200 or MAT 250.

Instructor: Marcus Khuri, Math Tower 3-122. Office Hours: Tuesdays and Fridays 2:30-4pm. Email: marcus.khuri@stonybrook.edu

Course Assistants: Eunice Ng, Math Tower S-240A. Click here for office hours. Email: Eunice.Ng@stonybrook.edu

Class schedule: MF 1:00-2:20pm, Earth and Space 131

Homework: Homework is a fundamental part of this course, and you will have to work hard on the assigned problems in order to succeed. Assignments will be posted on the course website at the beginning of each week, and will be due on Wednesday of the following week at 3pm. A box or envelop will be placed outside the office of the course assistant, where you may turn in your homework. Late homework will not be accepted. Homework will account for 30% of the total grade. In order to receive full credit for any problem you must show all of your work, and must provide full justification for your answer.

Homework 1 (Due 1/31) - §2: 4, 11; §3: 1, 2; §5: 1, 6; §6: 1, 9; §9: 1, 5ac;

Homework 2 (Due 2/7) - §11: 2, 6; §12: 1ac, 4d, 7a; §14: 1b, 4, 8, 9;

Homework 3 (Due 2/14) - §18: 2bc, 5, 7; §20: 2cd, 4, 8;

Homework 4 (Due 2/21) - §24: 1c, 2d, 3bc; §26: 1c, 2c, 4c, 7; §27: 2;

Homework 5 (Due 2/28) - §29: 1, 5; §30: 1ac, 4, 8c; §33: 1a, 2b, 7;

Homework 6 (Due 3/6) - §34: 4; §36: 1a, 2c, 6; §38: 2b, 9a; §39: 16a; §40: 1a;

The midterm exam solutions may be found here.

Homework 7 (Due 3/27) - §42: 2a, 4; §43: 5; §46: 1b, 3, 7; §47: 4; §49: 2b, 5;

Homework 8 (Due 4/3) - §53: 1e, 2c, 5, 7; §57: 1b, 3; §59: 1, 3, 5;

Homework 9 (Due 4/10) - §61: 2, 5; §65: 3, 6; §68: 3, 6; §72: 2, 4, 6; §73: 3;

Homework 10 (Due 4/17) - §77: 1c, 2a, 3, 6; §79: 1d, 2c, 3; §81: 1a, 2b, 5a;

Homework 11 (Due 4/24) - §83: 2, 4a, 6, 8; §86: 2, 4, 5, 8;

Homework 12 (Due 5/1) - §88: 3, 6, 10; §91: 2, 4; §92: 2, 3; §94: 1a, 6a;

Exams: There will be an in class midterm as well as a final, each respectively accounting for 30% and 40% of the total grade. The midterm exam will be on Friday, March 8, and the final exam will take place on Monday, May 13, 2:15pm-5:00pm in our classroom Earth and Space 131. By enrolling in this course, you are attesting to the fact that you will be available for the exams at these times.

Help: The Math Learning Center (MLC) is located in Math Tower S-235, and offers free help to any student requesting it. It also provides a locale for students wishing to form study groups. The MLC is open 10am-7pm Monday through Wednesday, 10am-6pm Thursday and 10am-2pm on Friday. A list of graduate students available for hire as private tutors is maintained by the Undergraduate Mathematics Office, Math Tower P-143.

 
Disability Support Services (DSS)
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities

 
Academic Integrity
Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html

 
Critical Incident Management
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.