| Course title | |||||
| 関数論 [Function Theory] | |||||
| Course category | technology speciality courses | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | 3rd | |
| Course type | 3rd | Course code | 022563 | ||
| Instructor(s) | |||||
| 陸名 雄一 [RIKUNA Yuichi] | |||||
| Facility affiliation | Graduate School of Engineering | Office | afjgxte/L1151 | Email address | |
| Course description |
|
As an advanced course of calculus, this course provides students with the foundation for complex functions. This theory is applied to many areas such as electromagnetism, fluid mechanics, etc. Yuichi Rikuna (a part-time lecturer) will be in charge of this course. |
| Expected Learning |
|
Learners who successfully complete this course will be able to: 1. Understand complex functions and holomorphic functions 2. Understand the definition and basic properties of complex integrals, and handle it with high calculation ability 3. Understand residues, and apply it to calculate real and complex integrals. Corresponding criteria in the Diploma Policy: See the Curriculum maps. |
| Course schedule |
|
Week 1: Complex Numbers (Chapter 1.1) Week 2: Series, Power Series, Complex Functions (Chapter 1.3) Week 3: Holomorphic Functions, Cauchy-Riemann Equations (Chapter 2.1-2) Week 4: Exponential, Trigonometric, and Hyperbolic Functions (Chapter 2.3) Week 5: Logarithms, n-th Root, Multivalued Functions (Chapter 1.2, 2.3) Week 6: Exercises in Week 1-5 Week 7: Review, and Midterm Examination Week 8: Complex Integrals (Chapter 3.1) Week 9: Cauchy's Integral Theorem, Cauchy's Integral Formula (Chapter 3.2-3) Week 10: Taylor Series, Laurent Series (Chapter 4.1) Week 11: Singularities, Residues (Chapter 4.2) Week 12: Evaluating Real Integrals Using Complex Functions (Chapter 4.3) Week 13: Conformal Transformations (Chapter 4.4) Week 14: Exercises in Week 8-13 Week 15: Review, and Term Examination Homework: "Problems" and "Exercises" in the relevant part of the textbook |
| Prerequisites |
|
Students entering this class are assumed to have learned Calculus I-II and Linear Algebra I-II. In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University and using the lecture handouts as well as the references specified below. |
| Required Text(s) and Materials |
| YANO Kentaro, et al., Fukuso Kaiseki (Complex Analysis), Shokabo |
| References |
| Supplementary materials of the textbook will be given. |
| Assessment/Grading |
| A midterm and a term examination will be given. They are worth 40% and 60% of your grade respectively. |
| Message from instructor(s) |
| It is required that you clarify your questionable points by reading the textbook before attending each lecture. I want you to acquire the ability which can be applied to other subjects by enough exercises. |
| Course keywords |
| Complex functions, Holomorphic functions, Cauchy's integral theorem, Residues |
| Office hours |
| After lecture |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 1/24/2021 6:40:34 PM |