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جامعة الملك سعود

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الخطة الدراسية لمقرر 150 ريض
 
نشرت في : 23/10/1430 10:05 ص
آخر تعديل  : 09/04/1435 11:17 ص
 

  

 

 Course Coordinator 

 Dr. Khaled Khashan

 Phone

 94018

 Office

  2481

 E-mail

 mathcoo@py.ksu.edu.sa

 Semester

 Second Semester 1434-1435

 

 

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

Objectives

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, one-sided 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, 8th Edition, 2005

§  Salas, Hill, Etgen. Calculus: One and Several Variables, 9th 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

Self-learning

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

3,5,6,7

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