參考講義
參考講義可當作上課前預習:可以將不懂的在上課時弄清楚。
也可當成課後複習: 上完課，做講義的基本練習，當作複習。
0 簡介
1 極限,連續單元(Limit, Continuity)
1.1 極限之概念 (Introduction to Limits)
1.2 求極限之技巧 (Techniques for Finding Limits)
1.3 與無窮有關之極限，漸進線 (Limits Involving Infinity; Asymptotes)
1.4 連續 (Continuity)
2 微分單元(Derivatives)
2.1 導數的概念 (Derivatives)
2.2 微分基本運算 (Basic Rules of Differentiation)
2.3 三角函數微分公式 (Derivatives of Trigonometric Functions)
2.4 鏈鎖律 (The Chain Rule)
2.5 隱函數微分 (Implicit Differentiation)
2.6 指對數函數微分公式 (Derivatives of Exponential and Logarithm Functions)
2.7 線性逼近與微分量 (Differentials and Linear Approximations)
3 微分應用單元(Applications of Derivative)
3.1 極大，極小值 (Extreme values of Functions)
3.2 均值定理 (Mean Value Theorem) --- (*彈性課程)
3.3 遞增，遞減與一階導數檢查法 (Increasing, Decreasing; 1-st Derivative Test)
3.4 凹向，反曲點 (Concavity and Inflection Points)
4 積分單元(Integration)
4.1 不定積分與反導函數 (Indefinite integral, Anti-derivative)
4.2 定積分 (Definition integral)
4.3 微積分基本定理 (Fundamental Theorem of Calculus)
4.4 代換積分 (Substitution rule) [商學院加上: tan x, cot x, sec x, csc x之積分 ]
4.5 兩曲線所圍面積 (Area between two curves)
5超越函數單元(Transcendental Functions )
5.1 反函數 (Inverse function) --- (商學院不教)
5.2 自然對數 (Natural Logarithm function) ， tan x, cot x, sec x, csc x之積分
5.3 自然指數 (Natural Exponential function)
5.4 一般指對數 (General exponential and logarithm functions)
5.5 反三角函數 (Inverse Trigonometric functions) --- (商學院不教)
5.6 羅必達 (L'Hopital's Rule )
6 積分技巧單元(Techniques of Integration)
6.1 分部積分 (Integration by parts)
6.2 三角函數的積分 (Trigonometric Integral)
6.3 三角代換法 (Trigonometric substitution ) --- (商學院不教)
6.4 分式型函數積分 (Integration of rational functions by partial fractions) --- (商學院不教)
6.5 瑕積分 (Improper Integral)
7無窮數列,級數單元(Infinite sequence, Infinite series) --- (*彈性課程)
7.1 數列 (Infinite sequence)
7.2 級數 (Infinite series)
7.3 發散Test與p-級數 (Divergent Test, p-series)
7.4 其他的正項審歛法 (Others Tests)
7.5 交錯級數，與絕對收斂，條件收斂 (Alternating series, Absolute and Condition Convergent)
8冪級數(Power series)
8.1 冪級數 (Power series)
8.2 泰勒級數，馬克勞林級數 (Taylor series, Maclaurin series)
9 多變數微分單元(Partial Derivatives)
9.1 多變數函數圖形 (The graph of the functions for more variables)
9.2 雙變數函數之極限 (The limit of the function as 2 variables) --- (*彈性課程)
9.3 偏微分 (Partial derivatives)
9.4 鏈鎖律 (Chain rule)
9.5 方向導數，梯度 (Direction Derivatives and Gradient vector) ---(商學院不教方向導數)
9.6 切平面，全微分(量) (Tangent plane, Total differential)
9.7 極值與鞍點 (local extreme, saddle point)
9.8 限制條件求極值 (The absolute extreme values on a constraint set) --- (*彈性課程)
10 重積分單元(Multiple Integrals)
10.1 重積分概念 (Double integral)
10.2 疊代積分，Fubini定理 (Iterated integral, Fubini's Theorem)
10.3 一般區域的Fubini定理 (Fubini's Theorem for general region)
10.4 重積分在極座標 (Double integral for polar coordinates)
10.5 重積分的代換法則 (Substitutions in Multiples integrals)--- (*彈性課程)