Bronx Community College of the City University of New York

Department of Mathematics and Computer Science

SYLLABUS: Math 32  Calculus and Analytic Geometry II (4 credits/ 6 hours per week)

PREREQUISITE: Math 31 or equivalent

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

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

James Stewart, published by Brooks/Cole.

________________________________________________________________________

SECTION TOPIC SUGGESTED EXERCISES

Chapter 6: Applications of Integration

6.1 Areas between Curves pg. 352: 129 odd

6.2 Volumes pg. 362: 135 odd, 56-62

6.3 Volumes by Cylindrical Shells pg. 368: 125 odd

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

Chapter 7: Inverse Functions

7.1 Inverse Functions pg. 391: odd 115, 23-27, 33- 41

Instructor’s option: 7.2-7.4 or 7.2*-7.4*

2. Exponential Functions and

Their Derivatives pg. 402: 1, 713 odd, 2345 odd, 73-81 odd

2. Logarithmic Functions pg. 409: 117 odd, 2533 odd, 45, 47, 49

7.4 Derivatives of Logarithmic Functions pg. 419: 129 odd, 4151 odd, 6979 odd

7.2* The Natural Logarithmic Function pg. 428: 1-35 odd, 59-71 odd

7.3* The Natural Exponential Function pg. 435: 5-11 odd, 27-47 odd, 75-83 odd

7.4* General Logarithmic and Exponential pg. 445: 1-9 odd, 21-41 odd, 45-49 odd

Functions

7.6 Inverse Trigonometric Functions pg. 461: 513 odd, 2335 odd, 43,45,5969 odd

7.7 Hyperbolic Functions pg. 468: 723 odd, 3147 odd, 5765 odd

7.8 Indeterminate Forms and

L'Hospital's Rule pg. 478: 14, 563 odd, 93, 94, 95

Review pg. 483: 547 odd, 6377 odd, 93105 odd

Chapter 8: Techniques of Integration

8.1 Integration by Parts pg. 493: 137 odd, 4352

Instructor’s option: 8.4 can be done immediately after 8.1.

8.2 Trigonometric Integrals pg. 501: 131 odd

8.3 Trigonometric Substitution pg. 508: 129 odd

4. Integration of Rational Functions pg. 517: 129 odd, 39-49 odd

by Partial Fractions

8.5 Strategy for Integration pg. 524: 157 odd

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

Review pg. 554: 125 odd, 4149 odd

Chapter 9: Further Applications of Integrals

9.1 Arc Length pg. 566: 117 odd

9.2 Area of a Surface of Revolution pg. 573: 115 odd, 25

Chapter 11: Parametric Equations and Polar Coordinates

11.3 Polar Coordinates pg. 683: 111 odd, 1525 odd 2947 odd

11.4 Areas and lengths in Polar Coordinates pg. 689: 131 odd, optional 45-48

11.5 Conic Sections pg. 696: 147, odd

Section 11.6 is an instructor’s option.

11.6 Conic Sections in Polar Coordinates pg. 704: 115 odd

Review pg. 706: 915 odd, 3139 odd, 4555 odd

Remark: Some elements of sections 11.1 and 11.2 can be discussed as a general introduction to the curves covered in Chapters 9 and 11.

5/08 I.P.