AP微積分輔導(dǎo)手冊

第1章AP微積分簡介 Introduction of AP Calculus001
1．1課程及考試The Courses and Examinations001
1．2AP微積分AB和BC大綱要求 The Examination Outline of AP Calculus AB & BC004
1．3AP微積分參考詞匯表 Reference Vocabulary of AP Calculus006
1．4圖形計算器的使用 Use of Graphing Calculators013
第2章函數(shù) Functions019
2．1函數(shù)的定義 Definition of Functions020
2．2函數(shù)的基本性質(zhì) Function Basic Properties022
2．3基本初等函數(shù) Basic Elementary Functions023
2．4反函數(shù)&復(fù)合函數(shù) Inverse Functions & Composite Functions033
2．5函數(shù)變換 Transforming of Functions035
2．6#參數(shù)方程&向量函數(shù) Parametric Equations & Vector Functions037
2．7#極坐標(biāo)函數(shù) Polar Functions039
2．8習(xí)題 Practice Exercises041
第3章極限 Limit043
3．1極限的定義 Definition of the Limit044
3．2極限存在的判定 The Limit does Exist or Not045
3．3極限的運算 Operations of Limit047
3．4極限的應(yīng)用 Applications of Limit052
3．5習(xí)題 Practice Exercises053
第4章連續(xù) Continuity055
4．1連續(xù)性的定義 Definition of the Continuity056
4．2間斷點的分類 Kinds of Discontinuities059
4．3連續(xù)函數(shù)定理 The Continuous Functions Theorem061
4．4習(xí)題 Practice Exercises063
第5章導(dǎo)數(shù)和微分 Derivative and Differential065
5．1導(dǎo)數(shù)的定義 Definition of the Derivative066
5．2可導(dǎo)性和連續(xù)性 Derivability and Continuity072
5．3導(dǎo)數(shù)的基本公式和法則 Basic Differentiation Formulas and Rules075
5．4鏈?zhǔn)椒▌t和反函數(shù)求導(dǎo) The Chain Rule & Derivative of an Inverse Function077
5．5隱函數(shù)求導(dǎo)和二階導(dǎo)數(shù) Implicit Differentiation & Second Derivatives082
5．6#參數(shù)方程求導(dǎo) Derivatives of Parametric Equations088
5．7#向量函數(shù)和極坐標(biāo)函數(shù)求導(dǎo) Derivatives of Vector Functions and Polar Functions090
5．8微分 Differential093
5．9習(xí)題 Practice Exercises096
第6章微分的應(yīng)用 Applications of Differential Calculus098
6．1切線方程和法線方程Equations of Tangent and Normal099
6．2最值問題The Problems of Maxima and Minima101
6．3運動問題The Problems of Motion112
6．4微分中值定理The Mean Value Theorem for Derivatives118
6．5洛必達法則L’Hpital’s Rule120
6．6估算問題The Problems of Estimate125
6．7#歐拉方法Euler’s Method129
6．8習(xí)題Practice Exercises130
第7章不定積分 The Indefinite Integral132
7．1不定積分的定義Definition of The Indefinite Integral133
7．2不定積分公式Formulas of The Indefinite Integral135
7．3U-替換法U-Substitution138
7．4#分部積分法Integration by Parts148
7．5#有理函數(shù)的積分Integration of Rational Functions153
7．6不定積分的應(yīng)用Applications of Indefinite Integral156
7．7習(xí)題Practice Exercises157
第8章定積分 The Definite Integral159
8．1黎曼和與梯形法則Riemann Sums and Trapezoid Rule160
8．2定積分的定義Definition of the Definite Integral165
8．3微積分基本定理The Fundamental Theorem of Calculus169
8．4定積分的性質(zhì)Properties of Definite Integral174
8．5積分中值定理The Mean Value Theorem for Integrals176
8．6定積分的計算The Operations of Definite Integrate178
8．7#廣義積分Improper Integrals180
8．8習(xí)題Practice Exercises185
第9章積分的應(yīng)用 Applications of Integral186
9．1面積Area187
9．2體積Volume195
9．3#弧長 Arc Length204
9．4位移和距離Displacement and Distance206
9．5習(xí)題 Practice Exercises207
第10章微分方程 Differential Equations209
10．1一階微分方程First-Order Differential Equations210
10．2求解可分離變量微分方程Solving Separable D．E．211
10．3斜率場 Slope Fields213
10．4指數(shù)增長與衰減 Exponential Growth and Decay216
10．5約束增長與衰減 Restricted Growth and Decay219
10．6#邏輯斯諦微分方程Logistic Differential Equation222
10．7習(xí)題 Practice Exercises225
第11章無窮級數(shù) Infinite Series226
11．1數(shù)列的極限 The Limit of The Sequence227
11．2無窮級數(shù) Infinite Series228
11．3四類重要級數(shù)Four Important Series232
11．4正項級數(shù)的四大判別法Four Tests of Nonnegative Series235
11．5絕對收斂和條件收斂 Absolute and Conditional Convergence240
11．6冪級數(shù) Power Series242
11．7泰勒級數(shù)和麥克勞林級數(shù) Taylor and Maclaurin Series245
11．8冪級數(shù)的計算 Computations with Power Series251
11．9習(xí)題 Practice Exercises254
習(xí)題答案Practice Answer255
附錄Appendix287
A．1常用公式和定理Common Formulas and Theorems287
A．2AP微積分公式總結(jié)Summary AP Calculus Formula291
A．3VIP服務(wù)及網(wǎng)站298
參考文獻References299