Title: 
Calculus II 

Credit: 
404 

Textbook: 
Calculus (Early Transcendental) by James. Stewart, 7^{th} edition, Brooks/Cole, 2012. 

Description: 
Definite and indefinite integrals of functions of a single variable. Fundamental Theorem of Calculus. Techniques of integration. Applications of the definite integral to area, volume, arc length and surface of revolution. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series. 

Learning Outcomes 
Upon completion of this course, students should be able to understand: 1) The concept of definite and indefinite integrals; 
Week 
Date (2016) 
Section 
Topics 
1 
January, 17 21 
5.1 
Areas and Distances 
5.2(1) 
The Definite Integral 

2 
January, 24 28 
5.3 
The Fundamental Theorem of Calculus 
5.4 
Indefinite Integrals and the Net Change Theorem 

3 
Jan, 31 Feb, 04 
5.5 
The Substitution Rule 
6.1 
Areas between Curves 

4 
February, 07 11 
6.2 
Volumes 
5 
February, 14 18 
6.3 
Volumes by Cylindrical Shells 
6.5 
Average Value of a Function 

6 
February, 21 25 
7.1 
Integration by Parts 
7.2 
Trigonometric Integrals 

Exam I 
Date: Feb 23, 2016; Time: TBA Building 54; Material [5.1 – 6.2] 

7 
Feb, 28 – Mar, 03 
7.3 
Trigonometric Substitution 
7.4 
Integration of Rational Functions by Partial Fractions + Exercise 59 

8 
March, 06 10 
7.5 
Strategy for Integration 
7.8 
Improper Integrals (up to end of Example 8) 

March, 13 17 Midterm Vacation 

9 
March, 20 24 
8.1 
Arc Length 
8.2 
Area of a Surface of Revolution 

10 
March, 27 31 
11.1 
Sequences 
11 
April, 03 07 
11.2 
Series 
11.3(2) 
The Integral Test and Estimates of Sums 

Exam II 
Date: April 05, 2016; Time: TBA Building 54; Material [6.3 – 8.2] 

12 
April, 10 14 
11.4 
The Comparison Tests 
11.5(3) 
Alternating Series 

13 
April, 17 21 
11.6 
Absolute Convergence and the Ratio and Root Tests 
11.7 
Strategy for Testing Series 

14 
April, 24 28 
11.8 
Power Series 
11.9 
Representation of Functions as Power Series 

15 
May, 01 05 
11.10(4) 
Taylor and Maclaurin Series 
Comprehensive Final Exam on Tuesday May 17, 2016 at 08:00 AM in Building 54. 

Notes: (1): Students should know Formulas 5, 6, and 7 on page 374. (2): Students should know the “Remainder Estimate for the Integral Test”. Example 5a and Example 6 are excluded. (3): Students should know the “Alternating Series Estimation Theorem”. Example 4 is excluded. (4): Students should know the Maclaurin Series listed in the table on page 762. 