Page Content
Course Coordinator 
Dr. Khaled Khashan 
Phone 
94018 
Office 
2481 
Email 
mathcoo@py.ksu.edu.sa 
Semester 
Second Semester 14341435 


Textbook: Calculus Made Simple  First Edition
Authors: Khashan A, Khashan K, Pbeidat S
Description: In this course students will study the following topics
Chapter
Number 
Chapter Name 
Description 
Chapter 1 
Limits and Continuity of Functions 
Concept of Limit
Computation of Limits
Infinite Limits
Limits at Infinity
Continuity and Consequences
Limits of Trigonometric Functions
Formal definition of limit 
Chapter 2 
Derivatives of Functions 
The Derivative
Computation of Derivatives
The Chain Rule
Derivatives of Trigonometric Functions
Derivatives of Logarithmic and Exponential Functions
Implicit Differentiation
The Mean Value Theorem 
Chapter 3 
Applications of Derivatives 
Indeterminate Forms and L'Hopital's Rule
Monotonic Behavior of Functions
Concavity and Inflection Points
Absolute Extrema
Curve Sketching 
This course is intended for students who have a thorough knowledge of analytic geometry and elementary functions in addition to college preparatory algebra, geometry, and trigonometry. The purpose of the course is to prepare the student for advanced placement in college calculus. In this course:
In this course the student will
· Define and apply the properties of limits of functions. This will include limits of a constant, sum, product, quotient, onesided limits, limits at infinity, infinite limits, and nonexistent limits.
· State the definition of continuity and determine where a function is continuous or discontinuous. This will include continuity at a point; continuity over a closed interval; application of the Intermediate Value Theorem; and graphical interpretation of continuity and discontinuity.
· Find the derivative of an algebraic function by using the definition of a derivative. This will include investigating and describing the relationship between differentiability and continuity.
· Apply formulas to find the derivative of algebraic, trigonometric, exponential, and logarithmic functions and their inverses.
· Apply formulas to find the derivative of the sum, product, quotient, inverse, and composite (chain rule) of elementary functions.
· Find the derivative of an implicitly defined function.
· Find the higher order derivatives of algebraic, trigonometric, exponential, and logarithmic functions.
· Use logarithmic differentiation as a technique to differentiate non logarithmic functions.
· State (without proof) the Mean Value Theorem for derivatives and apply it both algebraically and graphically.
· Use L'Hopital's rule to find the limit of functions whose limits yield the indeterminate forms: 0/0 and infinity/infinity. A Calculus, these functions will also include functions whose limits yield the indeterminate forms: 0 to the 0th power, 1 to the infinity power, infinity to the infinity power, infinity minus infinity.
· Apply the derivative to solve problems, including tangent and normal lines to a curve, curve sketching, velocity, acceleration, related rates of change, and optimization problems.
References
§ Anton, Bivens, Davis: Calculus: Early Transcendentals Combined, 8^{th} Edition, 2005
§ Salas, Hill, Etgen. Calculus: One and Several Variables, 9^{th} Edition, 2003.
Evaluation
The evaluation of the students will be continuous during the course and depends on the following:
Mid Term Exam 
30 
Quizzes & Activities 
10 
Selflearning 
10 
Final Exam 
50 
Course Schedule:
Week 
Sections to be covered 
Content 
1 
1.1
1.2 
Concept of Limit 
Computation of Limits 
2 
1.3 
Infinite Limits 
3 
1.4 
Limits at Infinity 
4 
1.5 
Continuity and Consequences 
5 
1.6 
Limits of Trigonometric Functions 
6 
2.1 
The Derivative 
7 
2.2 
Computation of Derivatives 
8 
2.3 
The Chain Rule 
9 
2.4 
Derivatives of Trigonometric Functions 
10 
2.6 
Derivatives of Logarithmic and Exponential Functions 
11 
2.7
2.8 
Implicit Differentiation 
The Mean Value Theorem 
12 
3.1 
Indeterminate Forms and L'Hopital's Rule 
13 
3.2 
Monotonic Behavior of Functions 
14 
3.3
3.4 
Concavity and Inflection Points 
Absolute Extrema 
15 
3.6 
Curve Sketching 
Contents:
Chapter 
Section 
Examples 
Exercises for Students 
Chapter One
Limits and Continuity of Functions 
1.1 Concept of Limit 
2,4,6,8 
1,9,10,11,12,22,25,28 
1.2 Computation of Limits 
1,2,3,4,5,6,7,8,9.10,12,13,17,18 
23,24,25,26,31,33,36,38,42,
53,54 
1.3 Infinite Limits 
1,2,3,4,5,6,7,8,9,10 
1,4,5,6,9,11,17,18,19,21,22 
1.4 Limits at Infinity 
1,2,3,4,5,6,7,8,9,10,11,13 
1,2,4,5,7,8,10,12 
1.5 Continuity and Consequences 
1,3,5,6,7,9,11,14,16,19,21 
1,14,16,20,25,27,30,33,41,43,49,51 
1.6 Limits of Trigonometric Functions 
1,2,3,4,5,9,11,12, 13 
2,8,9,11,12,13,15,16,20,23 
Chapter Two
Derivatives of Functions 
2.1 The Derivative 
1,3,5,7,9,10,11 
1,3,5,8,11,13,15,18,19 
2.2 Computation of Derivatives 
1,2,3,4,5,6,9,10,13,14,15,16 
1,3,5,11,17,18,19,20,21,22,23,24,
25,26,27,34,38 
2.3 The Chain Rule 
1,2,3,6,7,8,9,10 
1,3,9,11,13,18,24,26,28, 29,30,33,34,37 
2.4 Derivatives of Trigonometric Functions 
1,2,3,4,5,6,7,8,10 
1,5,8,12,13,16,28,29,33,36,38,39,
45,47 
2.6 Derivatives of Logarithmic and Exponential Functions 
1,2,3,4,5,6,7 
1,3,5,8,11,15,20,23,26,28,30,
39,41 
2.7 Implicit Differentiation 
1,2,3,4,5,6,7,8,9 
2,3,9,11,15,19,21,23,25,26,30,34,
37,38 
2.8 The Mean Value Theorem 
1,2,3,5,6 
3,5,7,11,12,15,16 
Chapter Three
Applications of Derivatives 
3.1 Indeterminate Forms and L'Hopital's Rule 
3,5,4,7 
1,2,3,4,5,7,13,15,16,17,19,25,27,
28, 29,30 
3.2 Monotonic Behavior of Functions 
1,2,3,4,5,6,7,8,9,10 
1,2,3,4,5,6,8,9,11,15,18,19 
3.3 Concavity and Inflection Points 
1,2,3,4,5,6,7 
1,2,3,4,5,6,7,8,11,13,19,20,22,26 
3.4 Absolute Extrema 
1,2,3,5,6,7,8,10,11 
1,2,3,4,18,19,21 
3.6 Curve Sketching 
1,3 
1,3,6,10 
