Goals and objectives  Course Outcomes  

1.  The students understand the notions of continuity and differentiability of a function and can check if concrete functions are continuous / differentiable or not with clear reasoning. 
A1

2.  The students can compute limits and derivatives of basic functions using the product & quotient rules, and the chain rule. 
A1

3.  The students can use the theory of derivatives to compute maximum and minimum values and to describe the shape of concrete functions. 
A1

4.  The students understand the notions of definite & indefinite integrals as well as the connection between derivatives and integrals, and can compute the integrals of basic functions. 
A1

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

1.  Guidance Trigonometric functions Exponential functions Inverse functions and logarithms 
Review the content of the lecture (Chapter 1 in the textbook)  180分 
Work on homework problems  200分  
2.  The limit of a function Calculating limits 
Review the content of the lecture (2.12.3 in the textbook)  120分 
Work on homework problems  260分  
3.  Continuity Derivatives and rates of changes 
Review the content of the lecture (2.52.7 in the textbook)  120分 
Work on homework problems  260分  
4.  The Derivative as a function Derivatives of polynomials and exponential functions The product and quotient rules 
Review the content of the lecture (2.8, 3.13.2 in the textbook)  120分 
Work on homework problems  260分  
5.  Derivatives of the trigonometric functions The chain rule Implicit differentiation 
Review the content of the lecture (3.33.5 in the textbook)  120分 
Work on homework problems  260分  
6.  Derivatives of logarithmic functions Linear approximation 
Review the content of the lecture (3.63.10 in the textbook)  160分 
Work on homework problems  220分  
7.  Midterm exam and discussion on the solutions afterwards  Preparation for presentations  380分 
8.  Maximum and minimum values The mean value theorem Derivatives and the shape of a graph 
Review the content of the lecture (4.14.3 in the textbook)  120分 
Work on homework problems  260分  
9.  Indeterminate forms and L’Hospital’s rule Summary of curve sketching 
Review the content of the lecture (4.34.5 in the textbook)  120分 
Work on homework problems  260分  
10.  Optimization problems Antiderivatives 
Review the content of the lecture (4.7 and 4.9 in the textbook)  120分 
Work on homework problems  260分  
11.  Areas and distances The definite integral 
Review the content of the lecture (5.15.2 in the textbook)  120分 
Work on homework problems  260分  
12.  The fundamental theorem of calculus  Review the content of the lecture (5.3 in the textbook)  100分 
Work on homework problems  260分  
13.  Indefinite integrals and the net change theorem The substitution rule 
Review the content of the lecture (5.45.5 in the textbook)  120分 
Work on homework problems  260分  
14.  Final exam and discussion on the solutions afterwards  Preparation for presentations  380分 
Total.      5300分 
Homework  Midterm  Final  Total.  

1.  4%  12%  8%  24% 
2.  6%  18%  12%  36% 
3.  7%  0%  16%  23% 
4.  3%  0%  14%  17% 
Total.  20%  30%  50%   
Work experience  Work experience and relevance to the course content if applicable 

N/A  N/A 