Fall 2006
Mathematics V1102
Calculus II
Call Number: 13096
Points: 3
Day/Time: Mondays and Wednesdays 6:10pm - 7:25pm
Location: 417
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 |
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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 |
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09/20, Wed |
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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 |
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09/27, Wed |
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10/02, Mon |
Review |
No homework |
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10/04, Wed |
Midterm I (click here for the
sample) |
No homework |
|
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|
10/09, Mon |
Improper
integrals (7.8) |
7.8:14,18,36 8.1:12,16,31 |
|
10/16, Mon |
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10/11, Wed |
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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 |
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10/23, Mon |
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10/18, Wed |
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10/23, Mon |
Series
(11.2) |
11.2: 29,30,33,56 |
|
10/30, Mon |
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10/25, Wed |
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10/30, Mon |
Comparison
test (11.4) |
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11/01, Wed |
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11/08, Wed |
Ratio and root tests(11.6) |
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11/13, Mon |
Strategy
for testing series (11.7) |
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11/15, Wed |
Midterm II |
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11/20, Mon |
Power
series, functions as series (11.8, 11.9), |
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11/22, Wed |
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11/27, Mon |
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11/29, Wed |
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12/04, Mon |
Introduction to differential equations, separable equations (9.1-9.3) |
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12/06, Wed |
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12/11, Mon |
Review, loose end… |
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12/13, Wed |
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12/15, Fri |
Final |
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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.