Goals and objectives  Course Outcomes  

1.  The students can use dot product and cross product of vectors to express lines and planes. 
A1

2.  The students can compute partial derivatives of various functions using the chain rule and use them to describe tangent lines and to compute maximum and minimum values of a given function. 
A1

3.  The students can compute double & triple integrals of various functions and use them to compute the volume of solids. 
A1

4.  The students can compute line & surface integrals of simple functions and use them to understand Green's Theorem, Stokes' Theorem, and Divergence Theorem. 
A1

5.  The students can solve simple secondorder linear equations in both homogeneous & nonhomogeneous cases. 
A1

Class schedule  HW assignments (Including preparation and review of the class.)  Amount of Time Required  

1.  2d and 3d Cartesian Coordinates Polar Coordinates Vectors Dot Product 
Read 10.3, 12.112.3  160分 
Work on exercises  220分  
2.  Dot Product (continued) Cross Product Equations of Lines and Planes 
Read 12.312.5  120分 
Work on exercises  260分  
3.  Parametric Equations and Vector Functions Derivatives and Integrals of Vector Functions Velocity and Acceleration 
Read 10.1,13.1, 13.2, 13.4  120分 
Work on exercises  260分  
4.  Functions of Several Variables Limits and Continuity Partial Derivatives 
Read 14.114.3  140分 
Work on exercises  240分  
5.  Tangent Planes and Linear Approximations The Chain Rule Directional Derivatives and the Gradient Vector 
Read 14.414.6  140分 
Work on exercises  240分  
6.  Maximum and Minimum Values Lagrange Multipliers 
Read 14.714.8  120分 
Work on exercises  260分  
7.  Midterm exam and discussions on the solutions afterwards  Preparation for midterm  380分 
8.  Double Integrals Double Integrals in Polar Coordinates Applications of Double Integrals 
Read 15.115.4  180分 
Work on exercises  200分  
9.  Triple Integrals Triple Integrals in Cylindrical and Spherical Coordinates 
Read 15.615.8  120分 
Work on exercises  260分  
10.  Vector Fields Line Integrals The fundamental Theorem of Line Integrals Green’s Theorem 
Read 16.116.4  160分 
Work on exercises  220分  
11.  Curl and Divergence Parametric Surfaces Surface Areas and Surface Integrals 
Read 16.516.7  160分 
Work on exercises  220分  
12.  Stokes’ Theorem Divergence Theorem 
Read 16.816.9  140分 
Work on exercises  220分  
13.  SecondOrder Linear Equations Nonhomogeneous Linear Equations 
Read 17.117.2  120分 
Work on exercises  260分  
14.  Final exam and discussions on the solutions afterwards  Preparation for final  380分 
Total.      5300分 
Midterm etc.  Final  Total.  

1.  10%  5%  15% 
2.  20%  10%  30% 
3.  5%  20%  25% 
4.  5%  20%  25% 
5.  0%  5%  5% 
Total.  40%  60%   
Work experience  Work experience and relevance to the course content if applicable 

N/A  N/A 