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AND
アイテム
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微分積分学II
http://hdl.handle.net/2237/00027501
e177057a-45cc-4144-a393-892ba79b90c0
名前 / ファイル | ライセンス | アクション | |
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Item type | 教材 / Learning Material(1) | |||||
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公開日 | 2018-03-19 | |||||
タイトル | ||||||
タイトル | 微分積分学II | |||||
言語 | ja | |||||
著者 |
山上, 滋
× 山上, 滋 |
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アクセス権 | ||||||
アクセス権 | open access | |||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||
権利 | ||||||
言語 | ja | |||||
権利情報 | 本資料は、名古屋大学の教員山上滋によって作成され、名大の授業Webサイトに掲載された「微分積分学II」(2015)をもとに(一部改変して)作成されたものです。Copyright(C)2015 山上滋 | |||||
抄録 | ||||||
内容記述 | 以下の授業内容は標準的に教えられるものであり,講義の順序を示すものではない.また,クラスによっては,さらに進んだ内容が教えられる場合もある.実際の講義予定は別に提示する. 1.多変数関数の極限と連続性 多変数関数(特に2変数関数)の極限に関する基本的事項と連続関数の基本性質を学ぶ. (キーワード)ユークリッド距離,点列の極限,多変数関数の極限と連続性 (発展的内容)近傍,開集合,閉集合,連続関数の性質 2.多変数関数の微分法 多変数関数(特に2変数関数)について微分法の基礎を理解する.さらにそれを用いて,平面上の関数の様々な性質について調べられるようにし,極値問題などへの応用を学ぶ. (キーワード)偏微分と方向微分,合成関数の偏微分,テイラーの定理,高階偏導関数,極値問題 (発展的内容)全微分,接平面の方程式,座標変換,勾配ベクトル,二次形式としてのヘシアン,陰関数定理,ラグランジュの未定乗数法,多変数関数 3.多変数関数の積分法 重積分の意味を理解し,累次積分による積分計算に習熟する.さらに,極座標変換などの例を通して,変数変換とその重積分への応用を学ぶ. (キーワード)重積分,累次積分,変数変換,ヤコビアン (発展的内容)積分順序交換,曲面積と体積,(多変数)広義積分,線積分,グリーンの定理 | |||||
言語 | ja | |||||
内容記述タイプ | Abstract | |||||
出版者 | ||||||
言語 | ja | |||||
出版者 | 名古屋大学オープンコースウェア委員会 | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_e059 | |||||
タイプ | learning object | |||||
関連情報 | ||||||
関連タイプ | isVersionOf | |||||
関連識別子 | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://ocw.ilas.nagoya-u.ac.jp/index.php?lang=ja&mode=c&id=652&page_type=index | |||||
書誌情報 |
発行日 2018-01-31 |
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著者版フラグ | ||||||
値 | publisher |