| 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 | 022355 | ||
| Instructor(s) | |||||
| 前田 博信 [MAEDA Hironobu] | |||||
| Facility affiliation | Faculty of Engineering | Office | 12-212 | Email address | |
| Course description |
|
In this course we will learn differentiation and integration of functions in one complex variable. This course belongs to basic courses in our department curriculum. |
| Expected Learning |
|
The goal of this course is (1) to be capable of performing practical computations on complex functions, and (2) to understand residue for calculating complex integral Corresponding criteria in the Diploma Policy: See the Curriculum maps |
| Course schedule |
|
week1: Complex numbers week2: Elementary Functions 1: Exponential function and Trigonometric functions. week3: Elementary Functions 2: Logarithmic function. week4: Cauchy-Riemann equations. week5: Complex integral week6: Cauchy's integral theorem: Introduction week7: Proofs of Cauchy's integral theorem week8: Cauchy's integral expression week9: Power series: Taylor series and Laurent series. week10: Identity theorem week11: Singularity week12: Residue week13: Application to real integral 1 week14: Application to real integral 2 week15: Exercise and final examination |
| Prerequisites |
|
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 |
| will be introduced in the first lecture. |
| References |
| moeglichst originale Werke von Riemann, Weierstrass, Cauchy, Eisenstein u.s.w. |
| Assessment/Grading |
| Evaluation will be done according to the Klausur(Final examination) |
| Message from instructor(s) |
| Course keywords |
| Holomorphic function, Meroimorphic Function, Laurent series, Residue. |
| Office hours |
| will be informed in the first lecture |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 1/29/2021 4:02:55 PM |