Oman College of Management & Technology
Department of Computer Science
Baraka, Oman
Tel. (968) 26893366, Fax (968) 26893068
502101 / Calculus I
Course Code:
Academic Year:
Credit Hours:
Instructor:
Website:
502101
2015/2016
3
Dr. Jai Arul Jose G.
www.omancollege.edu.om/
Course Title:
Semester:
Prerequisite:
Email:
Phone:
Calculus I
First
none
g.jai.areul@omancollege.edu.om
(968) 26893366/ ex. 102
Sections and Timings:
Section
1.
Days
Sun., Tue., and Thu.
Time
09:30
Room #
C5
Office Hours
Days
Sun, Tue and Thu.
Mon and Wed
Time
08:00 am to 3.00 pm
08:00 am to 3.00 pm
Course Description
Calculus I course deals with an important part of the mathematics and includes:
Preliminaries; Limits and Continuity; Derivative; Tangent and Vertical Lines, Related Rates,
Mean-Value Theorem and its Applications, L'Hopital's Rule, Vertical and Horizontal
Asymptotes, Extreme Values, The Definite Integral, The Fundamental Theorem of Integral
Calculus, The Indefinite Integral, Applications of integration, Area, Volume, Transcendental
Functions: The Logarithm Function, The Exponential Function.
Course Objectives
CALCULUS is one of the most exciting, wide-reaching courses in Mathematics that a student
will encounter. It is through Calculus that one understands the precise relationships that
allow predictions into the motions of moving bodies and the effects of forces. A deep
understanding of the physical world around uses impossible without Calculus. The student
will be expected to learn the fundamental concepts of limits and continuity of functions; to
understand the concept of derivative of a function; to learn how to differentiate algebraic,
exponential, trigonometric and logarithmic functions, as well as combination of these
functions. It also aims to recognize the usefulness of derivatives in applications, to
understand how to apply derivatives to find slop, minima and maxima, related rates and
approximations, to understand the concept of integration and its relationship to
differentiation; to grasp the Fundamental Theorem of Calculus. The student is expected to
demonstrate proficiency in these areas and to develop effective problem solving skills.
Learning Outcomes
On completing this course student should be able to apply the principles of calculus in some
real world problem.
Teaching Methods
The course will be based on the following teaching and learning activities:



Whiteboard for tutorial
Power point presentations that covers the theoretical part
Review questions
Course Delivery Plan:
Week
1.
2.
3.
4.
5.
Topics
Notes
What is Calculus?, Review of Elementary mathematics, Review
of Inequalities, Coordinate Plane,
Functions, The Elementary Functions, Combinations of
Functions,
The Idea of Limit, Definition of Limit, Some Limit Theorems,
Continuity, The Pinching Theorem, Two Basic Properties of
Continuous, Functions
6.
7.
8.
9.
10.
11.
Differentiation
12.
13.
14.
15.
16.
Integration
Second Exam
An Area Problem, The Definite Integral of a Continuous
Function, The Fundamental Theorem of Integral Calculus, Some
Area Problems, Indefinite Integrals, The u-Substitution,
Additional Properties of Definite Integral, The Mean-Value
Theorems for Integrals
Final Exam
The Derivative, Some Differentiation Formulas, The d /dx
Notation, Derivatives of Higher Order, The Derivative as a Rate
of Change, The Chain Rule, Differentiating the Trigonometric
Functions, Implicit Differentiation; Rational powers
First Exam
The Mean-Value Theorem and Applications
The Mean-Value Theorem, Increasing and Decreasing Functions
Local Extreme Values, Endpoint and Absolute Extreme Values,
Some Max-Min Problems, Concavity and Points of Inflection,
L'Hopital's Rule, Vertical and Horizontal Asymptotes, Some
Curve Sketching, Velocity and Acceleration; Speed, Rated Rates
of Change Per Units Time, Differentials
Application of the Integral
More on Area, Volume by Parallel Cross Sections, Volume by
the Shell Method
Evaluation Plan
Modes Of Assessment
Score
First Exam
20%
Second Exam
20%
Assignments
10%
Final Exam
50%
* Makeup exams will be offered for valid reasons only. Makeup exams may be different from regular exams in content and
format.
Attendance Policy
Lecture attendance is mandatory. Students are allowed maximally of 15% absentia of
the total module hours.
Teaching Resources
Textbook
Sallas, Hille, and Etgen, Calculus, One and Several Variables, Tenth Edition, 2007,
John Wiley &Sons, Inc.