Course title
関数論   [Function Theory]
Course category technology speciality courses,ets.  Requirement   Credit 2 
Department   Year 24  Semester Fall 
Course type Fall  Course code 022215
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
3/11/2017 10:25:21 AM