授業の目的 【日本語】
Goals of the Course(JPN) | | | 専門基礎科目として数学及び物理学等を学んだ後，さらに進んで工学への応用を視野に入れてベクトル解析と偏微分方程式を修得します。力学や電磁気に関連する分野，物質や熱等の移動現象を伴う分野など工学の多くの問題には、座標変換、ベクトル場、線積分などベクトル解析の知識とその応用が必要になります。また、振動・波動、熱拡散等を定量的に扱う上で、微分方程式を使いこなせることが必要となります。そこで、この授業ではベクトル解析および常微分方程式について学び、演習を通じてそれらの知識を実際の工学上の問題に利用できるよう修得することを目的とします。 |
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授業の目的 【英語】
Goals of the Course | | 5th period
This course is a companion course to Mathematical Physics II. This course introduces first order and second order ordinary differential equations and their solution methods. Students master analytical techniques for problems that arise in physics, engineering and chemistry. Questions of uniqueness of solutions and convergence are also discussed. Students are also introduced to Fourier series, the Fourier transform, convolution, Laplace transform, and the Dirac delta function. Students will find this mathematical methods course helpful in other units such as Quantum Mechanics, Analytical Mechanics, Electricity and Magnetism, as well as in Automotive Engineering and other engineering courses.
This course has dual aims: 1) to convey mathematical principles; 2) to improve students’ technical ability – i.e. ability to express intuition in mathematical terms and ability to solve problems.
4th period
Students taking Mathematical Physics I should also take this tutorial class. This course introduces first order and second order ordinary differential equations and their solution methods. Students master exact and approximate analytical techniques for initial value problems that arise in physics, engineering and chemistry. Questions of existence, uniqueness and convergence are also discussed. Fourier series follow naturally from the 2nd order theory and these are investigated, too. |
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到達目標 【日本語】
Objectives of the Course(JPN) | | | 専門基礎科目として数学及び物理学等を学んだ後，さらに進んで工学への応用を視野に入れてベクトル解析と偏微分方程式を修得します。力学や電磁気に関連する分野，物質や熱等の移動現象を伴う分野など工学の多くの問題には、座標変換、ベクトル場、線積分などベクトル解析の知識とその応用が必要になります。また、振動・波動、熱拡散等を定量的に扱う上で、微分方程式を使いこなせることが必要となります。そこで、この授業ではベクトル解析および常微分方程式について学び、演習を通じてそれらの知識を実際の工学上の問題に利用できるよう修得することを目的とします。 |
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到達目標【英語】
Objectives of the Course | | 5th period
This course is a companion course to Mathematical Physics II. This course introduces first order and second order ordinary differential equations and their solution methods. Students master analytical techniques for problems that arise in physics, engineering and chemistry. Questions of uniqueness of solutions and convergence are also discussed. Students are also introduced to Fourier series, the Fourier transform, convolution, Laplace transform, and the Dirac delta function. Students will find this mathematical methods course helpful in other units such as Quantum Mechanics, Analytical Mechanics, Electricity and Magnetism, as well as in Automotive Engineering and other engineering courses.
This course has dual aims: 1) to convey mathematical principles; 2) to improve students’ technical ability – i.e. ability to express intuition in mathematical terms and ability to solve problems.
4th period
Students taking Mathematical Physics I should also take this tutorial class. This course introduces first order and second order ordinary differential equations and their solution methods. Students master exact and approximate analytical techniques for initial value problems that arise in physics, engineering and chemistry. Questions of existence, uniqueness and convergence are also discussed. Fourier series follow naturally from the 2nd order theory and these are investigated, too. |
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授業の内容や構成
Course Content / Plan | | |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | |
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教科書・テキスト
Textbook | | |
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参考書
Reference Book | | |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | |
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使用言語
Language Used in the Course | | |
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授業開講形態等
Lecture format, etc. | | |
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遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class) | | |
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