Bronx Community College of the City University of New York

Department of Mathematics and Computer Science

SYLLABUS: MATH 31 - Calculus and Analytic Geometry I (4 credits/6 hours per week)

PREREQUISITE:              Math 30 or equivalent

TEXT: Calculus (Seventh Edition) by James Stewart, Brooks/Cole, Pub.

        (Students who do not need Math 33 may use

        Single Variable Calculus (Seventh Edition) by James Stewart, Brooks/Cole, Pub.)

SECTION           TOPIC                                          SUGGESTED EXERCISES

Chapter 1: Functions and Limits

1.4        The Tangent and Velocity Problems                  49/ 1, 3, 5, 7

1.5        The Limit of a Function                          59/ 1-5, 12-14, 17, 23-28

1.6        Calculating Limits Using Limit Laws                  69/ 1, 3-23 odd

1.8        Continuity                                          90/ 3, 7, 9, 11, 15-21 odd, 25, 33,

        37, 39, 41, 44, 45, 47, 51, 53. 55

Review                                          95/ 1-11 odd, 17, 23, 27, 29

Chapter 2: Derivatives

1.       Derivatives                                        110/1,37,19-29odd,35-43odd,47,51,53
2.       The Derivative as a Function                122/ 1, 3, 4, 7, 19, 20, 21, 25-45 odd
3.       Differentiation Formulas                        136/ 1-43 odd, 51, 53,67,75
4.       Derivatives of Trigonometric Functions        146/ 1-17 odd, 25, 29, 39-47 odd
5.       The Chain Rule                                154/ 1-45 odd, 47, 51, 55,69,71
6.       Implicit Differentiation                        161/ 1-19 odd, 25, 27, 35, 43, 45  
7.       Rates of Change in the Natural and Social         173/ 1-9 odd, 15, 18

   Sciences

8.       Related Rates                                180/ 1,3,7,8,9,11-31 odd
9.       Linear Approximations and Differentials        187/ 1,3,5,7-25 odd,31

   Review                                        191/ 3,5,11, 13-37, 45, 51, 59, 61,

        75,77, 79,82

Chapter 3: Applications of Differentiation

1.       Maximum and Minimum Values                204/ 3, 5, 15-27 odd, 29-55 odd
2.       The Mean Value Theorem                        212/ 1, 3, 7, 9,11, 15,19
3.       How Derivatives Affect the Shape of a         220/ 1, 5, 7, 8,9-17 odd, 29-37 odd

Graph

4.       Limits at Infinity; Horizontal Asymptotes        234/ 3, 9-27 odd, 35, 39
5.       Summary of Curve Sketching                        242/ 1-35 odd

3.7        Optimization Problems                        256/ 3, 5, 7, 11, 17, 19, 25, 29

3.8        Newton’s Method                                267/ 5, 7, 13-19 odd, 29

3.9        Antiderivatives                                273/ 1-39 odd, 41,43,45

Review                                        276/ 1-27 odd, 38, 41, 46, 49,

        53-57 odd

Chapter 4: Integrals

1.       Areas and Distance                                293/ 1, 3, 5, 13,15,19,23
2.       The Definite Integral                                306/ 3, 5, 9, 17, 21-25odd, 31,33, 37
3.       The Fundamental Theorem of Calculus        318/ 3,7-35 odd, 41, 45,49
4.       Indefinite Integrals and the Net Change         326/ 1-11 odd, 19-41 odd, 55,57

Theorem

5.       The Substitution Rule                                335/ 1-29 odd, 35-51 odd

Review                                        338/ 2, 5, 9-27 odd, 33, 35, 37

8/03 C.O’S.

8/07 MM

7/11 MM, 9/11 AM