| 知识点 – 中文 | 知识点 – 英文 | 知识点分类 | 知识点分类 – 英文 |
| 极限运算规则 | Limit | 极限 | Limit |
| 渐近线的求法 | Asymptote | 极限 | Limit |
| 两个基本极限和变形公式 | Two Basic Limits | 极限 | Limit |
| 洛必达法则 | L’Hopital’s Rule | 极限 | Limit |
| 间断点 | Discontinuity | 极限 | Limit |
| 导数定义和标记符号 | Derivative | 导数 | Derivative |
| 连续与可导 | Continuity and Differentiability | 导数 | Derivative |
| 导数近似 | Estimating Derivative | 导数 | Derivative |
| 导数基本法则 | Derivative Rules | 导数 | Derivative |
| 常见导数求导公式 | Common Derivatives | 导数 | Derivative |
| 链式法则 | Chain Rule of Derivatives | 导数 | Derivative |
| 隐函数求导 | Implicit Derivatives | 导数 | Derivative |
| 参数方程求导 | Parametric Derivatives | 导数 | Derivative |
| 极函数求导 | Polar Functions Derivatives | 导数 | Derivative |
| 反函数求导 | Inverse Function Derivatives | 导数 | Derivative |
| 微分中值定理 | Mean Value Theorem | 导数 | Derivative |
| 导数与切线 | Tangent Lines | 导数应用 | Derivative Application |
| 导数与法线 | Normal Lines | 导数应用 | Derivative Application |
| 导数与函数单调性 | Derivative and Monotonicity | 导数应用 | Derivative Application |
| 导数与极值和最值 | Local and Relative Max/Min | 导数应用 | Derivative Application |
| 导数与函数凹凸性 | Convexity and Concavity | 导数应用 | Derivative Application |
| 导数与拐点 | Derivative and Inflection Points | 导数应用 | Derivative Application |
| 导数与变化率 | Derivative and Change Rate | 导数应用 | Derivative Application |
| 导数与运动学 | Kinematics | 导数应用 | Derivative Application |
| 微分的应用 | Application of Differentiability | 导数应用 | Derivative Application |
| 积分的定于和符号 | Antiderivatives | 不定积分 | Indefinite Integral |
| 积分运算法则 | Antidifferentiation | 不定积分 | Indefinite Integral |
| 常见函数积分公式 | Common Integration Formula | 不定积分 | Indefinite Integral |
| 换元积分 | Integration by Substitution | 不定积分 | Indefinite Integral |
| 部分分数积分 | Integration by Partial Fractions | 不定积分 | Indefinite Integral |
| 分步积分法 | Integration by Parts | 不定积分 | Indefinite Integral |
| 定积分的定义 | What is Definite Integrals | 定积分 | Definite Integral |
| 定积分的性质 | How Definite Integrals Work | 定积分 | Definite Integral |
| 定积分的几何意义 | Geometrical View of Definite Integrals | 定积分 | Definite Integral |
| 微积分第一基本定理 | Fundamental Calculus Theorem I | 定积分 | Definite Integral |
| 微积分第二基本定理 | Fundamental Calculus Theorem II | 定积分 | Definite Integral |
| 黎曼求和 | Ricmann Sum | 定积分 | Definite Integral |
| 均值公式 | Average Value | 定积分 | Definite Integral |
| 第一反常积分 | Improper Integrals I | 定积分 | Definite Integral |
| 第二反常积分 | Improper Integrals II | 定积分 | Definite Integral |
| 求单曲线下面积 | One Curve Area | 定积分应用 | Definite Integral Application |
| 参数方程曲线面积 | Parametric Function Area | 定积分应用 | Definite Integral Application |
| 极坐标曲线面积 | Polar Function Area | 定积分应用 | Definite Integral Application |
| 两个曲线夹面积 | Area between Two Curves | 定积分应用 | Definite Integral Application |
| Washer体积模型 | Washer Volume Formula | 定积分应用 | Definite Integral Application |
| Shell体积模型 | Shell Volume Formula | 定积分应用 | Definite Integral Application |
| 交叉体积模型 | Cross Section Volume Formula | 定积分应用 | Definite Integral Application |
| 弧长公式 | Arc Length Formula | 定积分应用 | Definite Integral Application |
| 分离变量 | Separating Variables for DE | 微分方程 | Differential Equations |
| 斜率场 | Slope Fields | 微分方程 | Differential Equations |
| 欧拉法 | Euler’s Method | 微分方程 | Differential Equations |
| 指数模型 | Exponential DE Model | 微分方程 | Differential Equations |
| 限制模型 | Restricted DE Model | 微分方程 | Differential Equations |
| 逻辑模型 | Logistic DE Model | 微分方程 | Differential Equations |
| 级数的定义 | What is Series | 级数 | Series |
| 级数的种类 | Types of Series | 级数 | Series |
| 级数的收敛与发散 | Converge and Diverge of Series | 级数 | Series |
| 收敛级数 | Converge Series | 级数 | Series |
| 级数的审敛 | Series Converge Test | 级数 | Series |
| p级数法 | p-Series Test | 级数 | Series |
| 几何级数法 | Geometry Series Test | 级数 | Series |
| 比值法 | Ratio Test | 级数 | Series |
| 积分法 | Integral Test | 级数 | Series |
| 比较法 | Comparison Test | 级数 | Series |
| 交错级数 | Alternative Series | 级数 | Series |
| 绝对收敛 | Absolute Converge | 级数 | Series |
| 幂级数 | Power Series | 级数 | Series |
| 泰勒级数 | Taylor Series | 级数 | Series |
| 麦克劳林级数 | Maclaurin Series | 级数 | Series |
| 拉格朗日余项 | Lagrange Remainder | 级数 | Series |
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