544 件ヒット (0.014秒)：
Google Classroomのクラスコードは工学部Webページにて確認すること。
学部シラバス・時間割(https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html)
この科目ではGoogle Classroomを使用して、講義資料と講義情報を発信します。
Google Classroomにアクセスし、クラスコードを入力してください。
1. 目的
工学に応用されることの多い数学の分野の中から、下記の内容の基礎を学ぶ。
2. 概要
複素関数の微分と積分、複素級数と正則関数の基礎について、講義と演習を行う。
3. 達成目標等
以下のような能力を習得することを目標とする。
・本学科の学習・教育目標のA，B，C，Kに関する能力を含めて修得する。
・公式の適用条件、定理の内容を理解し、説明できる。
・公式および定理を、具体的な計算や基礎的な問題へ応用できる。
The class code for Google Classroom can be found on the Web site of
the School of Engineering:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html (JP Only)
This course provides lectures and exercises on the fundamentals of advanced engineering mathematics, shown below.
・Differentiation and integration of complex functions
・Complex series
・Holomorphic functions
Goal of study
This course is designed to help students understand the fundamental formulas and theorems and be able to apply them to specific calculations and basic problems.
Google Classroomのクラスコードは工学部Webページにて確認すること．
学部シラバス・時間割(https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html)
１．目的 フーリエ解析と複素解析について，それらの基礎を学習・理解し，計算力と応用力を身につける.
２．概要 工学に現れる現象の解明に重要な役割をはたす応用数学の一部であるフーリエ解析と工学に応用される解析学の基礎をなす複素解析について，それらの基礎を学習する.
３．達成目標等 フーリエ級数，フーリエ変換を理解して，それらの計算とその応用ができるようになること。複素変数の初等関数の扱いになれ，複素関数を用いて実定積分が計算できるようになること.
今年度の本講義は google classroom 上のGoogle Meets によるオンライン授業として行います．
本講義のクラスコードは工学部Webページのhttps://www.eng.tohoku.ac.jp/edu/syllabus-ug.htmlの中の【Google Classroomコード一覧】で「電子情報システム・応物系」を選択した上で各自確認してください．
Object and summary: Students learn and understand the concepts of Fourier analysis and complex analysis and develop relevant calculation and application abilities. Both Fourier analysis and complex analysis are important mathematical methods in engineering sciences. In this class, Fourier series and Fourier transformations are first introduced. Next, elementary functions and the concept of analytic function in the complex plane are explained in terms of the differentiability of complex functions. And by using these concepts, complex integrals, Laurent series and isolated singular points are explained. Finally, students learn how to calculate some definite and improper integrals by using complex analysis and how to solve some linear differential and integral equations by using Fourier transformations and complex analysis.
Goal: Students will develop the abilities necessary in calculating Fourier series and Fourier transformation and in applying them to solve some linear differential and integral equations which play important roles in some fundamental problems in engineering sciences.Students will understand some important concepts of complex functions and their isolated singular points in the complex plane. They will be able to calculate some definite and improper integrals by using some methods of complex analysis.
The lectures of the present class is provided as online from Google Meets in the google classroom of the present class.
The google class code of the google classroom for the present class should be confirmed in Class Code List of Google Classroom for each department in the Japanese website of the School of Engineering by students themselves:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html
Google Classroomのクラスコードは工学部Webページにて確認すること．
学部シラバス・時間割(https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html)
１．目的 フーリエ解析と複素解析について，それらの基礎を学習・理解し，計算力と応用力を身につける.
２．概要 工学に現れる現象の解明に重要な役割をはたす応用数学の一部であるフーリエ解析と工学に応用される解析学の基礎をなす複素解析について，それらの基礎を学習する.
３．達成目標等 フーリエ級数，フーリエ変換を理解して，それらの計算とその応用ができるようになること。複素変数の初等関数の扱いになれ，複素関数を用いて実定積分が計算できるようになること.
今年度の本講義は google classroom 上のGoogle Meets によるオンライン授業として行います．
本講義のクラスコードは工学部Webページのhttps://www.eng.tohoku.ac.jp/edu/syllabus-ug.htmlの中の【Google Classroomコード一覧】で「電子情報システム・応物系」を選択した上で各自確認してください．
Object and summary: Students learn and understand the concepts of Fourier analysis and complex analysis and develop relevant calculation and application abilities. Both Fourier analysis and complex analysis are important mathematical methods in engineering sciences. In this class, Fourier series and Fourier transformations are first introduced. Next, elementary functions and the concept of analytic function in the complex plane are explained in terms of the differentiability of complex functions. And by using these concepts, complex integrals, Laurent series and isolated singular points are explained. Finally, students learn how to calculate some definite and improper integrals by using complex analysis and how to solve some linear differential and integral equations by using Fourier transformations and complex analysis.
Goal: Students will develop the abilities necessary in calculating Fourier series and Fourier transformation and in applying them to solve some linear differential and integral equations which play important roles in some fundamental problems in engineering sciences.Students will understand some important concepts of complex functions and their isolated singular points in the complex plane. They will be able to calculate some definite and improper integrals by using some methods of complex analysis.
The lectures of the present class is provided as online from Google Meets in the google classroom of the present class.
The google class code of the google classroom for the present class should be confirmed in Class Code List of Google Classroom for each department in the Japanese website of the School of Engineering by students themselves:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html
実変数関数に対して，変数を複素数に自然に拡張して得られるのが正則関数であり，ラプラス変換やフーリエ変換を扱う上で重要となるほか，電磁気学や流体力学などにも多くの応用を持つ．正則関数の微分積分学の基礎を学び， オイラーの公式や留数定理を使いこなせるようにすることが目的である．同時に，複素積分を通してベクトル解析の初歩にも触れる．
The theory of holomorphic functions, a natural generalization of differentiable functions of a real variable to a complex variable, is an important ingredient in the theory of Laplace and Fourier transforms, and is applied to various areas in sciences such as electromagnetism and fluid mechanics. The purpose of this course is to present the calculus of holomorphic functions and to get acquainted with methods of using the residue formula. The course will also serve as an introduction to vector calculus via the notion of contour integration of complex functions.
この授業は複素関数論（= 複素数を変数に持ち複素数を値にとる関数に対する微積分学）に関するものである。全学教育では複素関数論の基礎を概観し、特に複素微分や線積分、留数計算やその実積分への応用など主に計算に重点が置かれていただろう。この授業では理論面の強化を目指し、全学教育では証明が十分に述べられなかった定理等についてその証明を与えたり、定理等の理論的背景や関連する諸定理についても紹介する。加えて全学教育では扱えなかった内容に関しても扱ってゆく。またイプシロン・デルタ論法の理解を深め、例えば関数項級数の（一様）収束性や項別微分・積分など、解析学の基礎を理解する上で欠かせない技術の習得も目指す。
This course is concerned with the foundation of Complex Analysis, which is Calculus for complex functions. Students are supposed to have already taken the introductory course of Complex Analysis in the general education. In this course, we shall reinforce the theoretical aspect of the content which has already been treated in the general education by giving complete proofs to theorems and by exhibiting further related theorems. Moreover, we will also treat topics which have not been covered in the general education. Furthermore, students are expected to develop an understanding of the arguments based on the (ε, δ)-definition of limit and to master a skill for proving, e.g., (uniform) convergence and termwise differentiation or integration for function series.
１セメの基礎物理数学に続き，物理学の理解に必要となる基礎的な数学（複素解析，フーリエ解析，偏微分方程式）を学ぶ。
This course introduces basic mathematics necessary for physics students. The topics include complex functions, fourier analysis and partial differential equations.
一変数の複素解析学の基礎について講義する. 正則関数の基本的な性質を理解させることやその扱い方を習熟させることを目指し, 複素数の持つ基本的な性質から出発して正則関数の概念やコーシーの積分定理を核とした理論について解説する.
Aiming to understand the basic properties of holomorphic functions, I will explain the foundations of complex analysis of one variable from basic properties of the complex number field to the theory of holomorphic functions and Cauchy's integral formula.
Google Classroomのクラスコードは工学部Webページにて確認すること。
学部シラバス・時間割(https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html)
１．目的 フーリエ解析と複素解析について，それらの基礎を学習・理解し，計算力と応用力を身につける.
２．概要 工学に現れる現象の解明に重要な役割をはたす応用数学の一部であるフーリエ解析と工学に応用される解析学の基礎をなす複素解析について，それらの基礎を学習する.
３．達成目標等 フーリエ級数，フーリエ変換を理解して，それらの計算とその応用ができるようになること。複素変数の初等関数の扱いになれ，複素関数を用いて実定積分が計算できるようになること.
The class code for Google Classroom can be found on the Web site of
the School of Engineering:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html (JP Only)
Object and summary: Students learn and understand the concepts of Fourier analysis and complex analysis and develop relevant calculation and application abilities. Both Fourier analysis and complex analysis are important mathematical methods in engineering sciences. In this class, Fourier series and Fourier transformations are first introduced. Next, elementary functions and the concept of analytic function in the complex plane are explained in terms of the differentiability of complex functions. And by using these concepts, complex integrals, Laurent series and isolated singular points are explained. Finally, students learn how to calculate some definite and improper integrals by using complex analysis and how to solve some linear differential and integral equations by using Fourier transformations and complex analysis.
Goal: Students will develop the abilities necessary in calculating Fourier series and Fourier transformation and in applying them to solve some linear differential and integral equations which play important roles in some fundamental problems in engineering sciences.Students will understand some important concepts of complex functions and their isolated singular points in the complex plane. They will be able to calculate some definite and improper integrals by using some methods of complex analysis.
一変数の複素解析学の基礎について講義する. 正則関数の基本的な性質を理解させることやその扱い方を習熟させることを目指し, 複素数の持つ基本的な性質から出発して正則関数の概念やコーシーの積分定理を核とした理論について解説する.
Aiming to understand the basic properties of holomorphic functions, I will explain the foundations of complex analysis of one variable from basic properties of the complex number field to the theory of holomorphic functions and Cauchy's integral formula.