| Course title | |||||
| 応用解析 [Applied Analysis] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | 3rd | |
| Course type | 3rd | Course code | 022321 | ||
| Instructor(s) | |||||
| 畠中 英里 [HATAKENAKA Eri] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
|
In this course we learn complex analysis. Complex analysis is widely used in applied mathematics, physics and engineering and so on. A complex function is the function in which the independent variable and dependent variable are both complex numbers. We will define differentiations and integrations of complex functions in a similar way of functions of real numbers. We will see a marvelous theory after learning particular properties of complex functions such as Euler's formula, Cauchy's integral theorem and the theorem of residue. |
| Expected Learning |
|
The goals of this course is (1) to understand and master basic methods of calculations of differentiations and integrations of complex functions, and (2) to understand particular properties on differentiable functions, and to be capable of performing practical computations by using Cauchy's integral theorem and the theorem of residue. Corresponding criteria in the Diploma Policy: See the Curriculum maps |
| Course schedule |
|
1. Complex numbers 2. Complex functions 3. Complex series 4. Differentiations of complex functions 5. Elementary functions 6. Integrations of complex functions I 7. Review, midterm examination 8. Integrations of complex functions I 9. Cauchy's integral theorem I 10. Cauchy's integral theorem II 11. Cauchy's integral formula 12. Taylor expansion 13. Isolated singularities 14. Applications for calculations of definite integrations of real functions 15. Review, term examination |
| Prerequisites |
|
Knowledge of the course of Calculus I/II and Exercise will be used in the lecture. 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 |
| References |
| Yano Kentarou and Ishihara Shigeru, "Fukuso-Kaiseki", Shouka-bou, in Japanese |
| Assessment/Grading |
| Results of the midterm examination and the term examination will be used for evaluation. |
| Message from instructor(s) |
| You should try to find your own suitable textbooks, and practice various problems in your private study hours. |
| Course keywords |
| Office hours |
| Friday 10:00-12:00 |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| http://www.tuat.ac.jp/~hataken/top.html |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/7/2019 10:41:15 AM |