This is the website for MAT 342: Applied Complex Analysis, Summer II 2025.
The textbook for this class is freely available using the following link: A First Course in Complex Analysis, by Matthias Beck, Gerald Marchesi, Dennis Pixton and Lucas Sabalka.
Instructor: Alex Rodriguez (alex [dot] rodriguez [at] stonybrook.edu). Office hours: TuTh from 5pm to 6pm in Physics P-112.
Grader: Shivam Mohite (shivam [dot] mohite [at] stonybrook.edu). Office hours: F from 4pm to 5pm (on Zoom, follow the previous link).
Meeting times: TuTh from 1:30pm to 4:55pm in Physics P-112 (we will take a couple of breaks in between).
Tuesday July 8: Presentation of the course. Complex Numbers. Topology of the Plane.
Suggested reading: Chapter 1 in [BMPS].
Thursday July 10: Review of Limits and differentiability. Holomorphicity. The Cauchy-Riemann equations.
Suggested reading: 2.1, 2.2 and 2.3 in [BMPS].
Tuesday July 15: Power series. Examples of Holomorphic
functions.
Suggested reading: 7.1, 7.2, 7.3, 7.4 and 3.4 in [BMPS]. [HW1 due]
Thursday July 17: Examples of holomorphic functions.
Line integrals.
Suggested reading: 3.4, 3.5 and 4.1 in [BMPS].
Tuesday July 22: Line integrals. Cauchy's theorem.
Winding number.
Suggested reading: 4.1, 4.2, 4.3 and 4.4 in [BMPS]. [HW2 due]
Thursday July 24: Cauchy's integral formula. Power
series expansion of a holomorphic function. Morera's theorem. Liouville's
theorem.
Suggested reading: 4.4, 5.1, 5.2, 5.3 and 8.1 in [BMPS].
Tuesday July 29: Zeros of holomorphic functions. Analytic
continuation. Open mapping theorem and maximum modulus principle.
Global Cauchy theorem. Laurent series.
Suggested reading: 8.1 and 8.2 in [BMPS]. [HW3 due]
Thursday July 31: Class canceled due to weather
conditions.
Suggested reading: 8.3, 9.1 and 9.2 in [BMPS].
Tuesday August 5: Isolated singularities. The residue theorem.
Applications.
Suggested reading: 8.3, 9.1 and 9.2 in [BMPS]. [HW4 due]
Thursday August 7: The argument principle and Rouche's theorem.
Suggested reading: 9.3 in [BMPS].
Sunday August 10: [HW5 due]
Tuesday August 12: Review session. [Practice Final]
Thursday August 14: Final exam. From 1:30pm to 4pm in
Physics P-112.
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