This course, Complex Analysis II, is intended for students who passed Complex Analysis I or are familiar with the basics of elementary complex function theory.
At the beginning of the course, we will explain the theory of meromorphic functions and singularities. We also explain conformal mappings and present some examples of conformal mappings on domains in the complex plane. After that, we will introduce the notion of "residue". As an application of this theory, we explain the computation of integrals.
By the end of this course, students will be able to:
1) understand the notion of meromorphic functions and isolated singularities.
2) understand the classification of isolated singularities.
3) compute integrals using the residue theorem.
Meromorphic function, isolated singularity, the residue theorem, conformal mapping.
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Standard lecture course with exercise.
Course schedule | Required learning | |
---|---|---|
Class 1 | Meromorphic functions, the reflection principle | Details will be provided during each class session. |
Class 2 | Recitation | Details will be provided during each class session. |
Class 3 | Isolated singularities of meromorphic functions | Details will be provided during each class session. |
Class 4 | Recitation | Details will be provided during each class session. |
Class 5 | Poles and residues of meromorphic functions | Details will be provided during each class session. |
Class 6 | Recitation | Details will be provided during each class session. |
Class 7 | Conformal mappings on plane domains | Details will be provided during each class session. |
Class 8 | Recitation | Details will be provided during each class session. |
Class 9 | The residue theorem, the computation of integrals | Details will be provided during each class session. |
Class 10 | Recitation | Details will be provided during each class session. |
Class 11 | Applications of the residue theorem and the integrals | Details will be provided during each class session. |
Class 12 | Recitation | Details will be provided during each class session. |
Class 13 | The argument principle | Details will be provided during each class session. |
Class 14 | Recitation | Details will be provided during each class session. |
Class 15 | Harmonic functions, comprehension check-up | Details will be provided during each class session. |
E. Freitag and R. Busan, Complex Analysis, Universitext, Springer 2005.
J. Gilman, I. Kra and R. Rodriguez: Complex Analysis (Springer, GTM 245)
Final exam 70%, exercise 30%.
Students are expected to have passed MTH.C301 : Complex Analysis I.