919 件ヒット (0.021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)
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
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.
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.
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，ルジャンドル関数，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。
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 Legendre functions and Bessel functions are also explained as the series solutions of Legendre and Bessel differential equations. In the third part, students learn how to solve some partial differential equations, Laplace equations, Poisson equations, 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, Legendre, 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.
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)
この科目では、講義に関する連絡やレポート提出には、Google Classroomを使用します。
１．目的
工学に応用されることの多い数学の分野のうち、下記の内容の基礎を学ぶ。
２．概要
フーリエ級数とフーリエ変換、ラプラス変換およびベクトル解析の基礎について、講義と演習を行う。
３．達成目標等
この授業では、主に以下のような能力を修得することを目標とする。
・本学科の学習・教育目標の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。
・公式および定理を使用し、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 will use Google Classroom for lecture-related instruction and report submission.
1. Objective
This course is designed to help students acquire the fundamentals of the following areas of mathematics that are frequently applied in engineering.
2. Summary
This course covers the fundamentals of the Fourier series, Fourier transform, Laplace transforms, and vector analysis in mathematics that are widely applied to engineering (e.g., materials engineering). Students learn the above contents through lectures and exercises.
3. Goal
At the end of this course, students are expected to gain our program outcomes of B, C, and K. Students are expected to understand and explain the theorems and the applicable conditions of formulas. They are also expected to use and apply the formulae and theorems.
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
フーリエ解析およびラプラス変換についての基礎を理解し，計算力を習得する．
２． 概要
理工学における様々な現象の解析に用いられている方法として，フーリエ解析およびラプラス変換を取り上げ，それらの数学的考え方および具体的問題に現れる理論と応用の結びつきについて学ぶ．
３． 達成目標等
フーリエ級数，フーリエ変換，ラプラス変換を理解して，それらの計算と種々の理工学問題への応用が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)
1. Objective
Students learn the basics of Fourier analysis and Laplace transform and develop relevant calculation abilities.
2. Overview
Fourier analysis and Laplace transform are mathematical tools applicable to the analysis of a wide variety of engineering and scientific problems. This course provides students with the basic mathematical principles as well as the knowledge that links the theory and application to specific problems.
3. Goal
This course is designed to help students understand Fourier analysis and Laplace transform and learn how to apply them to specific problems in engineering and science.