▶Japanese
Post to SNS
- Home
- > School of Science
- > Mathematics
- > Advanced courses in Analysis D
- School of Science
-
School of Engineering
- Group 2
- Group 3
- Group 4
- Group 5
- Group 6
- Metallurgical Engineering
- Organic and Polymeric Materials
- Inorganic Materials
- Chemical Engineering Course
- Chemical Engineering Course(Chemical Engineering)
- Applied Chemistry Course(Chemical Engineering)
- Polymer Chemistry
- Mechanical Engineering and Science
- Mechanical and Intelligent Systems Engineering
- Mechano-Aerospace Engineering
- International Development Engineering
- Control and Systems Engineering
- Industrial and Systems Engineering
- Electrical and Electronic Engineering
- Computer Science
- Civil Engineering
- Architecture and Building Engineering
- Social Engineering
- Common Cource of Engineering
- School of Bioscience and Biotechnology
- Common Course of Undergraduate School
-
Graduate School of Science and Engineering
- Mathematics
- Physics(Particle- Nuclear- and Astro-Physics)
- Physics(Condensed Matter Physics)
- Chemistry
- Earth and Planetary Sciences
- Chemistry and Materials Science
- Metallurgy and Ceramics Science
- Organic and Polymeric Materials
- Applied Chemistry
- Chemical Engineering
- Common Course of Mechanical Engineering
- Mechanical Sciences and Engineering
- Mechanical and Control Engineering
- Mechanical and Aerospace Engineering
- Common Course of Electronic Engineering
- Electrical and Electronic Engineering
- Physical Electronics
- Communications and Integrated Systems
- Communications and Computer Engineering
- Civil Engineering
- Architecture and Building Engineering
- International Development Engineering
- Nuclear Engineering
- Graduate School of Bioscience and Biotechnology
-
Interdisciplinary Graduate School of Science and Engineering
- Built Environment
- Energy Sciences
- Computational Intelligence and Systems Science
- Electronic Chemistry
- Materials Science and Engineering
- Innovative and Engineered Materials
- Environmental Chemistry and Engineering
- Environmental Science and Technology
- Mechano-Micro Engineering
- Information Processing
- Electronics and Applied Physics
- Graduate School of Information Science and Engineering
- Graduate School of Decision Science and Technology
- Graduate School of Innovation Management
- Common Course of Graduate School
- Program for Leading Graduate Schools
- Academic unit or major
- Mathematics
- Instructor(s)
- Shiga Hiroshige
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(H137)
- Group
- -
- Course number
- ZUA.C334
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 4Q
- Syllabus updated
- 2017/1/11
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This course is designed for advanced undergraduate students and first year graduate students who have had first course in complex analysis, and can be used as all or part of a second course in complex variables. In our exposition we have also kept in mind the potential reader interested in self-study, someone in the physical sciences or technology with a reasonable degree of proficiency and experience in mathematics, or even researcher in pure mathematics. This lecture is the continuation of Advanced courses in Analysis C.
Our subject matter, primarily, is the Jacobi elliptic functions and the Weierstrass elliptic functions and their interrelation with Riemann surfaces. Our purpose for basing a treatment of elliptic functions on Riemann surface theory is twofold. On the one hand, elliptic functions are indissolubly wedded to elliptic integrals, and for an intelligent discussion of the latter in the complex domain the use of Riemann surfaces is really essential.
On the other hand, for the student who wants to learn a little about Riemann surface theory, either for its applications to other areas or for itself, the connection with elliptic functions, particularly the Jacobi functions, forms a very natural and concrete path of introduction.
Student learning outcomes
By the end of this course, students will be able to:
1) Understand the relationship between elliptic functions and Riemann surfaces.
2) Understand additive formulas of elliptic functions.
3) Apply elliptic functions.
Keywords
Weierstrass elliptic functions, Riemann surfaces, Additive formulas of elliptic functions, modular functions.
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
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Constructions of Weierstrass elliptic functions | Details will be provided during each class session. |
| Class 2 | Weierstrass elliptic functions and elliptic integrals | |
| Class 3 | Elliptic functions and Riemann surfaces | |
| Class 4 | Elliptic functions as covering maps | |
| Class 5 | Elliptic functions and elliptic integrals | |
| Class 6 | Additive formulas of elliptic functions | |
| Class 7 | An application of elliptic functions--modular functions | |
| Class 8 | An application of elliptic functions--Latte's meromorphic functions |
Textbook(s)
None
Reference books, course materials, etc.
To be determined.
Assessment criteria and methods
Reports (100%).
Related courses
- MTH.C404 ： Advanced topics in Analysis D
- ZUA.C333 ： Advanced courses in Analysis C
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students have passed ZUA.C333 ： Advanced courses in Analysis C.
