微积分视频课程
- 极限与连续(limits and continuity)
- 极限的直观定义 intuitive definition of limits
- 极限的运算法则与初等方法 limits laws and elementary methods for finding limits
- 三明治定理及三角函数相关的极限 sandwich theorem and a limit related to trigonometric functions
- 函数在无穷远处的极限 limits at infinity
- 极限的严格定义 formal precise definition of limits
- 连续性与间断点 continuity and discontinuous points
- 连续函数的性质与介值定理 properties of continuous functions and intermediate value theorem
- 导数与求导法则(Derivative and Differential Rules)
- 导数的定义 definition of derivative
- 基本初等函数的导数 basic formula of derivative
- 导数的四则运算 rules of derivative
- 复合函数求导的链式法则 chain rule
- 隐函数求导法则 implicit differentiation
- 对数求导法 logarithm differentiation
- 反函数求导法 derivatives of inverse functions
- 反三角函数的导数 derivatives of inverse trigonometric functions
- 参数曲线 parametric curves
- 参数方程确定的函数的导数 derivative of functions defined by parametric equations
- 高阶导数 higher derivatives
- 相关变化率及计算 related rates
- 函数的近似值 linear approximation
- 函数的微分 differentials
- 导数的应用(Applications of Derivative)
微积分复习与总结
- 极限求法(一):极限的运算法则与初等方法 limits laws and elementary methods
- 极限求法(二):l’Hospital 法则 l’Hospital’s Rule
- 函数的连续性与间断点 continuity and discontinuous points
- 连续函数的性质 properties of continuous functions
- 导数的定义与切线方程 derivative and tangent line
- 基本求导公式与求导法则 formula and rules of derivatives
- 链式法则 chain rule
- 隐函数与对数求导法 implicit and logarithm differential
- 相关变化率 related rates
- 函数的微分与线性近似 differential and linear approximation
- 函数的增减、凹凸、极值与拐点 monotonicity, concavity, extrema and inflection points
- 函数作图 curve sketching
- 最大最小值与最优化问题 global maximum, minimum and optimization