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2018　Complex Analysis II

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Academic unit or major
Undergraduate major in Mathematics
Instructor(s)
Shiga Hiroshige 
Class Format
Lecture / Exercise     
Media-enhanced courses
Day/Period(Room No.)
Mon5-8(H136)  
Group
-
Course number
MTH.C302
Credits
2
Academic year
2018
Offered quarter
2Q
Syllabus updated
2018/3/20
Lecture notes updated
2018/8/1
Language used
Japanese
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Course description and aims

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.

Student learning outcomes

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.

Keywords

Meromorphic function, isolated singularity, the residue theorem, conformal mapping.

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

Class flow

Standard lecture course with exercise.

Course schedule/Required learning

  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.

Textbook(s)

Ravi P. Agarwal • Kanishka Perera Sandra Pinelas, An Introduction to Complex Analysis (Springer 2010)

Reference books, course materials, etc.

J. Gilman, I. Kra and R. Rodriguez: Complex Analysis (Springer, GTM 245)

Assessment criteria and methods

Final exam 70%, exercise 30%.

Related courses

  • MTH.C301 ： Complex Analysis I

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed MTH.C301 ： Complex Analysis I.

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