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Course Title
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English Code /No
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ARABIC code/no.
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credits
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Th.
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Pr.
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Tr.
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TCH
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Calculus(1)
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Math100
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ر100
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3
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-
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-
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3
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Pre-requisites
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None
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Course Description:
The course deals with the Limit's principle and theory, methods of dealing with the differentiation operations and its theorems as well as the trigonometric and implicit differentiation, the integral and its definition as limit's operations linking the differentiation to the integral rules.
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Objectives: The course aims at
1- Showing the importance of calculus in science and engineering and the correlation between them.
2- Providing the basic principles of calculus and its applications.
3- improving the students logical thinking and mathematical skills to solve mathematical problems.
Contents:
1-Basic concepts of algebra: Real number system, exponents, operations on polynomials, and factoring.
2-Functions : Definition, ways of representing a function, graph, domain, and range of a function. Types of functions, polynomials, and power functions.
3-The limit of a function: Definition, one-side limit, infinite limits, and vertical asymptote
4-Continuity: Continuity at a point, types of discontinuity, continuity on an interval, all theorems of continuity.
5-The derivative as a function: Identify the graph of a functions derivative, notations, and how function can fail to be differentiable.
The definite integrals: Riemann sum, evaluating, and properties of the definite integral. -6
Course Outcomes:
A- Knowledge:
1-Identifying calculus and its relation with the different domains such as science ,engineering and economy.
B-Cognitive Skills
1-Understanding concepts , theorems and applying them to different scientific and everyday issues.
C- Interpersonal skills and responsibilities
1-Solving mathematical problems and ways of dealing with calculus operations.
D- Analysis and communication:
1-Using the mathematical course in dealing with everyday life situations.
Assessment methods for the above elements
The first mid-term exam1. -1
-The second mid-term exam2 2
3-Class work
- Final exam 4
Text book:
[1] H. Anton, I. Bivens, and S. Davis. Calculus, 8 th Edition. John Wiley and Sons, 2005
Supplementary references
[1] James Stewart. Calculus Early Transcendentals, 5th edition. Thomson,2003.
[2]R.Larson, R. Hostetler, and B. Edwards. Calculus,7 th edition .Houghton Mifflin Company, 2002.
[3] H.Anton. Calculus, 7th edition . John Wiley Sons, 2002.
[4] E.Swokowski, M. Olinic, and D. Pence Calculus, 6th edition . PWS Publishing Company,1994.
Other Information Resources
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Time table for distributing Theoretical course contents
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week
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Experiment
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Remarks
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1
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Basic concepts of algebra-Equations and inequalities(first and second degree)
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Appendix B
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2
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Line and graphs of second degree equations-functions-types functions.
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APP-B ,1.1,1.2,1.3
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3
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Functions-combinations
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1.3
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4
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Limits-definition- average of change .
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2.1
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5
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Limits-laws.
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2.2,2.3
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6
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Continuity .
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2.5,2.6
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7
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The first mid-term exam1
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8
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The derivative- the derivative as of function-derivatives of polynomial
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3.1,3.1,3.3,3.4
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9
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The product and quotient rules-derivative of trigonometric
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3.5
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10
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The chain rule –implicit differentiation
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3.6,4.1
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11
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Higher derivative-some applications of differentiation
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3.7,3.8
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12
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The definite integrals -Riemann sum-the fundamental theorem integrals
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6.4,6.5,6.6
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13
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The second mid-term exam2
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14
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Indefinite integrals- the substitution integrals
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6.2,6.3
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15
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The substitution integrals
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6.8
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Final exam.
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