Bronx Community College of the City University of New York

Department of Mathematics and Computer Science

SYLLABUS: Math 32 - Calculus and Analytic Geometry II (5 credits/ 6 hours per week)

PREREQUISITE: Math 31 or equivalent

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

Students who do not need Math 33 may use Single Variable Calculus (Seventh Edition) by

James Stewart, published by Brooks/Cole.

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SECTION TOPIC SUGGESTED EXERCISES

Chapter 5: Applications of Integration

5.1 Areas between Curves pg. 349: 1-29 odd

5.2 Volumes pg. 360: 1-33 odd, 54-60

5.3 Volumes by Cylindrical Shells pg. 366: 1-25 odd

Review pg. 378: 1, 7, 9, 15, 23, 25

Chapter 6: Inverse Functions

6.1 Inverse Functions pg. 390: odd 1-15, 23-27, 35- 43

Instructor’s option: 6.2-6.4 or 6.2*-6.4*

6.2 Exponential Functions and

Their Derivatives pg. 401: 1, 7-13 odd, 23-49 odd, 79-89 odd

6.3 Logarithmic Functions pg. 408: 1-17 odd, 27-35 odd, 47, 49, 51

6.4 Derivatives of Logarithmic Functions pg. 418: 1-29 odd, 43-53 odd, 71-81 odd

6.2* The Natural Logarithmic Function pg. 428: 1-37 odd, 61-73 odd

6.3* The Natural Exponential Function pg. 434: 5-11 odd, 27-51 odd, 81-91 odd

6.4* General Logarithmic and Exponential pg. 444: 1-9 odd, 21-41 odd, 45-49 odd

Functions

6.6 Inverse Trigonometric Functions pg. 459: 5-13 odd, 23-35 odd, 43,45,59-69 odd

6.7 Hyperbolic Functions pg. 467: 7-23 odd, 31-45 odd, 59-67 odd

6.8 Indeterminate Forms and

L'Hospital's Rule pg. 477: 1-4, 5-65 odd, 71-74

Review pg. 481: 5-47 odd, 63-77 odd, 93-105 odd

Chapter 7: Techniques of Integration

7.1 Integration by Parts pg. 492: 1-41 odd, 47-54

Instructor’s option: 7.4 can be done immediately after 7.1.

7.2 Trigonometric Integrals pg. 500: 1-31 odd

7.3 Trigonometric Substitution pg. 507: 1-29 odd

7.4 Integration of Rational Functions pg. 516: 1-29 odd, 39-49 odd

by Partial Fractions

7.5 Strategy for Integration pg. 523: 1-59 odd

7.8 Improper Integrals pg. 551: 1, 5-31 odd, optional 49-54

Review pg. 554: 1-25 odd, 41-49 odd

Chapter 8: Further Applications of Integrals

8.1 Arc Length pg. 567: 1-17 odd

8.2 Area of a Surface of Revolution pg. 574: 1-15 odd, 25

Chapter 10: Parametric Equations and Polar Coordinates

10.3 Polar Coordinates pg. 686: 1-11 odd, 15-25 odd 29-45 odd

10.4 Areas and lengths in Polar Coordinates pg. 692: 1-31 odd, optional 45-48

10.5 Conic Sections pg. 700: 1-47, odd

Section 10.6 is an instructor’s option.

10.6 Conic Sections in Polar Coordinates pg. 708: 1-15 odd

Review pg. 710: 9-15 odd, 31-39 odd, 45-55 odd

Remark: Some elements of sections 10.1 and 10.2 can be discussed as a general introduction to the curves covered in Chapters 8 and 10.

10/2014 M.M. & I.P.