MATH 2253

 

CREDIT:  4 hours. 

 

PREREQUISITE:  A grade of C or higher in MATH 1113 or placement by the Mathematics Assessment Test.

     

COURSE DESCRIPTION:  A first course in calculus.  Topics include limits, derivatives explored in various contexts and applications of differentiation (maximum and minimum problems, curve sketching, and optimization problems), integration techniques and applications of integration (area, volume, work, average value, arc length, surface area, volume and work).  Other topics may be included at the discretion of the instructor.

 

TEXT:  Calculus, 7th e, James Stewart (Brooks/Cole)

 

CALCULATOR:  See instructor for calculator policy.

GOALS: Upon completing this course students should be able to:

         Find limits of functions and determine continuity of functions.

         Find derivatives of algebraic and some trigonometric functions, and use derivatives to solve applied problems.

         Find integrals of some algebraic and trigonometric functions, and use integrals to solve applied problems

 

 

NOTE: The pace may vary, so the following is a weekly rather than daily outline.

MATH 2253 CALCULUS I

COURSE OUTLINE

WEEK

SECTIONS/TOPICS

SAMPLE HOMEWORK ASSIGNMENTS

1

1.4: The Tangent and Velocity Problems

1.5: The Limit of a Function

pp. 48:  1, 3, 4, 5, 6, 7, 9

pp. 59: 1, 3, 5, 7, 9, 11, 13, 17, 19, 29, 31, 32, 35, 39

2

1.6: Calculating Limits Using the Limit Laws

1.8: Continuity

pp. 69: 1, 6, 7, 9, 10, 11, 15, 17, 21, 27, 41, 51, 53, 60

pp. 91: 1, 3, 7, 9, 13, 15, 19, 23, 27, 33, 34, 35, 42, 43, 46, 51, 53

 

3

2.1: Derivatives and Rates of Change

2.2: The Derivative as a Function

pp. 110: 1- 21 odd, 24, 27, 29, 32, 35, 39, 43, 45, 48.

pp. 122: 1, 3, 5, 6, 13, 19, 23, 24, 25, 27, 35, 38, 41, 45, 50

 

4

2.3: Differentiation Formulas

2.4: Derivatives of Trigonometric Functions

Exam 1

pp. 136: 5, 7, 9, 11, 14, 15, 17, 23, 25, 27, 28, 29, 34, 35, 51, 58, 59, 62, 64

pp. 146: 3, 5, 7, 9, 13, 15, 17, 18, 22, 23, 26, 30, 35, 39, 42, 45, 46

5

2.5: The Chain Rule

 

2.6: Implicit Differentiation

pp. 155: 7, 9, 13, 15, 19, 22, 25, 34, 47, 48, 49, 52, 53, 68, 77

pp. 161: 6, 9, 12, 14, 16, 20, 22, 28, 34, 53, 56, 59

6

2.7: Rates of Change in the Natural and Social Sciences

2.8: Related Rates

pp. 173: 1, 5, 6, 8, 9, 15, 17, 18, 19, 29, 30

pp. 181: 3, 4, 5, 7, 9, 10, 11, 14, 16, 23, 24, 27, 31, 35, 40

7

3.1: Maximum and Minimum Values

3.2: The Mean Value Theorem

pp. 205: 1, 3, 5, 9, 12, 17, 22, 25, 28, 32, 35, 38, 45, 49, 51, 54, 55, 65

pp. 213: 3, 4, 6, 10, 14, 16, 20, 22, 24, 29, 31

8

3.3: How Derivatives Affect the Shape of a Graph

3.4: Limits at Infinity; Horizontal Asymptotes

pp. 220: 1, 3, 7, 8, 9, 12, 13, 15, 17, 29, 35, 37, 38, 39, 58, 60, 68, 70

pp. 235: 1,3, 5, 9, 13, 14, 17, 19, 23, 25, 26, 29, 34, 35, 37, 42, 45, 49, 51, 53, 57

9

3.5: Summary of Curve Sketching

3.6: Graphing with Calculus and Calculators

Exam 2

pp. 243: 1, 5, 11, 12, 15, 19, 20, 23, 29, 30, 34, 35, 36, 46, 47, 52, 55

pp. 249: 1, 5, 6, 7, 9, 20

10

3.7: Optimization Problems

3.9 Antiderivatives

4.1: Areas and Distances

pp. 256: 3, 6, 7, 9, 16, 21, 24, 29, 33, 35, 38, 39, 47, 48, 64, 69

pp. 273: 3, 5, 13, 15, 19, 21, 23, 25, 27, 29, 39, 43, 51, 53, 57, 63

pp. 293: 1, 3, 5, 7, 8, 15, 17, 19, 24

11

4.2: The Definite Integral

4.3: The Fundamental Theorem of Calculus

Exam 3

pp. 307: 1, 5, 8, 9, 18, 22, 28, 33, 35, 37, 42, 43, 47, 55, 57, 59, 62

pp. 318: 3, 9, 11, 17, 21, 28, 35, 42, 45, 47, 49, 54, 61

12

4.4: Indefinite Integrals and the Net Change Theorem

4.5: The Substitution Rule

pp. 327: 5, 9, 11, 15, 17, 22, 26, 34, 35, 40, 45, 47, 52, 57

pp. 335: 3, 5, 11, 13, 16, 17, 21, 22, 23, 24, 30, 31, 39, 47, 49, 53, 56, 59, 62, 64

13

5.1: Areas Between Curves

5.2: Volumes

pp. 349: 1, 3, 5, 9, 11, 12, 13, 17, 18, 19, 24, 27, 32, 35, 36, 46

pp. 361: 1, 5, 7, 9, 11, 13, 14, 15, 25, 28, 29, 36, 38, 40

14

 

5.3: Volumes by Cylindrical Shells

Exam 4

5.4: Work

pp. 366: 1, 5, 7, 9, 12, 13, 15, 17, 21, 22, 37, 38, 45, 47

 

 

pp. 371: 1, 3, 4, 7, 9, 10, 11, 13, 14, 15, 19, 22

15

 

5.5: Average Value of a Function

Review for final examination

pp. 375: 1, 7, 9, 11, 12, 13, 17, 19, 24

 

 

 

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