《新東方?AP微積分》簡(jiǎn)介：AP，全稱Advanced Placement，中文名稱為大學(xué)預(yù)修課程。AP課程及考試始于1955年，由美國(guó)大學(xué)理事會(huì)（College Board）主辦，在高中階段開設(shè)的具有大學(xué)水平的課程，共有22個(gè)門類、37個(gè)學(xué)科。該項(xiàng)考試的目的在于使高中學(xué)生提前接觸大學(xué)課程，完成一些美國(guó)大學(xué)的學(xué)分課程及考試。
《新東方?AP微積分》為國(guó)內(nèi)第一本中英文結(jié)合的AP微積分教材，適合念完國(guó)內(nèi)高一上學(xué)期數(shù)學(xué)課程及以上的學(xué)生使用。在研究了國(guó)內(nèi)高中數(shù)學(xué)知識(shí)體系和教學(xué)體系的基礎(chǔ)上，本書構(gòu)建了最易于中國(guó)學(xué)生接受的AP微積分知識(shí)體系，第一次真正的全面覆蓋了AP微積分的考點(diǎn)。大量的例題和習(xí)題，豐富的講解和分析必將為您奪取AP微積分5分的桂冠鋪平道路。
目錄
Chapter 1 Introduction of AP Calculus Exam AP微積分考試介紹Chapter 2 Functions函數(shù) 2.1 Five Basic Elementary Functions五種基本初等函數(shù) 2.2 Inverse Functions反函數(shù) 2.3 Composite Functions復(fù)合函數(shù) 2.4 Parametric Functions參變量函數(shù) 2.5 Polar Functions極坐標(biāo)函數(shù) 2.6 Vector Functions向量函數(shù) 2.7 Transforming of Functions函數(shù)變換 【Practice Problems·課后練習(xí)】Chapter 3 Limit and Continuity極限與連續(xù) 3.1 Definition of a Limit極限的定義 3.2 Limit Laws極限（存在）定理 3.3 Rules of Limits極限的運(yùn)算法則 3.4 Two Important Limits兩個(gè)重要極限 3.5 Application of Limits：Finding Asymptotes極限的應(yīng)用：找漸近線 3.6 Continuity連續(xù) 【Practice Problems·課后練習(xí)】Chapter 4 Definition of Derivative導(dǎo)數(shù)定義 4.1 Definition of Derivative導(dǎo)數(shù)的定義 4-2 ORe—Sided Derivative單側(cè)導(dǎo)數(shù) 4.3 The Geometric Interpretation of Derivative導(dǎo)數(shù)的幾何意義 4.4 The Relation Between Differentiability and Continuity可導(dǎo)與連續(xù)的關(guān)系 【Practice Problems·課后練習(xí)】Chapter 5 Rules for Finding Derivatives求導(dǎo)法則 5.1 Basic Rules for Finding Derivatives導(dǎo)數(shù)基本運(yùn)算 5.2 High Order Derivatives高階導(dǎo)數(shù) 5.3 Implicit Differentiation“隱函數(shù)”求導(dǎo) 5.4 The Derivative of an Inverse Function反函數(shù)求導(dǎo) 5.5 Derivatives of Parametric Functions參數(shù)方程求導(dǎo) 5.6 Derivatives of Polar Functions極坐標(biāo)函數(shù)求導(dǎo) 5.7 Derivatives of Vector Functions向量函數(shù)求導(dǎo) 【Practice Problems·課后練習(xí)】Chapter 6 Applications of Derivatives導(dǎo)數(shù)應(yīng)用 6.1 Equations of Tangent Lines and Normal Lines切線和法線方程 6.2 The Mean Value Theorem for Derivatives微分中值定理 6.3 Related Rates相關(guān)變化率 6.4 Motion運(yùn)動(dòng)學(xué) 6.5 Maxima and Minima最大值和最小值 6.6 L’Hopital’S Rule洛比達(dá)法則 【Practice Problems·課后練習(xí)】Chapter 7 Differentials微分 7.1 Defi n ition of Differential微分定義 7.2 Linear Approximation線性估算 7 3 Euler’S Method歐拉法則 【Practice Problems·課后練習(xí)】Chapter 8 The Indefinite Integral不定積分 8.1 The Antiderivative原函數(shù) 812 Integration Formulas積分公式 8.3 U—Substitution換元法、 8.4 Integ ration by Parts分部積分 8.5 The Method of Partial Fractions分式拆分求積分 【Practice Problems·課后練習(xí)】Chapter 9 The Definite Integral定積分 9.1 A Limit of Riemann Sum（Left，Right and Midpoint）黎曼和的極限 9.2 The Fi rst Fundamental Theorem of Calculus微積分第一基礎(chǔ)理論 9.3 The Second Fundamental Theorem of Calculus微積分第二基礎(chǔ)理論 9.4 Improper Integrals反常積分（廣義積分） 【Practice Problems·課后練習(xí)】Chapter 10 Applications of Integral積分應(yīng)用 10.1 The Mean Value Theorem for Integ rals積分中值定理 10.2 Area面積 10.3 Volume體積 10.4 Length of a Curve曲線長(zhǎng)度 【Practice Problems·課后練習(xí)】Chapter 11 Differential Equations微分方程 11.1 Separation Variables可分離變量的微分方程 11.2 Logistic Differential Equation邏輯斯蒂微分方程 11.3 Slope Fields（Direction Fields）斜率場(chǎng) 【Practice Problems·課后練習(xí)】Chapter 1 2 Infinite Series無(wú)窮級(jí)數(shù) 12.1 ORe Definition for Infinite Series一個(gè)定義 12.2 Two Limits兩個(gè)極限 12.3 Three Tests of Series三大審斂法 12.4 Four Important Series四種重要級(jí)數(shù) 12.5 Five Formulas of Power Series and Taylor Series五個(gè)重要公式 【Practice Problems·課后練習(xí)】Answers
Chapter 1 Introduction of AP Calculus Exam AP微積分考試介紹Chapter 2 Functions函數(shù) 2.1 Five Basic Elementary Functions五種基本初等函數(shù) 2.2 Inverse Functions反函數(shù) 2.3 Composite Functions復(fù)合函數(shù) 2.4 Parametric Functions參變量函數(shù) 2.5 Polar Functions極坐標(biāo)函數(shù) 2.6 Vector Functions向量函數(shù) 2.7 Transforming of Functions函數(shù)變換 【Practice Problems·課后練習(xí)】Chapter 3 Limit and Continuity極限與連續(xù) 3.1 Definition of a Limit極限的定義 3.2 Limit Laws極限（存在）定理 3.3 Rules of Limits極限的運(yùn)算法則 3.4 Two Important Limits兩個(gè)重要極限 3.5 Application of Limits：Finding Asymptotes極限的應(yīng)用：找漸近線 3.6 Continuity連續(xù) 【Practice Problems·課后練習(xí)】Chapter 4 Definition of Derivative導(dǎo)數(shù)定義 4.1 Definition of Derivative導(dǎo)數(shù)的定義 4-2 ORe—Sided Derivative單側(cè)導(dǎo)數(shù) 4.3 The Geometric Interpretation of Derivative導(dǎo)數(shù)的幾何意義 4.4 The Relation Between Differentiability and Continuity可導(dǎo)與連續(xù)的關(guān)系 【Practice Problems·課后練習(xí)】Chapter 5 Rules for Finding Derivatives求導(dǎo)法則 5.1 Basic Rules for Finding Derivatives導(dǎo)數(shù)基本運(yùn)算 5.2 High Order Derivatives高階導(dǎo)數(shù) 5.3 Implicit Differentiation“隱函數(shù)”求導(dǎo) 5.4 The Derivative of an Inverse Function反函數(shù)求導(dǎo) 5.5 Derivatives of Parametric Functions參數(shù)方程求導(dǎo) 5.6 Derivatives of Polar Functions極坐標(biāo)函數(shù)求導(dǎo) 5.7 Derivatives of Vector Functions向量函數(shù)求導(dǎo) 【Practice Problems·課后練習(xí)】Chapter 6 Applications of Derivatives導(dǎo)數(shù)應(yīng)用 6.1 Equations of Tangent Lines and Normal Lines切線和法線方程 6.2 The Mean Value Theorem for Derivatives微分中值定理 6.3 Related Rates相關(guān)變化率 6.4 Motion運(yùn)動(dòng)學(xué) 6.5 Maxima and Minima最大值和最小值 6.6 L’Hopital’S Rule洛比達(dá)法則 【Practice Problems·課后練習(xí)】Chapter 7 Differentials微分 7.1 Defi n ition of Differential微分定義 7.2 Linear Approximation線性估算 7 3 Euler’S Method歐拉法則 【Practice Problems·課后練習(xí)】Chapter 8 The Indefinite Integral不定積分 8.1 The Antiderivative原函數(shù) 812 Integration Formulas積分公式 8.3 U—Substitution換元法、 8.4 Integ ration by Parts分部積分 8.5 The Method of Partial Fractions分式拆分求積分 【Practice Problems·課后練習(xí)】Chapter 9 The Definite Integral定積分 9.1 A Limit of Riemann Sum（Left，Right and Midpoint）黎曼和的極限 9.2 The Fi rst Fundamental Theorem of Calculus微積分第一基礎(chǔ)理論 9.3 The Second Fundamental Theorem of Calculus微積分第二基礎(chǔ)理論 9.4 Improper Integrals反常積分（廣義積分） 【Practice Problems·課后練習(xí)】Chapter 10 Applications of Integral積分應(yīng)用 10.1 The Mean Value Theorem for Integ rals積分中值定理 10.2 Area面積 10.3 Volume體積 10.4 Length of a Curve曲線長(zhǎng)度 【Practice Problems·課后練習(xí)】Chapter 11 Differential Equations微分方程 11.1 Separation Variables可分離變量的微分方程 11.2 Logistic Differential Equation邏輯斯蒂微分方程 11.3 Slope Fields（Direction Fields）斜率場(chǎng) 【Practice Problems·課后練習(xí)】Chapter 1 2 Infinite Series無(wú)窮級(jí)數(shù) 12.1 ORe Definition for Infinite Series一個(gè)定義 12.2 Two Limits兩個(gè)極限 12.3 Three Tests of Series三大審斂法 12.4 Four Important Series四種重要級(jí)數(shù) 12.5 Five Formulas of Power Series and Taylor Series五個(gè)重要公式 【Practice Problems·課后練習(xí)】Answers
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