Fall 2006 Mathematics V1102
Calculus II

Call Number:
13096

Points: 3
Day/Time: Mondays and Wednesdays 6:10pm - 7:25pm
Location:
  417 Mathematics Building

Instructor:
Xinyi Yuan
Office hours: 
Wednesdays 5:30pm-6:10pm in 417 Mathematics Building, or by appointment.

Email: xy2101@@columbia.edu

 

Textbook:  James Stewart's Calculus, edition 5e by Thomson.

Course description: We'll cover the following (Chapters 7, 8, 9, 11 of Stewart):

1.      Techniques of integration: parts, trig substitution, partial fractions.

2.      Improper integrals.

3.      Further applications of integration.

4.      Infinite series and sequences.

5.      Topics in differential equations.

Homework: Homework will be assigned every Monday and collected the next Monday. The assignments will also be posted below. Late homework will NOT be accepted unless a good reason is explained before the due date.  I will drop the two lowest homework grades.  Besides the homeworks, you are also encouraged to do the suggested problems in the table. They are also important for your study, but do not handle them in.

Quizzes: There will be about five quizzes in this course. Each quiz will be a few minutes and done at the beginning of a class. The date of a quiz will be notified in the table below and in class.

Exams: There will be two midterm exams and one final exam. Calculators are not allowed in these exams.

The percentages for this class are as follows:

Midterm I:    15%
Midterm II:   15%
Final Exam:  30%
Homework:   30%

Quizzes:        10%

Help: If you have any difficulty in studying the course, come to my office hour or to the help rooms. The Barnard Help Room at 333 Milbank is specifically for students in Calculus I,II,III.  And the Math Help Room at 406 Mathematics Building will also be helpful.

You will find homeworks in the schedule:

Date

Sections/Topics covered

Homework

  Suggested Problems

  Due date

09/06, Wed

Introduction. Quick review of integration and the Fundamental Theorem of Calculus (5.1-5.4).

No homework

5.5:1-44 , p.431: 9-38

  

 09/11, Mon

Quick review of substitution (5.5)

Integration by parts (7.1)

5.5: 3, 21, 22, 28, 29

7.1: 4,6,10,29,46

7.1:1-36

p. 431: 25, 32

09/18, Mon

09/13, Wed

09/18, Mon

Quiz 1, Trigonometric integrals (7.2)

Trigonometric substitution (7.3)

7.2: 5,29,42

7.3: 10, 16, 28, 32(a)

7.2: 1-46, 54

7.3: 1-31(a)

09/25, Mon

09/20, Wed

09/25, Mon

Partial fractions (7.4)

 Strategy for integration (7.5)

7.4: 4,16,32,46

7.5: 16,38,72

 

10/02, Mon

09/27, Wed

10/02, Mon

Review

No homework

 

 

10/04, Wed

Midterm I (click here for the sample)

No homework

 

 

10/09, Mon

Improper integrals (7.8)
Arc length (8.1)

7.8:14,18,36

8.1:12,16,31

Additional problem

 

10/16, Mon

10/11, Wed

10/16, Mon

Areas of surfaces of revolution (8.2)

Probability (8.5), sequences(11.1)

   8.2:12,14,27

                 8.5: 4,6 
            11.1:18,22,33   

 

10/23, Mon

10/18, Wed

10/23, Mon

Series (11.2)
Integral test (11.3)

          11.2: 29,30,33,56
          11.3: 18,20,22,34

 

10/30, Mon

10/25, Wed

10/30, Mon

Comparison test (11.4)
Alternating series (11.5)
Absolute convergence (11.6)

 

 

 

11/01, Wed

11/08, Wed

Ratio and root tests(11.6)

 

 

 

11/13, Mon

Strategy for testing series (11.7)
Review

 

 

 

11/15, Wed

Midterm II

 

 

 

11/20, Mon

Power series, functions as series (11.8, 11.9), Taylor series (11.10)

 

 

 

11/22, Wed

11/27, Mon

Taylor polynomials (11.12), Binomial series (11.11)

 

 

 

11/29, Wed

12/04, Mon

Introduction to differential equations, separable equations (9.1-9.3) 

 

 

 

12/06, Wed

12/11, Mon

Review, loose end…

 

 

 

12/13, Wed

12/15, Fri

Final

 

 

 

 

 

Academic honesty: It is the obligation of each student to understand the University's policies regarding academic honesty and to uphold these standards. Working in groups is a more efficient way of learning. You are strongly encouraged to meet with other students in the class to study the material of the course and/or get help for the homework. This being said, the homework should also involve a fair amount of personal work. In particular, just copying someone else's homework is not acceptable and will not be accepted.