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

1.  10%  5%  15% 
2.  20%  15%  35% 
3.  5%  20%  25% 
4.  5%  20%  25% 
Total.  40%  60%   
Work experience  Work experience and relevance to the course content if applicatable 

N/A  N/A 