Course title
関数論   [Function Theory]
Course category	technology speciality courses,ets.	Requirement		Credit	2
Department		Year	3～4	Semester	Fall
Course type	Fall	Course code	023511
Instructor(s)
前田 博信   [MAEDA Hironobu]
Facility affiliation	Faculty of Engineering	Office		Email address

Course description

In this course we will learn differentiation and integration of functions in one complex variable.

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

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: Final examination

Prerequisites

Required Text(s) and Materials

will be introduced in the first lecture.

References

moglichst originale Werke von Riemann, Weierstrass u.s.w.

Assessment/Grading

Midterm examination 50%. Final examination 50%

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

3/22/2018 9:45:41 AM