| Spring 2025 MAT 342: Applied complex analysis | ||
| Schedule | TR 3:30-4:50pm Frey Hall 201 | |
| Instructor | Robert Hough | |
| Office hours | M 3-5pm in Math Tower 4-118, Thurs 7-8pm in Math Learning Center | |
| Grader | Junbang Liu, Nick Chakraborty | |
| Description | Functions of a complex variable, calculus of residues including evaluation of real integrals, power and Laurent series, conformal mappings and applications, Laplace and Cauchy-Riemann equations, the Dirichlet and Neumann problems, and the Laplace and Hilbert transforms and their applications to ordinary and partial differential equations. | |
| Textbook | Brown and Churchill. Complex variables and applications. McGraw Hill (2013). | |
| Homework | Weekly problem sets will be assigned, and collected in class. Late homework is not accepted, but under documented extenuating circumstances the grade may be dropped. Your lowest homework grade will be dropped at the end of the class. | |
| Grading | Homework: 30%, Midterm: 30%, Final: 40%. | |
Accommodations for students with hearing and communication impairments:
Some students with hearing and communication impairments may need their instructor to wear a
clear mask for lip and facial expression purposes. If the student has registered with the Student
Accessibility Support Center (SASC) and has requested an accommodation for clear masks, SASC
will reach out to the students instructors and provide a clear mask for them to wear while teaching
and/or interacting with the student. If you have questions, please email sasc@stonybrook.edu or
call (631) 632-6748.
Syllabus/schedule (subject to change)
| Tu 1/28 | 1. | The complex numbers as vectors | pp.1-10 |
| Th 1/30 | 2. | The exponential form | Pictures of boards pp.11-20 |
| Tu 2/4 | 3. | Regions of the complex plane | Pictures of boards pp.21-35 HW 1 Due 2/6: p.4 #5, p.7 #6, p.13 #8, p.16 #13, p.23 #7,9, p.30 #7, p.34 #7 |
| Th 2/6 | 4. | Functions and limits | Pictures of boards pp.37-51 |
| Tu 2/11 | 5. | Continuity and derivatives | Pictures of boards pp.52-67 |
| Th 2/13 | 6. | Analytic and harmonic functions | Pictures of boards pp.68-86 HW 2 Due 2/18: p.43 #3, p.54 #4, p.61 #2, p.70 #1, p.76 #1,6, p.79 #1, p.84 #4 |
| Tu 2/18 | 7. | The complex exponential and logarithm | Pictures of boards pp.87-99 |
| Th 2/20 | 8. | The trigonometric and hyperbolic functions | Pictures of boards pp.100-114 |
| Tu 2/25 | 9. | Contours and contour integrals | Pictures of boards pp.115-130 HW 3 Due 2/27: p.89 #1,6, p.95 #6, p.99 #1, p.103 #6, p.107 #5, p.111 #7, p.114 #2 |
| Th 2/27 | 10. | Antiderivatives | Pictures of boards pp.131-147 |
| Tu 3/4 | 11. | Cauchy integral formula | Pictures of boards pp.148-163 |
| Th 3/6 | 12. | Liouville's theorem and fundamental theorem of algebra | Pictures of boards pp.164-178 HW 4 Due 3/11: p.119 #3, p.123 #6, p.132 #7, p.138 #2, p.147 #5, p.159 #3, p.170 #7, p.177 #4 |
| Tu 3/11 | 13. | Sequences and series, Taylor series | Pictures of boards pp.179-192 |
| Th 3/13 | Midterm Practice Midterm, Practice Midterm Solutions, Midterm solutions | ||
| Tu 3/18 | Spring break | ||
| Th 3/20 | Spring break | ||
| Tu 3/25 | 14. | Laurent series | Pictures of boards pp.193-207 |
| Th 3/27 | 15. | Integration and differentiation of power series | Pictures of boards pp.208-226 HW 5 Due 4/1: p.185 #3,4, p.195 #3,10, p.205 #2,5, p.218 #6, p.224 #2 |
| Tu 4/1 | 16. | Cauchy's residue theorem | Pictures of boards pp.227-237 |
| Th 4/3 | 17. | Poles and residues | pp.238-247 |
| Tu 4/8 | 18. | Zeros of analytic functions | Pictures of boards pp.248-258 HW 6 Due 4/10: p.237 #1,5, p.242 #2,4, p.246 #4,6, p.253 #5,6 |
| Th 4/10 | 19. | Improper integrals | Pictures of boards pp.259-273 |
| Tu 4/15 | 20. | Integration on a branch cut | Pictures of boards pp.274-286 |
| Th 4/17 | 21. | Argument principle | Pictures of boards pp.287-298 HW 7 Due 4/22: p.264 #2, p.273 #3,9, p.282 #1, p.287 #6, p.293 #1,5, p.297 #1 |
| Tu 4/22 | 22. | Linear fractional transformations | Pictures of boards pp.299-317 |
| Th 4/24 | 23. | Mapping by exponential and trig functions | Pictures of boards pp.318-327 |
| Tu 4/29 | 24. | Riemann surfaces | pp.328-344 HW 8 Due 5/1: p.301 #2, p.305 #4, p.311 #1, p.325 #1, p.330 #1, p.336 #5, p.340 #1, p.343 #3 |
| Th 5/1 | 25. | Conformal mapping | pp.345-353 |
| Tu 5/6 | 26. | Harmonic conjugates | pp.354-364 HW 9 Due 5/8: p.352 #1,4,8, p.357 #1,3,5, p.362 #1,8 |
| Th 5/8 | 27. | Selected topics |
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