Spring 2025: MAT 342

Applied Complex Analysis

Stony Brook University

Welcome to MAT 342!

Complex Analysis is a beautiful subject forming an essential component of modern mathematics, as well as having a variety of applications in physics and engineering. We'll be covering properties of complex numbers, analytic functions with examples, the Cauchy-Riemann equations, contour integrals, the Cauchy integral formula, the fundamental theorem of algebra, power series and Laurent series, residues and poles with applications, as well as conformal mappings and further applications if time permits.

Schedule: Monday & Wednesday, 2:00-3:20PM in Frey 201

Text: Complex Variables and Applications (9th Edition), Brown and Churchill

Full Course Syllabus: here

Office: 4-101B, (Office Hours)

Grader: Nick Chakraborty (Office Hours and Information)

Weekly Schedule (what we've covered so far)

Week 1: Textbook sections 1-10. We'll start next week by finishing up sections 10&11 before moving on to Week 2 of the syllabus.

Week 2: Textbook sections 11-15. Starting next week with section 16.

Week 3: Most of Textbook sections 16-26. If you are following along with the book, we are not covering section 24. Next week we'll go through some final topics from sections 25 and 26 before moving on to 27.

Week 4: Textbook sections 27 and 30-33.

Week 5: Textbook sections 34-39, and 103, together with some discussion of mappings by log(z).

Week 6: Mappings by branches of root functions, Textbook sections 40-46.

Week 7: Midterm!

Week 8: Spring break!

Week 9: Textbook sections 47-53.

Week 10: Textbook sections 54-61.

Week 11: Textbook sections 62-72. We'll be skipping section 73, and only come back to it if necessary. It isn't a bad idea to read through this but it isn't be strictly required.

Week 12: Textbook sections 74-81. We're skipping section 77 for now, but it's an interesting read if you like thinking about the Riemann sphere.

Week 13: Textbook sections 82-86.

Week 14: Textbook sections 87, 90 and the first part of section 93. Note that textbook section 87 is the last of the material that will be covered on the final.

Homework Schedule

Week 1: 2: #2,4; 3: #1; 5: #1(a,d),5; 6: #1, 9: #1,2,5(a,c), 11: #3,6 (Due 2/5)

Week 2: 14: #3,8(a,b); 18: #3(a,b),5; Additional Problems (Due 2/12)

Week 3: 18: #10; 20: #2 (b,c); 24: #1(a,c), 3(a,b); 26: #4(c); Additional Problems (Due 2/19)

Week 4: 26: #1(a,c), 2(c); 30: #1(a,b), 3, 8(a); 33: #1(a), 2(b,c), 7 (Due 2/26)

Week 5: 36: #1(a), 2(a); 38: #1, 2(b); 39: #9; Additional Problems (Due 3/5)

Week 6: 42: #2(a,c); 46: #1,3,7 (Due 3/12)

Week 7: No homework!

Week 8: No homework!

Week 9: 47: #1, 4; 49: 2(a,b); Additional Problems (Due 4/2)

Week 10: 53: #2(b,c); 57: # 1(b,e), 2, 3, 5; 59: #1, 2, 8; Additional Problem (Due 4/9)

Week 11: 61: #6; 65: #1, 3, 6; 68: #1, 5, 6; 72: #1, 4 (Due 4/16)

Week 12: 77: #1(b,c), 2(c,d); 79: #1(a,d), 2(b), 3; 81: 1(a), 2(a,b), 4 (Due 4/23)

Week 13: 83: #2; 86: #2, 5, 7; 88: #3, 6; Additional Problem (Due 4/30)