King Fahd University of Petroleum and Minerals

Department of Mathematical Science

# SYLLABUS

Semester I, 2005-2006 (051)

(Dr. M. Sarhan)

Course #:

## Math 101

Title:

Calculus I

Textbook:

Calculus (Early Transcendentals): by H. Anton, I. Bivens, and S. Davis; seventh edition (2002)

Objectives:

To introduce the student to basic concepts and methods of Calculus.  Topics  include: Limits and continuity. The Derivative. Exponential, logarithmic and inverse trigonometric functions. Applications: Related rates, Local linear approximation, Differentials, Graphing and Applied optimization problems.

Weeks

Dates

Secs.

Topics

1

Sept 10-14

2.1

Limits (An Intuitive Approach)

2

Sept 17-21

2.2

2.3

Computing Limits

Computing Limits (End Behavior)

3

Sept 25*-28

2.4

2.5

Limits (Discussed More Rigorously)

Continuity

4

Oct 01-05

2.6

3.1

Limits and Continuity of Trigonometric Functions

Slopes and Rates of Change

5

Oct 08-12

3.2

## Suggested Date for Major Exam I: Sunday, October 09, 2005.

6

Oct 15-19

3.3

3.4

Techniques of Differentiation

Derivatives of Trigonometric Functions

7

Oct 22-26

3.5

3.6

The Chain Rule

Implicit Differentiation

###### Eid Al-Fitr Vacation

8

Nov 12-16

3.7

3.8

Related Rates

Local Linear Approximation; Differentials

9

Nov 19-23

4.1

4.2

Inverse Functions

Exponential and Logarithmic Functions

10

Nov 26-30

4.3

Derivatives of Logarithmic and Exponential Functions

Suggested Date for Major Exam II: Tuesday, December 06, 2005.

11

Dec 03-07

4.4

4.5

Inverse Trigonometric Functions and Their Derivatives

L’Hopital’s Rule; Indeterminate Forms

12

Dec 10-14

5.1

5.2

Analysis of Functions I: Increase, Decrease and Concavity

Analysis of Functions II: Relative Extrema; First and Second Derivative Tests

13

Dec 17-21

5.3

5.4

Analysis of Functions III: Applying Technology and the Tools of Calculus

Rectilinear Motion (Motion Along a Line)

14

Dec 24-28

5.5

5.6

Absolute Maxima and Minima

Applied Maximum and Minimum Problems (Optimization)

15

Dec 31-Jan 04

5.7

5.8

Newton’s Method

Rolle’s Theorem; Mean-Value Theorem

Eid Al-Adha Vacation

16

Jan 21

Review

* Saturday, Sept 24 : National Day Break.

 § The Suggested dates for Major Exams I and II are set by the College of Sciences to avoid  conflicts with other exams. § The date, time and the place of the Final Examination will be announced by the Registrar.  The Final Exam is Comprehensive. § Attendance is compulsory. KFUPM policy with respect to attendance will be strictly enforced. § For details about Homework and Recitation Problems and CAS Assignments, see the following page.

King Fahd University of Petroleum and Minerals

Department of Mathematical Sciences

Math 101 – Semester (051)

(Dr. M. Sarhan)

#### Homework and Recitation Problems and CAS Assignments

Secs.

Homework Problems

*CAS Assignments

Recitation Problems

2.1

2, 10, 14, 15, 31

29

6, 12, 13, 32,

2.2

2, 7, 10, 15, 20, 36, 38

---

1, 3, 8, 16, 17, 34, 40

2.3

16, 18, 26, 27, 32

---

2, 6, 8, 11, 20, 29, 31

2.4

11, 21, 48

---

12, 22, 72

2.5

20, 22, 24, 27, 29, 43

31

19, 23, 26, 30, 42

2.6

9, 10, 23, 24, 26, 30, 35, 40

### Example # 3(a,b)

2, 8, 14, 18, 21, 28, 42

3.1

1, 8, 11, 18

---

2, 6, 13, 20

3.2

1, 3, 10, 16, 25, 28, 45, 46

31

2, 4, 5, 11, 14, 23, 41, 43, 47

3.3

6, 8, 12, 18, 20, 22, 40, 44, 51, 61

56

14, 24, 26, 43, 49, 60, 65

3.4

6, 17, 22, 25(b), 27(a), 37(i)

---

8, 10, 23, 29(b), 37(g)

3.5

4, 10, 22, 32, 43, 55, 72

41, 42

2, 13, 16, 25, 38, 47, 54, 70

3.6

12, 22, 25, 28, 30, 36, 47

33, 35

19, 24, 31, 40, 46

3.7

3, 8, 10, 13, 14, 25, 29, 40

---

12, 17, 26, 32, 37

3.8

2, 5, 10, 21, 27, 28, 37, 41, 53,

---

4, 6, 19, 23, 30, 42, 54

4.1

1(a,b), 8, 12, 16, 18, 26, 46

---

5, 11, 24, 40, 45

4.2

6, 18, 21, 22, 30, 34, 57

38, 39

12, 15, 16, 24, 33, 35, 58

4.3

7, 14, 18, 29, 31, 34, 35, 42, 45, 48, 50, 57

---

3, 4, 8, 30, 32, 33, 38, 40, 47

4.4

8, 11, 12, 27, 29, 32

--

2, 5, 7, 13, 24, 28, 31

4.5

1, 8, 11, 18, 27, 32, 33, 49, 51

42, 47

2, 12, 16, 23, 35, 39, 40

5.1

4, 7, 15, 18, 22, 26

42

2, 6, 8, 17, 25, 35

5.2

8, 9, 19, 22, 34, 36, 53

54

5, 12, 15, 17, 23, 32, 36

5.3

3, 14, 23, 34, 44, 53, 58, 67

---

4, 18, 24, 38, 50, 68

5.4

2, 3, 12, 20

---

4, 14, 18, 38

5.5

7, 12, 21, 25, 38, 43

---

5, 14, 20,. 31, 41

5.6

3, 4, 6, 9, 22, 29, 51

---

2, 8, 19, 49, 55

5.7

3, 6, 21, 27, 31

20

2, 4, 8, 24

5.8

7, 8, 13, 20, 26, 37, 46

---

6, 16, 31, 38

§         Homework and recitation problems may be extended or adjusted by the instructor as appropriate.  CAS assignments are at the discretion of the instructor.  In any case, the students are strongly urged to solve much more problems than indicated here.

 * Computer Algebra Systems (CAS): Mathematica, Matlab, Maple, …, etc. See Section 1.3 of the textbook for details. Also refer to pages vii and xi for details about the Calculus Resource CD packaged with the textbook.

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