Qatar University
College of Arts and Sciences
Department of Mathematics and Physics
CALCULUS 1, SYLLABUS
COURSE INFORMATION:
 Course Number: Math 101
 Course title: Calculus 1
 Course Hours: 3 (2+2)
 Prerequisites: None
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.
Course Objectives
The course aims at:
1. Introduce limits and continuity, and develop skills for their determination.
2. Introduce the derivative, and develop skills for using rules of differentiation.
3. Provide skills related to applications of the derivative.
4. Introduce the definite and indefinite integrals, and develop skills for their evaluation.
5. Provide skills related to some applications of the integral .
Learning Outcomes
By the end of the course, the students should be able to:
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1.
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3.
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5.
6.
7.
8.
9.
10.
Evaluate Limits of functions using various techniques including L’Hopital’s Rule
Discuss the continuity functions
Identify the properties of inverse functions and their derivatives
Find the derivative of algebraic, trigonometric, exponential, and logarithmic functions
Sketch the graph of a function using the information for the first and second
derivatives
Solve problems involving applications of derivatives including, related rates and
optimization
Identify the definition and properties associated with definite integrals
Solve problems using the Fundamental Theorem of Calculus
Evaluate integrals using the method of substitution
Solve problems involving applications of integrals including finding volume of solids
of revolution and area between curves.
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.
 Using Math packages explaining some material including Autograph.
 The lecture will be posted on the e-learning tool Blackboard, so pay you attention
to the class and try to understand everything.
Learning Resources & Media
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In class we will use Digital Camera to explain mathematical formulas
Data show will be used also to visualize some important graphs in the three
dimension space
We will use some math packages including Autograph 3.2 and MATHEMATICA.
Blackboard will be used frequently: http://mybb.qu.edu.qa/
The Student companion site for the text:
http://www.stewartcalculus.com/media/4_home.php
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%
 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.
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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
SYLLABUS ITEMS:
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Limits and Continuity:
The limit. One-sided limits. Limit theorems. Vertical and horizontal asymptotes.
Continuity. Continuity of trigonometric functions. The intermediate-value
theorem. The extreme-value theorem.
Differentiation:
Tangent lines and rates of change. The derivative. Rules of differentiation.
Derivatives of higher order. Differentiation of trigonometric, logarithmic and
exponential functions. The chain rule. Implicit differentiation.
Applications of Derivatives:
Increasing and decreasing functions. Relative extreme values. The first derivative
test. The second derivative test. Absolute extreme values. Concavity. Points of
inflection. Vertical tangents and cusps. Curve sketching. Max-Min problems.
Mean-Value theorem. Rolle's Theorem.
Integration:
Antiderivatives. Indefinite and definite integrals. The fundamental theorem of
Calculus. Properties. Integral formulas. Average value. Integration by substitution.
Inverse Functions: Review of the inverse functions, continuity and
differentiability of the inverse. Integration and differentiation of logarithmic and
exponential functions. L’Hopital’s Rule.
Applications of the Integral: Area between two curves. Volumes by slicing.
Volumes by cylindrical shells
3
Week
1
Date
Fe. 21- Feb. 25
2
Feb. 28 – Mar. 4
3
Mar. 7 – Mar 11
4
Mar. 14 – Mar 18
5
Mar. 21 – Mar. 25
6
Mar. 28 – Apr. 1
7
Apr. 4 – Apr. 8
8
Apr. 9 - Apr. 18
9
Apr. 18 – Apr. 22
10
Apr. 25 – Apr. 29
11
May 2– May 6
12
May 9 – May 13.
13
May 16 – May 20
14
May 23– May 27
Sec.
2.1
2.2
2.3
2.5
2.6
Topics
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
Continuity
Limits at Infinity, Horizontal Asymptote
Infinite Limits, Vertical Asymptotes
Derivatives and Rates of Change
The Derivative as a Function
Differentiation of Polynomials
The Product and Quotient Rules
Derivatives of Trigonometric Functions and limits
The Chain Rule
Implicit Differentiation
Related Rates
Maximum and Minimum Values
The Mean Value Theorem
2.7
2.8
3.1
3.2
3.3
3.4
3.5
3.9
4.1
4.2
Spring Brake
4.3
4.5
4.7
4.9
5.1
5.2
5.3
5.4
5.5
6.1
6.2
6.3
6.5
(1.2 ,1.5
How Derivatives Affect the Shape of a Graph
Summary of Curve Sketching
Optimization Problems
Antiderivatives
Areas and Derivatives
The Definite Integral
The Fundamental Theorem of Calculus
The Indefinite Integral and Net Change Theorem
The Substitution Rule
Areas between Curves
Volumes
Volumes by Cylindrical Shells
Average Value of a Function
Exponential and Logarithmic Functions.
Derivative and Integrals Involving Logarithmic
Functions.
Inverse Functions. Derivative and Integrals Involving Exp
Functions.
Indeterminate Forms and L’Hospital’s Rule.
1.6,
3.1,3.4,3.6&
appendix G)
15
May 30– June 3
4.4
Final Exam; Wednesday June 9th , 14:00 – 16:00
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TEXTBOOK
Calculus, Early Transcendentals, by James Stewart, 6th Edition, 2008,
Brooks/Cole.
REFERENCEMS

Calculus with Analytic Geometry. By C. H. Edwards and D. E. Penny, 5th
Edition, 1998, Prentice Hall

Calculus . Howaer Anton 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-Hil
Recommended Problems in the Textbook, to be attempted by the students
1.5: 2,3,5,9-12 ,13,15-18,21
1.6: 1-19,21,24,26,29,30,31,33-52odd, 59-69odd
2.1: 3,4,5,9a,c
2.2: 4,7,9,15,25-32
2.3: 1,3,4,8,10,11-30,35-37,39-44,46,49
2.5: 3,17,18,19,31-39,41,45,47
2.6: 2,3,4,7,15-36,41,39-44,55,65
2.7: 5,7,9,13,14,15,18,19,23a, 24a,25-35odd,51
2.8: 3,19-29odd,35,41,51,53
3.1: 3-35odd,46,49,51-55,57,59,73,77
3.2: 1-33odd,35a,36,40a,41,43,44,45,47,55
3.3: 1-24,25a,28a,29,33,39-48,51
3.4: 7-46odd,49-53odd,55a,56a,59-65odd,69,71,73,74,75,95
3.5: 1-19odd,21,22,23,25,27,35,39,45-53odd,61
3.8: 1,3,5,9,12,13,14,15,16,19
3.9: 2,4,5,7,9,10,13,14,17,19,23
3.10: 1-4,13,15,19,25,28,33
3.11: 1-21odd,30-47odd
4.1: 5,17-21,25,29-43odd,47-61odd
4.2: 1,3,5,11,12,14,15,18,19,23,25
4.3: 1,5,11,14,17,19,25,38,39,41,43,45,75,76
4.4: 1-63odd,69,78
5
4.5: 5,7,9,17,19,33,37,41,57
4.7: 2-6,12,13,17,19,23,27,28,33,37
4.9: 1-45odd,57-63odd
5.1: 5,19,21
5.2: 3,9,17-20,23,35-41,47,49,53,56
5.3: 3,7-45odd,53,55,72-74
5.4: 2,5-18,21-44,48,57,59
5.5: 1-45odd,51-69odd
6.1: 1-31odd
6.2: 1-35odd,49,51,57,63
6.3: 1,2,3-25odd,37-42
6.5: 1-10,13
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