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).
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: Examples of Holomorphic functions.
Suggested reading: 3.1, 3.2, 3.4 and 3.5 in [BMPS].
Thursday July 17: Review of integration and basic properties. Cauchy's theorem.
Suggested reading: 4.1, 4.2 and 4.3 in [BMPS].
Tuesday July 22: Cauchy's theorem and consequences.
Suggested reading: 4.4, 5.1, 5.2 and 5.3 in [BMPS].
Thursday July 24: Power series. Examples.
Suggested reading: 7.1, 7.2, 7.3 and 7.4 in [BMPS].
Tuesday July 29: Power series expansion of a holomorphic function. Analytic continuation.
Suggested reading: 8.1 and 8.2 in [BMPS].
Thursday July 31: Isolated singularities. Laurent series. The Residue theorem. Applications.
Suggested reading: 8.3, 9.1 and 9.2 in [BMPS].
Tuesday August 5: Applications of the Residue theorem. Computing integrals and infinite sums.
Suggested reading: 9.2 in [BMPS].
Thursday August 7: Applications of the Residue theorem. The argument principle and Rouche's theorem.
Suggested reading: 9.3 in [BMPS].
Tuesday August 12: Review session.
I will send a practice final before then.
Thursday August 14: Final exam.
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