Goals and objectives  Course Outcomes  

1.  The students can compute integrals of various functions using integration by parts, trigonometric integrals, and trigonometric substitution. 
A1

2.  The students can compute areas between curves, volumes of solids, arc length, and area of a surface of revolution using integration. 
A1

3.  The students can solve basic differential equations such as separable equations and linear equations. 
A1

4.  The students can argue to see whether a given infinite series is convergent or not using integral tests, comparison tests, ratio tests, and root tests. 
A1

5.  The students can use Taylor and Maclaurin series to represent a given function and you can use Taylor polynomials to approxiate a value of a given function. 
A1

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

1.  Review of integration Areas between curves Volumes 
Review the content of the lecture (5.25.5, 6.16.3 in the textbook)  180分 
Work on homework problems  200分  
2.  Integration by parts Trigonometric integrals 
Review the content of the lecture (7.17.2 in the textbook)  120分 
Work on homework problems  260分  
3.  Trigonometric substitution Integration of rational functions 
Review the content of the lecture (7.37.4 in the textbook)  120分 
Work on homework problems  260分  
4.  Strategy for integration Improper integrals 
Review the content of the lecture (7.5, 7.8 in the textbook)  120分 
Work on homework problems  260分  
5.  Arc length Area of a surface of revolution 
Review the content of the lecture (8.18.2 in the textbook)  120分 
Work on homework problems  260分  
6.  Modeling with differential equations Separable equations 
Review the content of the lecture (9.1, 9.3 in the textbook)  120分 
Work on homework problems  260分  
7.  Midterm presentation and discussions on the solutions afterwards  Preparation for the midterm presentation  380分 
8.  Linear equations Secondorder linear equations 
Review the content of the lecture (9.5, 17.1 in the textbook)  120分 
Work on homework problems  260分  
9.  Parametrized curves Polar coordinates, area length in polar coordinates 
Review the content of the lecture (10.110.4 in the textbook)  120分 
Work on homework problems  260分  
10.  Sequences Series and the integral test 
Review the content of the lecture (11.111.3 in the textbook)  120分 
Work on homework problems  260分  
11.  Comparison tests Alternating series, absolute convergence, ratio and root tests 
Review the content of the lecture (11.411.6 in the textbook)  120分 
Work on homework problems  260分  
12.  Strategy for testing series Power series, representations of functions as power series 
Review the content of the lecture (11.711.9 in the textbook)  100分 
Work on homework problems  260分  
13.  Taylor and Maclaurin series Applications of Taylor polynomials 
Review the content of the lecture (11.1011.11 in the textbook)  120分 
Work on homework problems  260分  
14.  Final exam and discussions on the solutions afterwards  Preparation for the final exam  380分 
Total.      5300分 
Homework  Midterm presentation  Final exam  Total.  

1.  20%  4%  5%  29% 
2.  15%  4%  5%  24% 
3.  10%  4%  3%  17% 
4.  10%  3%  10%  23% 
5.  7%  7%  
Total.  55%  15%  30%   
Work experience  Work experience and relevance to the course content if applicable 

N/A  N/A 