Course title
関数論   [Function Theory]
Course category technology speciality courses,ets.  Requirement   Credit 2 
Department   Year 24  Semester 3rd 
Course type 3rd  Course code 022215
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 u.s.w.
Assessment/Grading
Evaluation will be done according to the Klausur(Final examination)
Message from instructor(s)
Course keywords
Complex numbers, Holomorphic 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
9/5/2019 1:09:48 PM