Qatar University
College of Arts and Sciences
Department of Mathematics and Physics
Math 102 (Calculus 2) Course Syllabus
COURSE INFORMATION:
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Course Number: Math 102
Course title: Calculus II
Course Hours: 3
Prerequisites: Math 101
Name: Dr. Hussain Mohammed Al-Qassem
Contact Tel.: 485-2200
E-mail: husseink@qu.edu.qa
Office Number: C216 Building: Boys
Office Hours:
Time
Sunday
Monday
Wednesday
3-4
12:30-1:30
12:30-1:30
OR by
Appointment
These office hours will be held in SA 210. I strongly encourage you to take advantage of my
office hours.
INSTRUCTIONS & REGULATIONS
 Using Mobile phones during lectures or exams is prohibited. Shut off your cell phone during
class, any one uses mobile will be asked to leave the lecture room.
Students are expected to attend all classes, if they do not show up for more than 25% of the classes, they
fail the course. There are no grades for attendance.
 Quizzes have no make up, so try not to miss any.
 Students are expected to participate actively in the class.
 Check your e-mail regularly.
 Be responsible for all class activities, announcements, and assignments when you miss a class.
 Do not hesitate to see me if you have any question.
 Prior to class, look over the section that will be covered.
Regularly check the BlackBoard site at: http://mybb.qu.edu.qa
Course Description
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Transcendental Functions:
Inverse trigonometric functions. Hyperbolic functions. Inverse hyperbolic
functions. Derivative of inverse hyperbolic functions. Integrals involving inverse
trigonometric and inverse hyperbolic functions.
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Techniques of Integration:
Integration by parts. Integrals involving trigonometric functions. Trigonometric
substitutions. Partial fractions. Rationalizing substitutions. Improper Integrals.
Sequences and Infinite Series:
Sequences. Infinite series. Convergence tests. Absolute and conditional
convergence of alternating series. Power series. Taylor series.
Parametric Equations and Polar Coordinates:
Polar coordinates. Curves defined by parametric equations. Tangent lines and
length for parametric and polar curves. Area in polar coordinates.
OURSE OBJECTIVES:
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To provide knowledge on basic transcendental functions and their properties.
To develop skills to evaluate integrals using different integration techniques.
To introduce indeterminate forms.
To introduce improper integrals and methods for their evaluation.
To introduce infinite series and develop skills to determine their convergence.
To introduce power series and expansion of functions in Taylor series.
To introduce the polar coordinate system and use parametric equations to study some properties of
plane curves.
LEARNING OUTCOMES:
1. Identify the properties of inverse trigonometric functions, hyperbolic, and inverse
hyperbolic functions.
2. Find the derivatives and integrals of inverse trigonometric, hyperbolic, and inverse
hyperbolic functions.
3. Evaluate the indefinite and improper integrals by using different integration techniques.
4. Identify the properties of sequences and their limits.
5. Use various tests to determine convergence of series.
6. Perform standard operations with convergent power series, including the method of
differentiating and integrating term by term.
7. Use Taylor and Maclaurin series to approximate functions.
8. Sketch the graphs of parametric and polar equations.
10. Use parametric and polar equations to solve applied problems including area and
arclength.
Delivery Methods
We will use different types of teaching methods including:
 Presentation explaining material.
 Problem solving.
 Discussion - actively involving students in learning by asking questions that provoke
thinking and verbal response.
 Cooperative Learning - small group structure emphasizing learning from and with others.
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Learning Resources & Media
1. In class we will use head projector to explain mathematical formulas
2. Data show will be used also to visualize some important graphs in the plane.
3. Blackboard will be used frequently
GRADING PLOICY
Three major exams and three quizzes will be given according to the following details:
Exam
First
Second
Quizes
Final Exam
Total
percentage
25%
25%
10%
40%
100%
Date and time
Saturday April 3, 2010, 11:00-1:00
Saturday May 15, 2010, 11:00-1:00
3 quizes (We will count the best two qiuzes)
Wednesday June 9, 2010. Time:14:00-16:00.
The rules of QU to transfer numeral grades to letter grades as follows
Percent grade
Letter grade
Earned Points
90 -100 85 - 89
A
B+
4.0
3.5
80 - 84 75 -79 70 - 74
B
C+
C
3.0
2.5
2.0
65 - 69
D+
1.5
60 - 64
D
1.0
below 60
F
0.0
Text Book:
TEXTBOOK
Calculus, Early Transcendentals, by James Stewart, 6th Edition, 2008, Brooks/Cole.
REFERENCES
 Calculus, by James Stewart, 6th Edition, 2008, Brooks/Cole.
 Calculus with Analytic Geometry, by C. H. Edwards and D. E. Penny, 5th
Edition, 1998, Prentice Hall.
 Calculus, by R.T. Smith and R.B. Minton, Second Edition, 2002, McGraw-Hill.
 Calculus, by R.T. Smith and R.B. Minton, Second Edition, 2002, McGraw-Hill
 Calculus, by H. Anton, I. Bivens, and S. Davis, 8th Edition, 2007, Wiley.
SYLLABUS ITEMS:
Week
1
Date
Feb. 21- 25
Topics
Review of inverse functions
Inverse Trigonometric Functions, Derivatives and Integrals Involving Inverse
Trigonometric Functions.
2
Feb 28 - Mar 4
3.11: Hyperbolic Functions, Inverse Hyperbolic Functions. Derivatives and
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Integrals Involving Inverse Hyperbolic Functions.
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Mar 7 – 11
7.1: Integration by Parts
7.2: Trigonometric Integrals
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Mar 14 – 18
7.3: Trigonometric Substitution
7.4: Integrating Rational Functions by Partial Fractions
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Mar 21– 25
7.5: Strategy for Integration
7.8: Improper Integrals
First Exam: Saturday March 27, 2010. Time: 11:00 – 13:00
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Mar 28 – Apr 1
11.1 Sequences
11.2: Series
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Apr 4 - 8
11.3: The Integral Test and Estimates of Sums
11.4: The comparisons Tests
Apr. 11 – 15
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Apr 18 – 22
Spring Break
11.5: Alternating series
11.6: Absolute Convergence and the Ratio and Root Tests
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Apr 25 – 29
11.7: Strategy for Testing Series
11.8: Power Series
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May 2 – 6
11.9: Representations of Functions as Power Series
11.10: Taylor and Maclaurin Series
Second Exam: Saturday May 8, 2010. Time: 11:00 – 13:00
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May 9 – 13
8.1: Arc Lengths
10.1: Curves Defined by Parametric Equations
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May 16 – 20
10.2: Calculus with Parametric Curves
10.3: Polar Coordinates
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May 23 – 27
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May 30 – Jun 3
10.4: Areas and Lengths in Polar Coordinates
Final Exam: Wednesday June 9, 2010, 14:00 – 16:00
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Recommended Problems for Calculus 2
Note to the students: The following problems are meant for the least practice. They only
show the type of the problems you will encounter in this course. You are strongly urged to
solve much more problems to get an excellent skill.
Exercise 3.11: 1-21odd, 23-47odd
Exercise 7.1: 1-37odd, 43, 45, 47, 57
Exercise 7.2: 1-49odd, 61, 67, 68, 69
Exercise 7.3: 1-31odd
Exercise 7.4: 1-49odd, 55, 57
Exercise 7.5: 1-79odd
Exercise 7.8: 1-39 odd, 57, 61, 69
Exercise 8.1: 1-17odd
Exercise 10.1: 1-21odd, 24, 28, 31, 33, 41
Exercise 10.2: 1-7odd, 11-19odd, 25, 31, 33, 39, 41, 44
Exercise 10.3: 1-47odd, 49, 55, 59, 63, 69
Exercise 10.4: 1-41odd
Exercise 11.1: 1-45odd, 54, 61, 80
Exercise 11.2: 1, 9, 11-51odd, 52, 55, 59, 65, 71, 76
Exercise 11.3: 3-25odd, 33, 39
Exercise 11.4: 1,2, 3-35odd, 39, 40, 41, 42
Exercise 11.5: 1-19odd, 23, 25, 27
Exercise 11.6: 1-33odd
Exercise 11.7: 1-37odd
Exercise 11.8: 1-31odd
Exercise 11.9: 1-17odd, 23, 27, 29, 35, 37
Exercise 11.10: 1-37odd, 45, 47-50, 53, 57, 59, 63, 67
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