Qatar University
College of Arts and Sciences
Department of Mathematics and Physics
CALCULUS 1, SYLLABUS
COURSE INFORMATION:
 Course Number: 1051101
 Course title: Calculus 1
 Course Hours: 3 (2+2)
 Prerequisites: None
COURSE OBJECTIVES:
1.To introduce limits and continuity, and develop skills for their
determination.
2.To introduce the derivative, and develop skills for using rules of
differentiation.
3.To provide skills related to applications of the derivative.
4.To introduce the definite and indefinite integrals, and develop skills
for their evaluation.
5. To provide skills related to some applications of the integral.
6.To introduce the concept of the inverse of a function.
LEARNING OUTCOMES:
The students are expected to be able to:
Objective 1:
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Evaluate limits and one-sided limits of algebraic functions.
Evaluate limits and one-sided limits involving trigonometric functions.
Evaluate limits of a function f (x) as x tends to  
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Identify and determine horizontal and vertical asymptotes.
Determine the continuity of trigonometric functions.
Determine whether a function is continuous at a given point.
Identify points of discontinuity of a given function.
Verify the intermediate value theorem for a given function on a given interval.
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Use the intermediate value theorem to verify the existence of a root to given
equation on a given interval.
1
Objective 2:
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Define the derivative of a function.
Recognize the derivative of a function as its rat of change.
Recognize the derivative of a function as the slope of the tangent To its graph.
Use differentiation rules, including the chain rule.
Evaluate the derivative of a given function, involving algebraic, Trigonometric,
logarithmic and exponential functions.
Evaluate the derivative of a given implicit function.
Evaluate higher-order derivatives.
Determine equation of tangent and normal lines.
Use differentials to evaluate a liner approximation of a function, and to estimate
relative errors.
Objective 3:
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Solve problems of related rates.
Find the intervals of decrease and increase of a function.
Determine the critical points of a function.
Classify the critical points using the first derivative test and the Second derivative
test.
Determine the concavity of the graph of a function.
Find the points of inflection of a function.
Identify vertical tangents and cusps.
Use the above properties to sketch graphs of functions.
Distinguish between the endpoints, relative and absolute extrema.
Solve max-min problems.
Verify the mean value theorem and Roll’s theorem.
Apply Newton’s method to compute an approximate root of a given equation.
Objective 4:
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Identify the antiderivatives of known functions.
Distinguish between definite and indefinite integrals.
State and use the fundamental theorem of integral calculus.
Evaluate definite and indefinite integrals.
Evaluate definite and indefinite integrals by substitution.
Objective 5:
 Express the area of a region in terms of a definite integral.
 Evaluate the area between two curves.
 Express the volume of a solid of revolution in terms of a definite Integral, using
disks, washers and cylindrical shells.
 Evaluate the volume of a solid of revolution
Objective 6:
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Derive relationship between the derivative of function and the derivative of its
inverse
Compute deivative formulas for logarithmic and Exponential
2
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Evaluate integral involving logarithmic and Exponential functions
Discuss. L’Hopital’s Rule, a poweful tool for evaluatng limits
INSTRUCTOR:
Dr. huda Al Thani
 E-mail: h.m.althani@qu.edu.qa
 Office : 485-1624
 Location: SB208
OFFICE HOURS:
 12 -2 Sunday
 12 -2 Thursday
 Or by Appointment
I strongly encourage you to take advantage of my office hours.
.
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.
 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
3
SYLLABUS ITEMS:
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Week
1
2
4
5
6
7
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
Sec.
2.1
2.2
2.3
2.5
2.6
3.1
3.2
3.3
3.4
3.5
3.6
3.7
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Topics
Quick Review of Functions,
Limits, Computing Limits
Computing Limits: End Behavior
Continuity
Limits Continuity of Trigonometric Functions
Slopes and Rates of Change
The Derivative
Techniques of Differentiation
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Related Rates
Vacation
9
4.1
4.2
10
4.3
Analysis of Functions I: Increase, Decrease and Concavity
Analysis of Functions II: Relative Extrema; First and Second
Derivative Tests
Analysis of Functions III: Applying Technology and the Tools of
Calculus
4
11
12
4.5
4.6
4.8
5.2
5.3
Absolute Maxima and Minima
Applied Maximum and Minimum Problems (Optimization)
Rolle’s Theorem; Mean-Value Theorem
The Indefinite Integral
Integral Curves and Direction Fields
13
5.5
Integration by Substitution
The Definite Integral
The Fundamental Theorem of Calculus
5.6
14
15
16
5.8
6.1
6.2
1.5
7.1
7.2
7.3
7.4
7.5
Evaluating Definite Integral by Substitution
Area Between Two Curves
Volumes by Slicing; Disks and Washers
Invers funactions
Exponential and logarthmic functions
Derivatives and integrals involving logarthmic and exponential
functions
Derivatives of inverse functions; Derivatives and integral involving
exponential functions
Graphs and applications involving logarthmic and exponential
functions
L'Hopital's Rule; indeterminante forms.
REFERENCEMS
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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
5
Recommended Problems in the Textbook, to be attempted by the students
Chapter#
1
2
3
4
5
6
Section
#
Page # Problems #
1
3
4
5
1
27
40
51
1
2
84
96
11,19,20
1,5,11,19,29,33,35,42
17,20,21
1[c,d],3[b,c],7,8,9,10,11,13,17,18,19,21,23,26
,27,29,33
1,2,3,4,5,6,7,12
1,6,7,8,9,10,11,18,20,23,27,31,33,34,35,36,37
3
105
5,9,15,19,21,23,31,33
5
125
11,13,14,17,18,21,22,23,27,29,30,33,55
6
137
1
2
3
4
5
6
7
8
1
2
3
4
5
7
2
3
5
6
8
1
2
6
1
146
159
171
179
185
190
198
206
225
227
245
254
262
281
308
318
337
347
370
380
388
414
435
1,3,7,9,12,13,15,17,19,23,26,27,28,29,32,33,3
4, 35,36,37,39,41,46
2,5,9,13,14,15
9,10,12,15,19,23,26,28,30
3,5,10,13,16,18,19,23,35,37,41,43,32
1,3,5,7,13,14,15,17,22,25
1,3,6,7,11,15,18,22,39,37
2,4,5,8,13,15,17,20,21,28,30,31,33,37,62
8,10,12,13,28,32,34,35,51
12,14,16,17,32,38,39
2,3,5,7,9,15,17,19,24,29,33,35
2,3,7,9,10,15,16,20,25,27,33,36,41,49,59
3,5,7,11,12,13,14,18,25,27,29,36,37,40,41
4,5,6,9,10,12,13,15,16,17,24,33,35
1,2,3,5,6,8,9,10,12,14,16,17,19,20,24,25,43
3,5,6,7,10,11,15,16,22,29
2,7,8,9,10,13,14,15,17,28,29,30,37,41
1,2 (a,b,c,d),3(a,b,c,e),15,16,28,31
11,12,14,15,17,20,21,25,34,[a,b]
3,6,8,9,11,19,22,30,32,35,43,45,47,59
3,7,10,25,27,29,31,37
1,2,3,4,7,11,12,9,5,13,17,23
1,3,6,7,9,11,13,15,17,20
1,4,5,7,9,23
1,2,5,6,11,13,15,16,18,21,25,28,30,31,33,35,
36,39,43,45
6
7
2
447
3
453
4
460
5
467
1,3,8,9,10,13,15,20,21,23,24,26,27,29,33,34,
35,38,41,49,51,53,55,56,57,59,60,62,64,65
2,4,5,8,10,13,14,15,16,17,19,21,26,27,29,32,
33,37,41,47,49,52,55,58,59,60,61,62,63,65,66
,67
1,2,3,4,5,7,9,15,17,20,23,27,32,37,39,40,42,
45,54
1,2,5,6,8,9,11,12,14,15,16,18,19,20,21,24,25,
27,30,31,32,33,34,36,37,39,41,43,46,47,49,58
7