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

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

1.  Guidance 3d Coordinates Vectors Dot Product Conic Sections in Polar Coordinates 
Read the lecture notes and work on exercises (Content is 10.6, 12.112.3 in the textbook) 
160分 
Work on homework  220分  
2.  Cross Product Equations of Lines and Planes 
Read the lecture notes and work on exercises (Content is 12.412.5 in the textbook) 
120分 
Work on homework  260分  
3.  Parametric Equations and Vector Functions Derivatives and Integrals of Vector Functions Velocity and Acceleration 
Read the lecture notes and work on exercises (Content is 13.1, 13.2, 13.4 in the textbook) 
120分 
Work on homework  260分  
4.  Functions of Several Variables Limits and Continuity Partial Derivatives 
Read the lecture notes and work on exercises (Content is 14.114.3 in the textbook) 
140分 
Work on homework  240分  
5.  Tangent Planes and Linear Approximations The Chain Rule Directional Derivatives and the Gradient Vector 
Read the lecture notes and work on exercises (Content is 14.414.6 in the textbook) 
140分 
Work on homework  240分  
6.  Maximum and Minimum Values Lagrange Multipliers 
Read the lecture notes and work on exercises (Content is 14.714.8 in the textbook) 
120分 
Work on homework  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 the lecture notes and work on exercises (Content is 15.115.4 in the textbook) 
180分 
Work on homework  200分  
9.  Triple Integrals Triple Integrals in Cylindrical and Spherical Coordinates 
Read the lecture notes and work on exercises (Content is 15.615.8 in the textbook) 
120分 
Work on exercises  260分  
10.  Vector Fields Line Integrals The fundamental Theorem of Line Integrals Green’s Theorem 
Read the lecture notes and work on exercises (Content is 16.116.4 in the textbook) 
160分 
Work on homework  220分  
11.  Curl and Divergence Parametric Surfaces Surface Areas and Surface Integrals 
Read the lecture notes and work on exercises (Content is 16.516.7 in the textbook) 
160分 
Work on homework  220分  
12.  Stokes’ Theorem Divergence Theorem 
Read the lecture notes and work on exercises (Content is 16.816.9 in the textbook) 
140分 
Work on homework  220分  
13.  Reviews  Work on exercises  120分 
Work on homework  260分  
14.  Final exam and discussions on the solutions afterwards  Preparation for final  380分 
Total.      5300分 
Midterm etc.  Final  Total.  

1.  12%  3%  15% 
2.  30%  5%  35% 
3.  20%  10%  30% 
4.  8%  12%  20% 
Total.  70%  30%   
Work experience  Work experience and relevance to the course content if applicable 

N/A  N/A 