College Board · AP Calculus AB+BC
AP 微积分（AB+BC）资料
Calculus (AB+BC)
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单元与课题
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单元 1 - 极限与连续16 个课题
打开此单元 →- 课题 1.1 微积分导论：变化能发生在瞬间吗？Topic 1.1 Introducing Calculus: Can Change Occur at an Instant?查看资料
- 课题 1.2 极限的定义与符号Topic 1.2 Defining Limits and Using Limit Notation查看资料
- 课题 1.3 根据图像估计极限值Topic 1.3 Estimating Limit Values from Graphs查看资料
- 课题 1.4 根据表格估计极限值Topic 1.4 Estimating Limit Values from Tables查看资料
- 课题 1.5 用极限的代数性质求极限Topic 1.5 Determining Limits Using Algebraic Properties of Limits查看资料
- 课题 1.6 通过代数变形求极限Topic 1.6 Determining Limits Using Algebraic Manipulation查看资料
- 课题 1.7 选择求极限的方法Topic 1.7 Selecting Procedures for Determining Limits查看资料
- 课题 1.8 用夹逼定理求极限Topic 1.8 Determining Limits Using the Squeeze Theorem查看资料
- 课题 1.9 极限的多种表示之间的联系Topic 1.9 Connecting Multiple Representations of Limits查看资料
- 课题 1.10 探究间断点的类型Topic 1.10 Exploring Types of Discontinuities查看资料
- 课题 1.11 函数在一点处连续的定义Topic 1.11 Defining Continuity at a Point查看资料
- 课题 1.12 验证函数在区间上的连续性Topic 1.12 Confirming Continuity over an Interval查看资料
- 课题 1.13 消除间断点Topic 1.13 Removing Discontinuities查看资料
- 课题 1.14 无穷极限与垂直渐近线的联系Topic 1.14 Connecting Infinite Limits and Vertical Asymptotes查看资料
- 课题 1.15 无穷远处的极限与水平渐近线的联系Topic 1.15 Connecting Limits at Infinity and Horizontal Asymptotes查看资料
- 课题 1.16 应用介值定理（IVT）Topic 1.16 Working with the Intermediate Value Theorem (IVT)查看资料
单元 2 - 微分：定义与基本性质10 个课题
打开此单元 →- 课题 2.1 平均变化率与一点处瞬时变化率的定义Topic 2.1 Defining Average and Instantaneous Rates of Change at a Point查看资料
- 课题 2.2 函数导数的定义与符号Topic 2.2 Defining the Derivative of a Function and Using Derivative Notation查看资料
- 课题 2.3 估计函数在一点处的导数Topic 2.3 Estimating Derivatives of a Function at a Point查看资料
- 课题 2.4 可导性与连续性：判断导数是否存在Topic 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist查看资料
- 课题 2.5 应用幂函数求导法则Topic 2.5 Applying the Power Rule查看资料
- 课题 2.6 求导法则：常数、和、差与常数倍Topic 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple查看资料
- 课题 2.7 cos x、sin x、e^x与ln x的导数Topic 2.7 Derivatives of cos x, sin x, e^x, and ln x查看资料
- 课题 2.8 乘积求导法则Topic 2.8 The Product Rule查看资料
- 课题 2.9 商求导法则Topic 2.9 The Quotient Rule查看资料
- 课题 2.10 正切、余切、正割和／或余割函数的求导Topic 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions查看资料
单元 3 - 微分：复合、隐式与反函数6 个课题
打开此单元 →- 课题 3.1 链式法则Topic 3.1 The Chain Rule查看资料
- 课题 3.2 隐函数求导Topic 3.2 Implicit Differentiation查看资料
- 课题 3.3 反函数求导Topic 3.3 Differentiating Inverse Functions查看资料
- 课题 3.4 反三角函数求导Topic 3.4 Differentiating Inverse Trigonometric Functions查看资料
- 课题 3.5 选择计算导数的方法Topic 3.5 Selecting Procedures for Calculating Derivatives查看资料
- 课题 3.6 计算高阶导数Topic 3.6 Calculating Higher-Order Derivatives查看资料
单元 4 - 微分的实际应用7 个课题
打开此单元 →- 课题 4.1 结合实际情境解读导数的意义Topic 4.1 Interpreting the Meaning of the Derivative in Context查看资料
- 课题 4.2 直线运动：位置、速度与加速度的联系Topic 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration查看资料
- 课题 4.3 运动以外实际情境中的变化率Topic 4.3 Rates of Change in Applied Contexts Other Than Motion查看资料
- 课题 4.4 相关变化率入门Topic 4.4 Introduction to Related Rates查看资料
- 课题 4.5 求解相关变化率问题Topic 4.5 Solving Related Rates Problems查看资料
- 课题 4.6 用局部线性与线性化近似函数值Topic 4.6 Approximating Values of a Function Using Local Linearity and Linearization查看资料
- 课题 4.7 用洛必达法则求未定式的极限Topic 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms查看资料
单元 5 - 微分的分析应用12 个课题
打开此单元 →- 课题 5.1 应用微分中值定理Topic 5.1 Using the Mean Value Theorem查看资料
- 课题 5.2 最值定理、全局与局部极值及临界点Topic 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points查看资料
- 课题 5.3 确定函数的递增与递减区间Topic 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing查看资料
- 课题 5.4 用一阶导数判别法确定相对（局部）极值Topic 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema查看资料
- 课题 5.5 用候选点检验法确定绝对（全局）极值Topic 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema查看资料
- 课题 5.6 确定函数在定义域上的凹凸性Topic 5.6 Determining Concavity of Functions over Their Domains查看资料
- 课题 5.7 用二阶导数判别法确定极值Topic 5.7 Using the Second Derivative Test to Determine Extrema查看资料
- 课题 5.8 绘制函数及其导函数的图像Topic 5.8 Sketching Graphs of Functions and Their Derivatives查看资料
- 课题 5.9 函数、一阶导数与二阶导数的联系Topic 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative查看资料
- 课题 5.10 最优化问题入门Topic 5.10 Introduction to Optimization Problems查看资料
- 课题 5.11 求解最优化问题Topic 5.11 Solving Optimization Problems查看资料
- 课题 5.12 探究隐式关系的性质Topic 5.12 Exploring Behaviors of Implicit Relations查看资料
单元 6 - 积分与变化的累积14 个课题
打开此单元 →- 课题 6.1 探究变化量的累积Topic 6.1 Exploring Accumulations of Change查看资料
- 课题 6.2 用黎曼和近似面积Topic 6.2 Approximating Areas with Riemann Sums查看资料
- 课题 6.3 黎曼和、求和符号与定积分符号Topic 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation查看资料
- 课题 6.4 微积分基本定理与累积函数Topic 6.4 The Fundamental Theorem of Calculus and Accumulation Functions查看资料
- 课题 6.5 解读与面积有关的累积函数的性质Topic 6.5 Interpreting the Behavior of Accumulation Functions Involving Area查看资料
- 课题 6.6 应用定积分的性质Topic 6.6 Applying Properties of Definite Integrals查看资料
- 课题 6.7 微积分基本定理与定积分Topic 6.7 The Fundamental Theorem of Calculus and Definite Integrals查看资料
- 课题 6.8 求原函数与不定积分：基本法则与符号Topic 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation查看资料
- 课题 6.9 换元积分法Topic 6.9 Integrating Using Substitution查看资料
- 课题 6.10 用多项式长除法与配方法积分Topic 6.10 Integrating Functions Using Long Division and Completing the Square查看资料
- 课题 6.11 分部积分法（仅BC）Topic 6.11 Integrating Using Integration by Parts (BC only)查看资料
- 课题 6.12 使用线性部分分式（仅BC）Topic 6.12 Using Linear Partial Fractions (BC only)查看资料
- 课题 6.13 计算反常积分（仅BC）Topic 6.13 Evaluating Improper Integrals (BC only)查看资料
- 课题 6.14 选择求原函数的方法Topic 6.14 Selecting Techniques for Antidifferentiation查看资料
单元 7 - 微分方程9 个课题
打开此单元 →- 课题 7.1 用微分方程建立情境模型Topic 7.1 Modeling Situations with Differential Equations查看资料
- 课题 7.2 验证微分方程的解Topic 7.2 Verifying Solutions for Differential Equations查看资料
- 课题 7.3 绘制斜率场Topic 7.3 Sketching Slope Fields查看资料
- 课题 7.4 利用斜率场推理Topic 7.4 Reasoning Using Slope Fields查看资料
- 课题 7.5 用欧拉法近似求解（仅BC）Topic 7.5 Approximating Solutions Using Euler's Method (BC only)查看资料
- 课题 7.6 用分离变量法求通解Topic 7.6 Finding General Solutions Using Separation of Variables查看资料
- 课题 7.7 用初始条件与分离变量法求特解Topic 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables查看资料
- 课题 7.8 微分方程的指数模型Topic 7.8 Exponential Models with Differential Equations查看资料
- 课题 7.9 微分方程的逻辑斯蒂模型（仅BC）Topic 7.9 Logistic Models with Differential Equations (BC only)查看资料
单元 8 - 积分的应用13 个课题
打开此单元 →- 课题 8.1 求函数在区间上的平均值Topic 8.1 Finding the Average Value of a Function on an Interval查看资料
- 课题 8.2 用积分联系位置、速度与加速度函数Topic 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals查看资料
- 课题 8.3 在实际情境中应用累积函数与定积分Topic 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts查看资料
- 课题 8.4 求以x为自变量的曲线之间的面积Topic 8.4 Finding the Area Between Curves Expressed as Functions of x查看资料
- 课题 8.5 求以y为自变量的曲线之间的面积Topic 8.5 Finding the Area Between Curves Expressed as Functions of y查看资料
- 课题 8.6 求有两个以上交点的曲线之间的面积Topic 8.6 Finding the Area Between Curves That Intersect at More Than Two Points查看资料
- 课题 8.7 由横截面求体积：正方形与长方形Topic 8.7 Volumes with Cross Sections: Squares and Rectangles查看资料
- 课题 8.8 由横截面求体积：三角形与半圆Topic 8.8 Volumes with Cross Sections: Triangles and Semicircles查看资料
- 课题 8.9 圆盘法求体积：绕x轴或y轴旋转Topic 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis查看资料
- 课题 8.10 圆盘法求体积：绕其他轴旋转Topic 8.10 Volume with Disc Method: Revolving Around Other Axes查看资料
- 课题 8.11 圆环法求体积：绕x轴或y轴旋转Topic 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis查看资料
- 课题 8.12 圆环法求体积：绕其他轴旋转Topic 8.12 Volume with Washer Method: Revolving Around Other Axes查看资料
- 课题 8.13 光滑平面曲线的弧长与运动路程（仅BC）Topic 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC only)查看资料
单元 9 - 参数方程、极坐标与向量值函数（仅 BC）9 个课题
打开此单元 →- 课题 9.1 参数方程的定义与求导Topic 9.1 Defining and Differentiating Parametric Equations查看资料
- 课题 9.2 参数方程的二阶导数Topic 9.2 Second Derivatives of Parametric Equations查看资料
- 课题 9.3 求参数方程曲线的弧长Topic 9.3 Finding Arc Lengths of Curves Given by Parametric Equations查看资料
- 课题 9.4 向量值函数的定义与求导Topic 9.4 Defining and Differentiating Vector-Valued Functions查看资料
- 课题 9.5 向量值函数的积分Topic 9.5 Integrating Vector-Valued Functions查看资料
- 课题 9.6 用参数函数与向量值函数求解运动问题Topic 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions查看资料
- 课题 9.7 极坐标的定义与极坐标形式的求导Topic 9.7 Defining Polar Coordinates and Differentiating in Polar Form查看资料
- 课题 9.8 求极坐标区域或单条极坐标曲线围成区域的面积Topic 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve查看资料
- 课题 9.9 求两条极坐标曲线围成区域的面积Topic 9.9 Finding the Area of the Region Bounded by Two Polar Curves查看资料
单元 10 - 无穷数列与级数（仅 BC）15 个课题
打开此单元 →- 课题 10.1 收敛与发散无穷级数的定义Topic 10.1 Defining Convergent and Divergent Infinite Series查看资料
- 课题 10.2 应用几何级数Topic 10.2 Working with Geometric Series查看资料
- 课题 10.3 第n项发散判别法Topic 10.3 The nth Term Test for Divergence查看资料
- 课题 10.4 积分收敛判别法Topic 10.4 Integral Test for Convergence查看资料
- 课题 10.5 调和级数与p级数Topic 10.5 Harmonic Series and p-Series查看资料
- 课题 10.6 比较收敛判别法Topic 10.6 Comparison Tests for Convergence查看资料
- 课题 10.7 交错级数收敛判别法Topic 10.7 Alternating Series Test for Convergence查看资料
- 课题 10.8 比值收敛判别法Topic 10.8 Ratio Test for Convergence查看资料
- 课题 10.9 判断绝对收敛或条件收敛Topic 10.9 Determining Absolute or Conditional Convergence查看资料
- 课题 10.10 交错级数的误差界Topic 10.10 Alternating Series Error Bound查看资料
- 课题 10.11 用泰勒多项式近似函数Topic 10.11 Finding Taylor Polynomial Approximations of Functions查看资料
- 课题 10.12 拉格朗日误差界Topic 10.12 Lagrange Error Bound查看资料
- 课题 10.13 幂级数的收敛半径与收敛区间Topic 10.13 Radius and Interval of Convergence of Power Series查看资料
- 课题 10.14 求函数的泰勒级数或麦克劳林级数Topic 10.14 Finding Taylor or Maclaurin Series for a Function查看资料
- 课题 10.15 用幂级数表示函数Topic 10.15 Representing Functions as Power Series查看资料
教学课件
此课程已有 111 份 PPTX 文件上架。以下列出部分入口；完整课件和预览请打开对应课题。