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微分積分学II

http://hdl.handle.net/2237/00027501

	Name / File	License	Actions
	cal2015aki(1) (291.9 kB)

item type

教材 / Learning Material(1)

公開日

2018-03-19

タイトル

微分積分学II

言語

著者

山上, 滋

権利

権利情報

抄録

内容記述タイプ

Abstract

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

出版者

名古屋大学オープンコースウェア委員会

言語

jpn

資源タイプ

資源

http://purl.org/coar/resource_type/c_e059

タイプ

learning object

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Ver.1

2021-03-01 13:30:53.495674

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微分積分学II

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