Function Theory of a Complex Variable-E2
| Numbering Code | U-LAS10 20010 LE55 | Year/Term | 2022 ・ First semester | |
|---|---|---|---|---|
| Number of Credits | 2 | Course Type | Lecture | |
| Target Year | Mainly 2nd year students | Target Student | For science students | |
| Language | English | Day/Period | Fri.2 | |
| Instructor name | LI，Douglas (Graduate School of Informatics Program-Specific Senior Lecturer) | |||
| Outline and Purpose of the Course | Based upon knowledge of calculus, this is an introductory course to the function theory of one complex variable (i.e. introduction of complex analysis), and its goal is to understand fundamentals about holomorphic functions and meromorphic ones, which are dealt through the Cauchy's integral formula. The purpose of this course is not only to understand rigorous theories but to obtain some skills about the residue calculus. The theory for complex functions are not only beautiful in a mathematical sense but also very useful in applied fields e.g. physics, engineering and medical sciences etc. Almost all the mathematical theories in this course are rigorously dealt with, and some examples related with physics are also explained. An additional goal of this course is to give a chance to the students to present and discuss mathematics in English. | |||
| Course Goals | The goal is to understand fundamentals about holomorphic functions and meromorphic ones, which are dealt through the Cauchy's integral formula. In addition to learning modern mathematics and proofs, students can also learn how to discuss and present mathematical topics in English through this course. | |||
| Schedule and Contents |
The course will cover the following topics, and each of them is read in 2 or 3 weeks: 1. complex numbers, the complex number plane and the Riemann sphere 2. differential of complex functions; holomorphic functions and the Cauchy- Riemann equation etc. 3. power series and analytic functions 4. integral; the Stieltjes integral and Cauchy's integral formula 5. fundamental theories for holomorphic functions 6. singularities and residue; the Laurent expansion and the residue calculus. Total：14 classes, 1 Feedback session |
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| Evaluation Methods and Policy |
The evaluation of the course will take into account the following criteria: -homework (40%) -presentation (20%) -final report (40%) |
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| Course Requirements |
(Eligible students) mainly the sciences of the second grade Students are required good understanding of both calculus and linear algebra. |
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| Study outside of Class (preparation and review) | The students are requested to solve exercises given in class by themselves even though they are not assigned as homework. | |||
| Textbooks | Textbooks/References | Not Specified | ||
| References, etc. |
Complex Function Theory, Donald Sarason, (AMS: American Mathematical Society) Complex Analysis, Elias Stein, Rami Shakarachi, (Princeton University Press), ISBN:3-540-90328-3 複素関数論入門, 磯 祐介, (サイエンス社), ISBN:978-4-7819-1326-1 |
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