Mathematics 110
Course Title
English Code /No
Calculus I
Math. 110
Pre-requisites:
None
contact hours / week
C.H.
Th.
Pr.
Tr.
TCH
3
-
-
3
Brief contents, to be posted in university site and documents(4-5 lines):
‫دليل السنة التحضيرية‬
Real numbers and Functions – Functions and Their Graphs -Shifting and Scaling Graphs
-Trigonometric Functions -Limits and Continuity - One Sided Limits -Limits at Infinity- Vertical Asymptotes –Continuity - Tangent and Derivatives - Derivatives Rules- The Chain rule Implicit Differentiation -Applications of Derivatives- Extreme Values of Functions- The Mean
Value Theorem- Monotonic Functions -Concavity and Curve Sketching- L’Hôpital’s Rule.
Objectives :
On completion of the course, the students should be able to
•Handle functions occurring in calculus and in the mathematical modeling of real-world
problems;
•Grasp the central idea of limit and continuity, and its application in a variety of problems;
•Understand the main theme of calculus and its applications involving rates of change and
the approximation of functions;
•Differentiate standard functions by applying the fundamental rules of differentiation;
•Compute the optimal values of functions and handle the optimization problems;
•Apply the concepts of monotonicity and concavity in sketching the plane curves;
•Deal with indeterminate forms and L’Hôpital’s rule;
•Understand the connection between derivatives and antiderivatives..
Contents :
•Real numbers and Functions: Real numbers, Lines, Circles, and Parabolas, Functions and
Their Graphs, Identifying Functions, Combining Functions, Shifting and Scaling Graphs,
Trigonometric Functions, Exponential Functions, Inverse Functions and Logarithms.
•Limits and Continuity: Rates of Change and Limits, Calculating Limits Using the Limit laws,
One Sided Limits and Limits at Infinity, Infinite Limit and Vertical Asymptotes, Continuity,
Tangent and Derivatives
•Differentiation: the Derivatives as a Function, Rules, the Derivatives as a Rate of Change,
Derivatives of Trigonometric Functions, Exponential Functions, Inverse Functions and
Logarithms, The Chain rule and Implicit Differentiation.
•Applications of Derivatives: Extreme Values of Functions, The Mean Value Theorem,
Monotonic Functions and the First Derivative Test, Concavity and Curve Sketching,
Indeterminate Forms and L’Hôpital’s Rule, Antiderivatives.
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Course Outcomes :
o Knowledge :
(Specific facts and knowledge of concepts, theories, formula etc.)
•(i) Description of the knowledge that required.
(ii) Teaching strategies to be used to develop that knowledge:
Activities such as open discussion, problems sheet home-work
•(iii) Methods of assessment of knowledge acquired exams.
Students will get the knowledge of thinking, solving practical problems in functions, limits,
derivatives and integration.
o Cognitive Skills:
‫دليل السنة التحضيرية‬
(Thinking, problem solving)
•Cognitive skills to be developed.
All lectures are accompanied by problem sheet, which students work privately، which is
supported by problems solved in classes.
•Teaching strategies to be used to develop the cognitive skills.
•There is access to lectures informally and formal through office hours.
•Methods of assessment of students cognitive skill, students solve problems of home-work
sheet and extra exercises in their text book alone beside the home work online through
the web site of the book.
•Interpersonal skills and responsibilities
•(group participation, leadership, personal responsibility, ethic and moral behavior, capacity
for self directed learning)
•Description of the interpersonal skills and capacity to carry responsibility to be developed.
The use of the text book and other material is developed through course work.
•Teaching strategies to be used to develop these skills and abilities.
•Teach them how to improve the independent study skills required for future studies.
•Methods of assessment of students interpersonal skills and capacity to carry responsibility
solving home-work sheets, extra problems from text book and homework online.
•
o Analysis and communication :
•(communication, mathematical and IT skills)
•Description of the skills to be developed in this domain is taught through course work and
developed through feedback on their deduced work.
•Teaching strategies to be used to develop these skills solving problems in classes during
lecture, open discussion.
•Methods of assessment of students numerical and communication skills.
•These skills are assessed through course work and written exams.
Text book :
•H. Anton, I. Bivens, and S. Davis. Calculus, 8th 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, 7th edition . Houghton Mifflin
Company, 2002. [3] H. Anton. Calculus, 7th Edition. John Wiley and Sons, 2002.
3. E. Swokowski, M. Olinic, and D. Pence Calculus, 6th Edition. PWS Publishing
Company,1994.
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Other Information Resources :
The website of the book : http://www.kau.mylabsplus.com
Time table for distributing theoretical/practical course contents :
Experiment
1
Real Number and the Real Line, Lines, Circles and parabola
2
Functions and Their Graphs, Combining Functions
3
Trigonometric Functions, Exponential Functions, Inverse Functions
and Logarithms.
4
Rates of Change and Limits, Calculating Limits Using the Limit
Laws
5
One-sided Limits and Limits at Infinity
6
Infinite Limits and Vertical Asymptotes, Continuity
7
The derivative as a Function Differentiation Rules
8
Derivatives of Trigonometric function, The chain Rule and parametric Equations, Implicit Differentiation
9
Extreme Value of Functions, The Mean value Theorem
10
Monotonic Functions and The First Derivative Test. Concavity and
Curve Sketching
11
Indeterminate Form and L’Hôpital’s Rule
12
Antiderivatives
13
Revision
14
Final exam.
Remarks
‫دليل السنة التحضيرية‬
Week
46