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                2016年成人高考專升本《高等數學》必背資料(6)

                時間:2015-12-30 10:47:35作者:深圳智學學習網

                多元函數、二元函數

                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)

                無窮級數

                ()數項級數

                1、知識范圍

                (1)數項級數

                數項級數的概念、級數的收斂與發散、級數的基本性質級數收斂的必要條件

                (2)正項級數收斂性的判別法

                比較判別法、比值判別法

                (3)任意項級數

                交錯級數、絕對收斂、條件收斂、萊布尼茨判別法

                2、要求

                (1)理解級數收斂、發散的概念。掌握級數收斂的必要條件,了解級數的基本性質。

                (2)掌握正項級數的比值判別法。會用正項級數的比較判別法。

                (3)掌握幾何級數、調和級數與級數的收斂性。

                (4)了解級數絕對收斂與條件收斂的概念,會使用萊布尼茨判別法。

                (責任編輯:馬老師 )

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