重要觀念重申   &   指定練習
(在下一個 pdf 檔還沒出現以前，最後一個 pdf 檔仍會增修！)

• Functions
  §1.3 # 3,35∼40,41∼44,51~55
• Limits and Continuity
  §2.2 # 6,9,10,11,15∼18,19∼22,32,40
  §2.3 # 19,20,22,23,25,26,28∼38,43,44,47,58,59
  §2.4 # 7,8,22,27,28,29,31,37,{§2.4#39,§2.5#57,58},§2.5#53
  
• Derivative & Differential
  You don't need to do innumerable exercises, as long as you know every in and out of limit and those derivative rules ..... drill
  §3.1 # 15~24, 35,36
  §3.2 # 4,5~13, 24~27, 35,36, 41~45
  §3.3 # 55~60, 61~68, 73,74,87
  §3.5 # 35~44, 46,47 (limit problems, done before)
  §3.6 # 1~41, 53~64, 71,72,74 【chain rule】
  §3.7 # 1~22,23,24 【implicit differentiation】
  §3.8 # [29~32],64,65,66
  §3.10 # 11~14, 15~20, 21~26, 31~36, [45]
  
• Finding Local and Global Extrema
  §4.3 # 1,2,7,8,27,28,51,52
  §4.4 # 21~23,32,33,34,41,42,51~54 極限問題
  §4.5 # 19,20,21,23,25,39,40,44,45,51 自己檢查: 有無漸進線、critical point、local extrema、inflection point 後畫圖)
  
• Various Mean Value Theorems and L'Hopital Rule
  §7.7 # 15~18,23,28,31,37,47~62 盡量用最簡單的方法,少用 L'Hopital Rule;
         # 85~89
  求漸近線(求極限),極值,反曲點,畫圖的幾個例子

• 1st Order ODE, Anti-derivative/Indefinite Integral
  
• Anti-derivative(續),Riemann Sum, Definite Integral, Fundamantal Theorem of Calculus
  §4.10 # 1∼16 太簡單了,用眼睛看出答案。  #17∼36.
  §5.1 # 17∼26.
  §5.2 # 17∼20,61,62,65,66,67,68,69
  limit of finite sum <==> definite integral 練習範例
  §5.3 # 13∼18,43∼47,53,54,(55),56,57
  §5.4 # 3,4,13,14,33,34,39,40,43,44
  §5.5 # 27,28,31,32,36,61∼66,69,(75),77,78,83
  Review # true-false 全, #4,41,42,51∼56
  不定積分/定積分問題 我一定是出有點技巧/難度的。太簡單的問題,你自己高興做就做。
  

  { } 內是同一型的問題,以標紅色者為典型; ( ) 內的是比較簡單的問題, 請自行斟酌選擇練習。
  

• §8.1
  • # {3,6,7,8,19,24*,35,37},
  • # {4,5,14,20,23,26*,36*,39, 46,50 },
  • # {9,12,13,21,22*,31, 45,49 },
  • # 其他: {10,25}, 11, {15,16,32}, (27), 28, 29*, 30*, 33, 34, 38*, {41,Eg6, 42,43,44}, 62*, 64*, 65, 66* .
  §8.2
      各種三角函數(sin x, cos x, tan x, cot x, sec x, csc x) 的整數次方乘積, 皆可寫成 cos^m x sin^n x 的樣子。
      若 m,n 有奇, 則 cos^m x sin^n x 的 anti-derivative 很簡單, 所以不太勾。
      "偶偶" 除了用 倍角公式 或 DeMoore 公式以外, 亦可用類似 §8.1 Eg6, 42 方式降階。
  • # 有奇 {(17,18,20*,(21),27∼31,33,34,36,37,39,40,49)},
  • # 偶偶 {22∼26,35,38,47,50,52},
  • # 積化和差 {41,42,43,51},
  • # 其他: 11, 12*, 15*, (16), {19}, 44, 45, 46, {65,66,67}, 68*, .....
  
  §8.3 # 以三角函數代換 4∼30
  §8.4 # 將分式分解 7∼54
  §8.5 # (全)
• Applications of Definite Integrals
  §6.1 面積 # 4,10,13,14,19,20,24,29,30,33∼38,49∼51(考試時不給圖)
  §6.2 旋轉體體積 (可視為圓薄片加總) # {1∼38}, {50∼52}, {53∼56}, {61*,64*}
  §6.3 旋轉體體積 (亦可視為圓柱殼加總)# {1∼26}, {37∼42}
  §9.1 弧長 # 3∼20
  §9.2 旋轉體表面積 # 1∼16
  §9.3 質心=重心∼圖心 (算了,不考)