American University of Beirut
Faculty of Arts and Sciences
Department of Mathematics
Math 101: Calculus I
Fall 2022
Dr. H. Yamani
Office: Bliss 322
Office Phone: 4277
Office Hours: MWF 9 am
E-mail:
Class Meetings: MWF 10 am
Text
Thomas’ Calculus, 14th edition by Thomas, Weir, and Hass.
Objective:
Introduce mathematical techniques that are useful in different technical fields, and acquire
the skills that are necessary for success in any subsequent study of calculus.
Section
Functions
1.1
Graphs
Assigned homework problems
1.2
Functions
1, 2, 5, 8,11,14, 16, 17, 23, 25, 29, 34, 37, 41, 49,57,59, 60, 67,71, 77
1.3
Trigonometric Functions 5, 6, 8, 10, 12, 14, 20, 32, 34, 36, 43, 44
3–10, 16–20, 24, 26, 28 ,29, 30b, 31, 36
Limits and Continuity
2.2
Limits 1, 3, 5, 6, 9, 15, 18, 21-24, 28, 30, 32, 33, 36, 38, 40, 42, 47, 49, 51, 53, 60,
61, 63, 65a, 66a, 78, 79
2.3
Precise Def. of Limits 2, 3, 7, 10, 16, 18, 25, 31, 33, 34, 38, 47, 49
2.4
One-Sided Limits
2.5
Continuity
2.6
Limits involving infinity 1, 5, 8, 11, 13, 16, 19, 22, 23, 30, 36, 39, 45, 48, 49, 50,
1–5, 9, 12, 13, 16, 18, 24, 25, 27, 31–39, 43, 53
1–6, 8, 14, 16, 19, 22, 23, 26, 30, 41, 44, 46, 48, 61, 65, 67
55, 57, 60, 85, 88
Differentiation
3.1
Tangents and Derivative 7, 8, 13, 18, 21, 24, 26, 33, 34, 36, 38
3.2
The Derivative 2, 6, 8, 9, 13, 16, 21, 23, 26-31, 40, 46–52, 55
3.3
Differentiation Rules 5, 8, 12, 16, 18, 24, 26, 27, 29, 31, 38, 40, 42, 46, 49, 54a, 59
3.5
Derivatives of Trig. Functions
1–3, 7, 11, 12, 14, 16, 19, 22, 23, 25–27, 34, 36,
38, 49, 51, 52, 56, 59, 60
3.6
Chain Rule
2,3,6,9,11,14,17, 20, 22,23, 25, 29, 31–33, 36, 39,40, 43,50, 51,62,
68, 72, 73, 75, 80, 82
3.7
Implicit Differentiation 3, 6, 8, 13, 17, 23, 28, 30, 33, 40, 41, 45, 47
Applications of Derivatives
4.1
Extremes Value of Functions 3, 4, 6, 9, 11–15, 17, 24, 26, 29, 30, 32, 35, 38, 41, 45,
48–50, 53, 55, 58, 60,61, 68
4.2
Mean Value Theorem 3, 4, 6, 11, 15, 16–18, 21, 24, 25, 28, 29, 31, 33, 35, 45, 47,
58, 59, 61, 62, 63
4.3
First Derivative Test 3, 5, 8, 9, 13, 16, 19, 33, 35, 41ab, 44–46ab, 57a, 63, 69, 71,72
4.4
Graphing
4.7
Antiderivatives 5, 7, 8, 10, 12, 16, 19, 22, 24, 26, 27, 32–34, 37, 46, 49, 55,
2, 3, 8, 9, 11, 20, 27, 43, 51, 61, 65, 70, 77, 85, 109, 110
59, 63, 67, 73, 75,83, 85
Integration
5.2
Limits of Finite Sum
5.3
1, 4, 5, 13, 16, 19, 22, 24, 28, 32, 38, 44, 50
Definite Integrals 3–5, 9, 10, 14, 16–20, 22, 24, 26, 28, 30, 31, 36, 43, 44, 48, 52,
54, 64, 71
5.4
Fundamental Theorem of Calculus 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27,
30, 36, 39, 40, 42, 45, 48, 51,54, 67–71
5.5
Indefinite Integrals 2, 4, 5, 6, 11,19, 21, 24, 26, 29, 31, 47, 49
5.6
Area between Curves 1–4, 6, 8, 13, 16, 24, 30, 35, 36, 42, 44, 46, 49, 52, 54, 78, 86
Applications of Definite Integrals
6.1
Volumes using Cross Sections 1, 2, 4, 6, 23, 24, 26, 29, 37, 41, 47–51, 53
6.2
Volumes using Cylindrical Shells 2, 4–6, 8, 10, 19, 22, 23, 30–32, 34–36
6.3
Arc Length 1, 5, 10–12, 21, 23–25
Method of Grading:
Grades for this course will be determined as follows:
Exam # 1:
Saturday October 1,
10 am. 25 %
Exam # 2:
Saturday November 5, 10 am 25 %
Final Exam:
TBA
50 %
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