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 (Eighth Edition) by James Stewart, published by Brooks/Cole. ISBN-10: 1285740629

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

James Stewart, published by Brooks/Cole. ISBN-10: 1305266633

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SECTION TOPIC SUGGESTED EXERCISES

Chapter 5: Applications of Integration

5.1       Areas between Curves                                               pg. 362: 1-29 odd

5.2       Volumes                                                          pg. 374: 1-33 odd, 54-60

5.3       Volumes by Cylindrical Shells                        pg. 381: 1-25 odd

            Review                                                            pg. 393: 1, 7, 9, 15, 23, 25

Chapter 6: Inverse Functions

6.1       Inverse Functions                                           pg. 406: 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. 418: 1, 7-13 odd, 23-49 odd, 79-89 odd

6.3       Logarithmic Functions                                    pg. 426: 1-17 odd, 27-35 odd, 47, 49, 51

6.4       Derivatives of Logarithmic Functions            pg. 436: 1-29 odd, 43-53 odd, 71-81 odd

6.2*     The Natural Logarithmic Function                 pg. 445: 1-37 odd, 61-73 odd

6.3*     The Natural Exponential Function                 pg. 452:  5-11 odd, 27-51 odd, 81-91 odd

6.4*     General Logarithmic and Exponential pg. 463: 1-9 odd, 21-41 odd, 45-49 odd

            Functions

6.6       Inverse Trigonometric Functions                    pg. 481: 5-13 odd, 23-35 odd, 43,45,59-69 odd

6.7       Hyperbolic Functions                                     pg. 489: 7-23 odd, 31-45 odd, 59-67 odd

6.8       Indeterminate Forms and

L'Hospital's Rule                                            pg. 499: 1-4, 5-65 odd, 71-74

Review                                                            pg. 505: 5-47 odd, 63-77 odd, 93-105 odd

Chapter 7: Techniques of Integration

7.1       Integration by Parts                                        pg. 516: 1-41 odd, 47-54

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

7.2       Trigonometric Integrals                                   pg. 524: 1-31 odd

7.3       Trigonometric Substitution                             pg. 531: 1-29 odd

7.4       Integration of Rational Functions                   pg. 541: 1-29 odd, 39-49 odd

by Partial Fractions   

7.5       Strategy for Integration                                   pg. 547: 1-59 odd

7.8       Improper Integrals                                          pg. 574: 1, 5-31 odd, optional 49-54

            Review                                                            pg. 577: 1-25 odd, 41-49 odd

Chapter 8: Further Applications of Integrals

8.1       Arc Length                                                      pg. 588: 1-17 odd

8.2       Area of a Surface of Revolution                      pg. 595: 1-15 odd, 27

Chapter 10: Parametric Equations and Polar Coordinates

10.3     Polar Coordinates                                           pg. 706: 1-11 odd, 15-25 odd 29-45 odd

10.4     Areas and lengths in Polar Coordinates          pg. 712: 1-31 odd, optional 45-48

10.5     Conic Sections                                                pg. 720: 1-47, odd

Section 10.6 is an instructor’s option.

10.6     Conic Sections in Polar Coordinates               pg. 728: 1-15 odd

            Review                                                            pg. 730: 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.

08/2016 A.W.