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            2017年成人高考專升本數學復習資料-復習指導(一)

            福建成人高考信息網www.laiwobuy.com 發布時間: 2017年04月01日

            高數一考試大綱

              本大綱適用于工學理學(生物科學類、地理科學類、環境科學類、心理學類等四個一級學科除外)專業的考生。

              總要求考生應按本大綱的要求,了解或理解“高等數學”中函數、極限和連續、一元函數微分學、一元函數積分學、向量代數與空間解析幾何、多元函數微積分學、無窮級數、常微分方程的基本概念與基本理論;學會、掌握或熟練掌握上述各部分的基本方法。應注意各部分知識的結構及知識的內在聯系;應具有一定的抽象思維能力、邏輯推理能力、運算能力、空間想象能力;能運用基本概念、基本理論和基本方法正確地推理證明,準確地計算;能綜合運用所學知識分析并解決簡單的實際問題。

              本大綱對內容的要求由低到高,對概念和理論分為“了解”和“理解”兩個層次;對方法和運算分為“會”、“掌握”和“熟練掌握”三個層次。

              復習考試內容

              一、函數、極限和連續

              (一)函數

              1.知識范圍

              (1)函數的概念

              函數的定義 函數的表示法 分段函數 隱函數

              (2)函數的性質

              單調性 奇偶性 有界性 周期性

              (3)反函數

              反函數的定義 反函數的圖像

              (4)基本初等函數

              冪函數 指數函數 對數函數 三角函數 反三角函數

              (5)函數的四則運算與復合運算

              (6)初等函數

              2.要求

              (1)理解函數的概念。會求函數的表達式、定義域及函數值。會求分段函數的定義域、函數值,會作出簡單的分段函數的圖像。

              (2)理解函數的單調性、奇偶性、有界性和周期性。

              (3)了解函數與其反函數 之間的關系(定義域、值域、圖像),會求單調函數的反函數。

              (4)熟練掌握函數的四則運算與復合運算。

              (5)掌握基本初等函數的性質及其圖像。

              (6)了解初等函數的概念。

              (7)會建立簡單實際問題的函數關系式。

              (二)極限

              1.知識范圍

              (1)數列極限的概念

              數列 數列極限的定義

              (2)數列極限的性質

              唯一性 有界性 四則運算法則 夾逼定理單調有界數列極限存在定理

              (3)函數極限的概念

              函數在一點處極限的定義 左、右極限及其與極限的關系趨于無窮 時函數的極限 函數極限的幾何意義

              (4)函數極限的性質

              唯一性 四則運算法則 夾通定理

              (5)無窮小量與無窮大量

              無窮小量與無窮大量的定義 無窮小量與無窮大量的關系無窮小量的性質 無窮小量的階

              (6)兩個重要極限

              2.要求

              (1)理解極限的概念(對極限定義中“ ”、“ ”、“ ”等形式的描述不作要求)。會求函數在一點處的左極限與右極限,了解函數在一點處極限存在的充分必要條件。

              (2)了解極限的有關性質,掌握極限的四則運算法則。

              (3)理解無窮小量、無窮大量的概念,掌握無窮小量的性質、無窮小量與無窮大量的關系。會進行無窮小量階的比較(高階、低階、同階和等價)。會運用等價無窮小量代換求極限。

              (4)熟練掌握用兩個重要極限求極限的方法。


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