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            2017年成人高考專升本數學復習資料-復習指導五

            福建成人高考信息網www.laiwobuy.com 發布時間: 2017年03月29日

            五、多元函數微積分學

              (一)多元函數微分學

              1.知識范圍

              (1)多元函數

              多元函數的定義 二元函數的幾何意義 二元函數極限與連續的概念

              (2)偏導數與全微分

              偏導數 全微分 二階偏導數

              (3)復合函數的偏導數

              (4)隱函數的偏導數

              (5)二元函數的無條件極值與條件極值

              2.要求

              (1)了解多元函數的概念、二元函數的幾何意義。會求二次函數的表達式及定義域。了解二元函數的極限與連續概念(對計算不作要求)。

              (2)理解偏導數概念,了解偏導數的幾何意義,了解全微分概念,了解全微分存在的必要條件與充分條件。

              (3)掌握二元函數的一、二階偏導數計算方法。

              (4)掌握復合函數一階偏導數的求法。

              (5)會求二元函數的全微分。

              (6)掌握由方程 所確定的隱函數 的一階偏導數的計算方法。

              (7)會求二元函數的無條件極值。會用拉格朗日乘數法求二元函數的條件極值。

              (二)二重積分

              1.知識范圍

              (1)二重積分的概念

              二重積分的定義二重積分的幾何意義

              (2)二重積分的性質

              (3)二重積分的計算

              (4)二重積分的應用

              2.要求

              (1)理解二重積分的概念及其性質。

              (2)掌握二重積分在直角坐標系及極坐標系下的計算方法。

              (3)會用二重積分解決簡單的應用問題(限于空間封閉曲面所圍成的有界區域的體積、平面薄板質量)。


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