273 件ヒット (0.028秒)：
この講義では複素微分幾何や多変数複素解析の基礎をセミナー形式で学ぶ.
これらの分野の基礎知識, 数学書の読み方, 試行錯誤の仕方を身に着けさせることを目的とする.
Students study the basics of complex differential geometry and the theory of several complex variables. The aim is to give the students a basic knowledge of these fields, how to read mathematical books, and how to make trial and error.
この講義では複素微分幾何や多変数複素解析の基礎をセミナー形式で学ぶ.
これらの分野の基礎知識, 数学書の読み方, 試行錯誤の仕方を身に着けさせることを目的とする.
Students study the basics of complex differential geometry and the theory of several complex variables. The aim is to give the students a basic knowledge of these fields, how to read mathematical books, and how to make trial and error.
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 ラプラス変換，特殊関数，２階線形偏微分方程式について，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ラプラス変換，２階線形微分方程式について，また工学に応用される特殊関数のうち，特にガンマ関数，ベータ関数，ベッセル関数について，それらの基礎を学習する。
３．達成目標等 上記のいくつかの特殊関数の基礎的な性質を理解し，その工学への応用とそれらの公式を用いた計算ができるようになること。ラプラス変換とその逆変換を理解し，それらが計算でき，微分・積分方程式などが解けるようになること。さらに，２階線形偏微分方程式が工学にどのように応用されているかを理解して，変数分離法を身につけること。
各クラスの授業形態は下記の通りである．．
・対面授業とGoogle Classroom (クラスコード: kbgph6s)
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 Laplace transformation, special functions, and partial differential equations. In the first part, students learn Laplace transformation and its applications for solving linear differential equations. In the second part, some special functions, gamma function, and beta functions are introduced, and the Bessel function is also explained as a series solution of Bessel differential equations. In the third part, students learn how to solve some partial differential equations, such as diffusion equations and wave equations. These concepts are important in engineering sciences.
Goal: Students will develop the abilities necessary to calculate Laplace transformation and in applying them to solve some differential and integral equations. Students will understand some concepts and mathematical properties of gamma, beta, and Bessel functions and their isolated singular points in the complex plane and will be able to calculate some improper integrals by using some theories of complex analysis.
Style: Face-to-face and Google Classroom （Class Code: kbgph6s)
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
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.
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.
各クラスのオンライン授業は下記の通りで実施される．
Aクラス [TB23043] (平野愛弓教授): Google Classroomを利用
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.
On-line lectures are proceeded as follows
Class A [TB23043] (Ayuki Hirano, Professor): Google Classroom
Google Classroomのクラスコードは工学研究科Webページ
https://www.eng.tohoku.ac.jp/edu/syllabus-g.html
（大学院シラバス・時間割・履修登録）にて確認すること。
力学に関する解析的研究では、微分幾何学あるいは多様体といった現代数学が幅広く活用されている。これらの分野で発展してきた記号や演算といった表現は、工学研究科に所属する学生が普段目にしないものであり、学習の弊害となっている。本講義では、これら現代数学の入門編として、それら表現を出来るだけ平易に導入し、力学との関係を解説する。
本講義は、Google Classroomを利用する。クラスコードは「dvmdc7f」である。
The class code for Google Classroom can be found on the Web site of the School of Engineering:
https://www.eng.tohoku.ac.jp/english/academics/master.html (under "Timetable & Course Description")
In the modeling of classical mechanics, we often meet the applied mathematics, such as differential geometry or manifolds theory. These have been developed from the viewpoint of mathematical universality and do not always provide new ideas directly. But, we often need such a background to make the theoretical models. Furthermore, symbols and calculations developed in these fields are not commonly used by general engineering students or graduate students of engineering, and this is considered to be an obstacle for learning them. In this lecture, I am going to introduce those mathematical expressions as simple as possible, so that the students can employ the advanced mathematics in the general mechanical engineering field. This course can also be considered as an introduction to the tools of physical mathematics.
Google Classroom will be used for this lecture. The class code is "dvmdc7f".
代数解析・代数幾何・特異点理論の基礎を扱った文献を精密に読み込み、
同時にその内容を他者に説明する技術を身につける。
To read textbooks on the foundations of algebraic analysis, algebraic geometry and singularity theory carefully, as well as to develop ability to explain its context to others.
代数解析・代数幾何・特異点理論の基礎を扱った文献を精密に読み込み、
同時にその内容を他者に説明する技術を身につける。
To read textbooks on the foundations of algebraic analysis, algebraic geometry and singularity theory carefully, as well as to develop ability to explain its context to others.