MATH 101 - Calculus I (4-0-4)

(Coordinator: Dr. A. Shawky Ibrahim)

Syllabus

## Catalog Description

Limits and continuity of functions of a single variable.  Differentiability. Techniques of differentiation.   Implicit differentiation.  Local extrema, first and second derivative tests for local extrema.  Concavity and inflection points.  Curve sketching.  Applied extrema problems.  The Mean Value Theorem and applications.

Prerequisite: One year preparatory mathematics or its equivalent

Textbook:  Calculus, A New Horizon by Howard Anton, sixth edition (1999).

Week(s)

Dates

Sec.

Topics

1and 2

Sept. 2 – 12

2.1

2.2

2.3

Limits (An intuitive Introduction)

Limits (Computational Techniques)

Limits (Discussed more rigorously)

3

Sept 15 – 19

2.4

2.5

Continuity

Limits and Continuity of Trigonometric Functions

4

Sept 22 – 26

3.1

3.2

Tangent Lines and Rates of Change

The Derivative

5

Sept. 29 – Oct 3

3.3

3.4

Techniques of Differentiation

Derivatives of Trigonometric Functions

# Wensday, OCTOBER 3, TIME FOR MAJOR EXAM I

6

Oct. 6 – 10

3.5

3.6

The Chain Rule

Local Linear Approximation; Differentials

7

Oct. 13 – 17

4.1

4.2

Inverse Functions

Logarithmic and Exponential Functions

8

Oct. 20 – 24

4.3

4.4

Implicit Differentiation

Derivatives of Logarithmic and Exponential Functions

9

Oct. 27 – 31

4.5

4.6

Derivatives of Inverse Trigonometric Functions

Related Rates

10

Nov. 3 – 7

4.7

L’Hopital’s Rule; Indeterminate Forms

# SATURDAY, NOVEMBER 10, TIME FOR MAJOR EXAM II

11, 12

Nov. 11 – 21

5.1

5.2

5.3

6.1

Increasing, Decreasing, and Concavity

Relative Extrema; First and Second Derivative Tests

Applying Technology and the Tools of Calculus

Absolute Maxima and Minima

13, 14, 15

Nov. 24 – Dec. 9

6.2

6.3

6.4

6.5

Applied Maximum and Minimum Problems

Rectilinear Motion

Newton’s Method

Rolle’s Theorem; Mean-Value Theorem

16

Dec. 29 – Jan. 2