1.点积-Dot product
2.行列式与叉积-Determinants & Cross Product
3.矩阵与逆矩阵-Matrices & Inverse Matrices
4.方阵系统与平面方程-Square Systems & Equations of Planes
5.直线与曲线的参数方程-Parametric Equations for Lines and Curves
6.速度、加速度与开普勒第二定律-Velocity, Acceleration & Kepler's Second Law
7.第一次复习-Review
8.等高线、偏导数与切平面-Level Curves, Partial Derivatives & Tangent Plane
9.极值问题与最小二乘法-Max-Min Problems & Least Squares
10.二阶导数检验、边界与无穷情况-Second Derivative Test, Boundaries & Infinity
11.微分与链式法则-Differentials & Chain Rule
12.梯度、方向导数与切平面-Gradient, Directional Derivative & Tangent Plane
13.拉格朗日乘数法-Lagrange Multipliers
14.非独立变量-Non-Independent Variables
15.偏微分方程与复习-Partial Differential Equations & Review
16.二重积分-Double Integrals
17.极坐标下的二重积分与应用-Double Integrals in Polar Coords & Applications
18.变量替换-Change of Variables
19.平面向量场与线积分-Vector Fields and Line Integrals in the Plane
20.路径无关性与保守场-Path Independence and Conservative Fields
21.梯度场与势函数-Gradient Fields and Potential Functions
22.格林定理-Green's Theorem
23.通量与格林定理的法向形式-Flux & Normal Form of Green's Theorem
24.单连通区域与复习-Simply Connected Regions & Review
25.直角与柱坐标系下的三重积分-Triple Integrals in Rectangular & Cylindrical Coords
26.球坐标系与表面积-Spherical Coordinates & Surface Area
27.三维向量场、曲面积分与通量-Vector Fields in 3D, Surface Integrals & Flux
28.散度定理-Divergence Theorem
29.散度定理（续）：应用与证明-Divergence Theorem (cont.) Applications & Proof
30.空间线积分与恰当性条件-Line Integrals in Space & Curl Exactness
31.斯托克斯定理-Stokes' Theorem
32.斯托克斯定理（续）与复习-Stokes' Theorem (cont.) & Review
33.拓扑学考量与麦克斯韦方程组-Topological Considerations & Maxwell's Equations
34.期末总复习-Final Review
35.期末总复习（续）-Final Review (cont.)