AP Calculus BC · ⁨AP 微积分 BC⁩

1.1 Introducing Calculus: Can Change Occur at an Instant? · ⁨微积分引入：变化能在某一瞬间发生吗？⁩ 1.2 Defining Limits and Using Limit Notation · ⁨定义极限与使用极限记号⁩ 1.3 Estimating Limit Values from Graphs · ⁨从图像估计极限值⁩ 1.4 Estimating Limit Values from Tables · ⁨从表格估计极限值⁩ 1.5 Determining Limits Using Algebraic Properties of Limits · ⁨利用极限的代数性质求极限⁩ 1.6 Determining Limits Using Algebraic Manipulation · ⁨利用代数变形求极限⁩ 1.7 Selecting Procedures for Determining Limits · ⁨选择求极限的方法⁩ 1.8 Determining Limits Using the Squeeze Theorem · ⁨利用夹逼定理求极限⁩ 1.9 Connecting Multiple Representations of Limits · ⁨联系极限的多种表示⁩ 1.10 Exploring Types of Discontinuities · ⁨探究间断点的类型⁩ 1.11 Defining Continuity at a Point · ⁨定义在某点的连续性⁩ 1.12 Confirming Continuity over an Interval · ⁨确认区间上的连续性⁩ 1.13 Removing Discontinuities · ⁨消除间断点⁩ 1.14 Connecting Infinite Limits and Vertical Asymptotes · ⁨联系无穷极限与竖直渐近线⁩ 1.15 Connecting Limits at Infinity and Horizontal Asymptotes · ⁨联系无穷远处的极限与水平渐近线⁩ 1.16 Working with the Intermediate Value Theorem (IVT) · ⁨运用介值定理（IVT）⁩

2.1 Defining Average and Instantaneous Rates of Change at a Point · ⁨定义某点的平均变化率与瞬时变化率⁩ 2.2 Defining the Derivative of a Function and Using Derivative Notation · ⁨定义函数的导数与使用导数记号⁩ 2.3 Estimating Derivatives of a Function at a Point · ⁨估计函数在某点的导数⁩ 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist · ⁨联系可微性与连续性：判断导数何时存在与不存在⁩ 2.5 Applying the Power Rule · ⁨应用幂法则⁩ 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple · ⁨导数法则：常数、和、差与常数倍⁩ 2.7 Derivatives of cos x, sin x, e^x, and ln x · ⁨cos x、sin x、e^x 与 ln x 的导数⁩ 2.8 The Product Rule · ⁨乘积法则⁩ 2.9 The Quotient Rule · ⁨商法则⁩ 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions · ⁨求正切、余切、正割与余割函数的导数⁩

3.1 The Chain Rule · ⁨链式法则⁩ 3.2 Implicit Differentiation · ⁨隐函数求导⁩ 3.3 Differentiating Inverse Functions · ⁨反函数求导⁩ 3.4 Differentiating Inverse Trigonometric Functions · ⁨反三角函数求导⁩ 3.5 Selecting Procedures for Calculating Derivatives · ⁨选择求导数的方法⁩ 3.6 Calculating Higher-Order Derivatives · ⁨计算高阶导数⁩

4.1 Interpreting the Meaning of the Derivative in Context · ⁨在实际情境中解释导数的意义⁩ 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration · ⁨直线运动：联系位置、速度与加速度⁩ 4.3 Rates of Change in Applied Contexts Other Than Motion · ⁨除运动之外的实际情境中的变化率⁩ 4.4 Introduction to Related Rates · ⁨相关变化率引入⁩ 4.5 Solving Related Rates Problems · ⁨求解相关变化率问题⁩ 4.6 Approximating Values of a Function Using Local Linearity and Linearization · ⁨利用局部线性性与线性化近似函数值⁩ 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms · ⁨利用洛必达法则求不定型极限⁩

5.1 Using the Mean Value Theorem · ⁨运用中值定理⁩ 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points · ⁨极值定理、整体极值与局部极值以及临界点⁩ 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing · ⁨确定函数递增或递减的区间⁩ 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema · ⁨用一阶导数判别法确定相对（局部）极值⁩ 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema · ⁨用候选点判别法确定绝对（整体）极值⁩ 5.6 Determining Concavity of Functions over Their Domains · ⁨确定函数在其定义域上的凹凸性⁩ 5.7 Using the Second Derivative Test to Determine Extrema · ⁨用二阶导数判别法确定极值⁩ 5.8 Sketching Graphs of Functions and Their Derivatives · ⁨绘制函数及其导数的图像⁩ 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative · ⁨联系函数、一阶导数与二阶导数⁩ 5.10 Introduction to Optimization Problems · ⁨最优化问题引入⁩ 5.11 Solving Optimization Problems · ⁨求解最优化问题⁩ 5.12 Exploring Behaviors of Implicit Relations · ⁨探究隐式关系的性态⁩

6.1 Exploring Accumulations of Change · ⁨探究变化的累积⁩ 6.2 Approximating Areas with Riemann Sums · ⁨用黎曼和近似面积⁩ 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation · ⁨黎曼和、求和记号与定积分记号⁩ 6.4 The Fundamental Theorem of Calculus and Accumulation Functions · ⁨微积分基本定理与累积函数⁩ 6.5 Interpreting the Behavior of Accumulation Functions Involving Area · ⁨解释涉及面积的累积函数的性态⁩ 6.6 Applying Properties of Definite Integrals · ⁨应用定积分的性质⁩ 6.7 The Fundamental Theorem of Calculus and Definite Integrals · ⁨微积分基本定理与定积分⁩ 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation · ⁨求原函数与不定积分：基本法则与记号⁩ 6.9 Integrating Using Substitution · ⁨用换元法积分⁩ 6.10 Integrating Functions Using Long Division and Completing the Square · ⁨用长除法与配方法积分⁩ 6.11 Integrating Using Integration by Parts · ⁨用分部积分法积分⁩ 6.12 Integrating Using Linear Partial Fractions · ⁨用线性部分分式积分⁩ 6.13 Evaluating Improper Integrals · ⁨计算反常积分⁩ 6.14 Selecting Techniques for Antidifferentiation · ⁨选择求原函数的方法⁩

7.1 Modeling Situations with Differential Equations · ⁨用微分方程为情境建模⁩ 7.2 Verifying Solutions for Differential Equations · ⁨验证微分方程的解⁩ 7.3 Sketching Slope Fields · ⁨绘制斜率场⁩ 7.4 Reasoning Using Slope Fields · ⁨利用斜率场进行推理⁩ 7.5 Approximating Solutions Using Euler's Method · ⁨用欧拉法近似求解⁩ 7.6 Finding General Solutions Using Separation of Variables · ⁨用分离变量法求通解⁩ 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables · ⁨用初始条件与分离变量法求特解⁩ 7.8 Exponential Models with Differential Equations · ⁨微分方程的指数模型⁩ 7.9 Logistic Models with Differential Equations · ⁨微分方程的逻辑斯谛模型⁩

8.1 Finding the Average Value of a Function on an Interval · ⁨求函数在区间上的平均值⁩ 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals · ⁨用积分联系函数的位置、速度与加速度⁩ 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts · ⁨在实际情境中运用累积函数与定积分⁩ 8.4 Finding the Area Between Curves Expressed as Functions of x · ⁨求以 x 为自变量表示的曲线之间的面积⁩ 8.5 Finding the Area Between Curves Expressed as Functions of y · ⁨求以 y 为自变量表示的曲线之间的面积⁩ 8.6 Finding the Area Between Curves That Intersect at More Than Two Points · ⁨求相交多于两点的曲线之间的面积⁩ 8.7 Volumes with Cross Sections: Squares and Rectangles · ⁨用横截面求体积：正方形与矩形⁩ 8.8 Volumes with Cross Sections: Triangles and Semicircles · ⁨用横截面求体积：三角形与半圆⁩ 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis · ⁨圆盘法求体积：绕 x 轴或 y 轴旋转⁩ 8.10 Volume with Disc Method: Revolving Around Other Axes · ⁨圆盘法求体积：绕其他轴旋转⁩ 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis · ⁨垫圈法求体积：绕 x 轴或 y 轴旋转⁩ 8.12 Volume with Washer Method: Revolving Around Other Axes · ⁨垫圈法求体积：绕其他轴旋转⁩ 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled · ⁨光滑平面曲线的弧长与所经过的距离⁩

9.1 Defining and Differentiating Parametric Equations · ⁨定义参数方程与其求导⁩ 9.2 Second Derivatives of Parametric Equations · ⁨参数方程的二阶导数⁩ 9.3 Finding Arc Lengths of Curves Given by Parametric Equations · ⁨求参数方程给定曲线的弧长⁩ 9.4 Defining and Differentiating Vector-Valued Functions · ⁨定义向量值函数与其求导⁩ 9.5 Integrating Vector-Valued Functions · ⁨向量值函数的积分⁩ 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions · ⁨用参数方程与向量值函数求解运动问题⁩ 9.7 Defining Polar Coordinates and Differentiating in Polar Form · ⁨定义极坐标与在极坐标形式下求导⁩ 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve · ⁨求极坐标区域的面积或单条极坐标曲线所围面积⁩ 9.9 Finding the Area of the Region Bounded by Two Polar Curves · ⁨求两条极坐标曲线所围区域的面积⁩

10.1 Defining Convergent and Divergent Infinite Series · ⁨定义收敛与发散的无穷级数⁩ 10.2 Working with Geometric Series · ⁨运用几何级数⁩ 10.3 The nth Term Test for Divergence · ⁨判断发散的第 n 项检验⁩ 10.4 Integral Test for Convergence · ⁨判断收敛的积分检验⁩ 10.5 Harmonic Series and p-Series · ⁨调和级数与 p-级数⁩ 10.6 Comparison Tests for Convergence · ⁨判断收敛的比较检验⁩ 10.7 Alternating Series Test for Convergence · ⁨判断收敛的交错级数检验⁩ 10.8 Ratio Test for Convergence · ⁨判断收敛的比值检验⁩ 10.9 Determining Absolute or Conditional Convergence · ⁨判断绝对收敛或条件收敛⁩ 10.10 Alternating Series Error Bound · ⁨交错级数的误差界⁩ 10.11 Finding Taylor Polynomial Approximations of Functions · ⁨求函数的泰勒多项式近似⁩ 10.12 Lagrange Error Bound · ⁨拉格朗日误差界⁩ 10.13 Radius and Interval of Convergence of Power Series · ⁨幂级数的收敛半径与收敛区间⁩ 10.14 Finding Taylor or Maclaurin Series for a Function · ⁨求函数的泰勒级数或麦克劳林级数⁩ 10.15 Representing Functions as Power Series · ⁨将函数表示为幂级数⁩