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            復習指導(4)-2019年高等數學一復習資料-福建專升本

            福建成人高考信息網www.laiwobuy.com 發布時間: 2018年11月27日

            復習指導(4)

            (二)平面與直線

              1、知識范圍

              (1)常見的平面方程,點法式方程、一般式方程

              (2)兩平面的位置關系(平行、垂直和斜交)

              (3)點到平面的距離

              (4)空間直線方程

              標準式方程(又稱對稱式方程或點向式方程、一般式方程參數式方程

              (5)兩直線的位置關系(平行、垂直)

              (6)直線與平面的位置關系(平行、垂直和直線在平面上)

              2、要求

              (1)會求平面的點法式方程、一般式方程。會判定兩平面的垂直、平行。會求兩平面間的夾角。

              (2)會求點到平面的距離。

              (3)了解直線的一般式方程,會求直線的標準式方程、參數式方程。會判定兩直線平行、垂直。

              (4)會判定直線與平面間的關系(垂直、平行、直線在平面上)。

                  (三)簡單的二次曲面

              1、知識范圍

              球面、母線平行于坐標軸的柱面 旋轉拋物面圓錐面、橢球面

              2、要求

              了解球面、母線平行于坐標軸的柱面、旋轉拋物面、圓錐面和橢球面的方程及其圖形。

              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。


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