Bronx Community College of the City University of New York

Department of Mathematics and Computer Science

SYLLABUS: MTH 33 – Calculus and Analytical Geometry III (5 Credits – 5 Hours per week)

PREREQUISITE: MTH 32 – Calculus and Analytical Geometry II

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

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SECTION TOPIC SUGGESTED EXERCISES

Infinite Sequences and Series

12.1 Sequences 720/ 13 – 55 odd

12.2 Series 730/ 1-5, 7, 8, 9, 15-19, 43 – 47 odd

12.3 The Integral Test 739/ 1 – 25 odd

12.4 The Comparison Tests 770/ 15 – 29 odd, 41, 43, 45

12.5 Alternating Series 749/ 1, 3, 7, 9, 11, 15, 17, 19, 21

12.6 Absolute Convergence and the Ratio

and Root tests 755/ 7 – 37

12.7 Strategy for Testing Series 758/ 1, 2, 3, 4, 7, 11, 13, 21 – 37 odd

12.8 Power Series 763/ 1 – 31 odd

12.9 Representation of Functions as Power

Series 769/ 5 – 39 odd

12. 10 Taylor and Maclaurin Series 782/ 1 – 31 odd, 43, 45, 71

12.11 Applications of Taylor Polynomials 791/ 1 – 25 odd

Review 796/ 1 – 43 odd

Vectors and the Geometry of Space

13.1 Three- Dimensional Coordinate Systems 805/ 1–13 odd, 17, 19, 21, 23-31 odd

13. 2 Vectors 813/ 5 - 29 odd

13.3 The Dot Product 820/ 3 – 47 odd

13. 4 The Cross Product 828/ 1- 43 odd

13. 5 Equations of Lines and Planes 838/ 7 – 45 odd

Review 849/ 1 – 13 odd

(OVER)

Vector Functions

14.1 Vector Functions and Space Curves 858/ 1 – 25 odd

14.2 Derivatives and Integrals of Vector

Functions 864/ 1 – 29 odd

14.3 Arc Length and Curvature 904/ 1 – 41 odd

Review 918/ 1 – 5 odd, 9 – 13 odd

Partial Derivatives

15.1 Functions of Several Variables 902/ 3 – 19 odd

15.2 Limits and Continuity 912/ 1 – 37 odd

15.3 Partial Derivatives 924/ 11 – 33 odd, 45 – 73 odd

15.4 Tangent Planes and Linear

Approximations 935/ 1 – 23 odd

15.5 The Chain Rule 943/ 1 – 35 odd

15.6 Directional Derivatives and the Gradient

Vector 956/ 7 – 33 odd

15.7 Maximum and Minimum Values 997/ 5 – 17 odd, 27 – 33 odd

Review 981/ 1 – 45 odd

Multiple Integrals

16.1 Double Integrals over Rectangles 994/ 1 – 15 odd

16.2 Iterated Integrals 1000/ 3 – 31 odd

16.3 Double Integrals over General Regions 1008/ 3, 7, 15, 17, 19, 25, 27

16.4 Double Integrals in Polar Coordinates 1014/ 1, 7, 9 – 27 odd

16.7 Triple Integrals 1034/ 1, 3, 9, 11- 19 odd

Review 1058/ 3, 7, 9, 11, 15 – 27 odd

5/ 16/ 08 (JP)