CALCULUS, Math102
Qatar University
College of Arts and Sciences
Department of Mathematics and Physics
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COURSE INFORMATION:
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Course Number: Math 102
Course title: Calculus 2
Course Hours: 3
Prerequisites: Math 101
COURSE OBJECTIVES
1. To introduce trigonometric inverse functions and their properties.
2. To introduce Hyperbolic functions and their inverses.
3. To develop skills to evaluate integrals using different integration techniques.
4. To introduce improper integrals and methods for their evaluation.
5. To introduce sequences and use it to develop the study of properties of infinite series.
6. To introduce infinite series and develop skills to determine their convergence.
7. To introduce power series and expansion of functions in Taylor series and Maclaurin series.
8. To introduce polar coordinate system and find the tangent lines and arc length for parametric
and polar curves.
9. To find area in polar coordinates.
LEARNING OUTCOMES
The students are expected to be able to:
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.
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8. Sketch the graphs of parametric and polar equations.
9. Use parametric and polar equations to solve applied problems including area and
arc length.
INSTRUCTOR:
Dr. Nada Al Thani
 E-mail: nannhm@qu.edu.qa
 Office : 485-1889
 Location: SB207
OFFICE HOURS:
 11-12 Sunday
 12-1 Tuesday
 11-1 Thursday
 Or by Appointment
I strongly encourage you to take advantage of my office hours.
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EVALUATION POLICY:
Three major exams will be given:
 First Exam: 25%, Saturday, April., 3, 2010.
 Second Exam: 25%, Saturday, May., 1,2010.
 Final Exam: 40% Wednesday June 9, 2010, 14:00 – 16:00
 Quizzes: 10%
INSTRUCTIONS & REGULATIONS:
 Using Mobile phones during lectures or exams is not allowed.
 Students are expected to attend at least 75% of the classes, otherwise they
fail the course. No grades for attendance.
 No make ups on quizzes.
 Students are expected to participate actively in the class.
 Made up tests cannot be arranged except in case of emergency or absence
due to official university business.
 Check Your e-mail regularly
 Check dohamath.com regularly
 Come and see me as soon as you have questions If you are a student with
special need, Please inform the professor. Then, arrangements can be done
with the Special Needs Section at the university
 Regularly check the BLACKBOARD
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REFERENCEMS

Calculus with Analytic Geometry. By C. H. Edwards and D. E. Penny, 5th Edition,
1998, Prentice Hall

Calculus . H. Anton, I. Bivens, and S. Davis, 8th edition (2007) by Howard Anton, (John
Wiley & Sons, Inc, New York).


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
TEXTBOOK
Calculus, Early Transcenfentals
Edition: 6th Edition, 2008, Brooks/Cole
Author: James Stewart
Additional Source :Online Source
The Student companion site for the text: http://www.stewartcalculus.com/media/4_home.php
SYLLABUS ITEMS:
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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.
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
DELIVERY METHOD
We will use different types of teaching methods including:
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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.
LEARNING RESOURCES AND MEDIA
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In class we will use head projector to explain mathematical formulas
Data show will be used also to visualize some important graphs in the two
dimension space
Blackboard will be used frequently
Content Distribution
Lectures schedule
Week
1
Topics
Review of inverse functions. Inverse trigonometric functions.
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The derivative of inverse trigonometric functions. Hyperbolic
functions.
3
Inverse hyperbolic functions and their derivatives.
4
Integrals involving inverse trigonometric and inverse
hyperbolic functions.
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Integration by Parts. Trigonometric Integrals.
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7
Trigonometric Substitution. Integrating Rational Functions by
Partial Fractions.
Types of Improper Integrals and Methods of Evaluation
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Vacation
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Sequences and their limits, monotone sequences
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Infinite series. The comparison.
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Ratio and Root tests. Alternating series.
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Conditional convergence. Maclaurin and Taylor series,
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and their approximation. Power series.
Differentiating and Integrating Power series.
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Polar coordinates. Curves defined by parametric equations.
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Tangent lines and length for parametric and polar curves. Area in
polar coordinates.
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LIST OF SELECTED PROBLEMS
Exercise 1.6 : 59 to 68 & 71
Exercise 3.5 : 45 to 54
Exercise 3.11: 1 to 21odd, 23 to 47odd
Exercise 7.1: 1 to 37odd, 43, 45, 47, 57
Exercise 7.2: 1 to 49odd, 61, 67, 68, 69
Exercise 7.3: 1 to 31odd
Exercise 7.4: 1 to 49odd, 55, 57
Exercise 7.5: 1 to 79odd
Exercise 7.8: 1 to 39 odd, 57, 61, 69
Exercise 8.1: 1 to 17odd
Exercise 10.1: 1 to 21odd, 24, 28, 31, 33, 41
Exercise 10.2: 1 to 7odd, 11 to 19odd, 25, 31, 33, 39, 41, 44
Exercise 10.3: 1 to 47odd, 49, 55, 59, 63, 69
Exercise 10.4: 1 to 41odd
Exercise 11.1: 1 to 45odd, 54, 61, 80
Exercise 11.2: 1, 9, 11 to 51odd, 52, 55, 59, 65, 71, 76
Exercise 11.3: 3 to 25odd, 33, 39
Exercise 11.4: 1,2, 3 to 35odd, 39, 40, 41, 42
Exercise 11.5: 1 to 19odd, 23, 25, 27
Exercise 11.6: 1 to 33odd
Exercise 11.7: 1 to 37odd
Exercise 11.8: 1 to 31odd
Exercise 11.9: 1 to 17odd, 23, 27, 29, 35, 37
Exercise 11.10: 1 to 37odd, 45, 47-50, 53, 57, 59, 63, 67
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