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 (Eighth Edition) by James Stewart, Publisher: Brooks/ Cole

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SECTION      TOPIC                                               SUGGESTED EXERCISES

Infinite Sequences and Series

11.1     Sequences                                                        744/ 3 – 55 odd

11.2     Series                                                               755/ 1-10, 15, 17-20, 43 – 47 odd

11.3     The Integral Test                                            765/ 1 – 25 odd

11.4     The Comparison Tests                                   771/ 1, 2, 3 – 29 odd, 41, 43

11.5     Alternating Series                                            776/ 1–19 odd, 35

11.6     Absolute Convergence and the Ratio

and Root tests                                                 782/ 7 – 37 odd

11.7     Strategy for Testing Series                              786/ 1– 37 odd

11.8     Power Series                                                   791/ 1 – 31 odd

11.9     Representation of Functions as Power

Series                                                               797/ 5 – 19 odd, 25 – 31

11. 10  Taylor and Maclaurin Series                           811/ 1 – 33 odd

11.11   Applications of Taylor Polynomials              820/ 1 – 22 odd

Review                                                            825/ 1 – 43 odd

Vectors and the Geometry of Space

12.1     Three- Dimensional Coordinate Systems       836/ 1–13 odd, 17, 19, 21, 25-35 odd

12. 2    Vectors                                                            845/ 1 - 25 odd

12.3     The Dot Product                                             852/ 1 – 53 odd

12. 4    The Cross Product                                          861/ 1- 43 odd

12. 5    Equations of Lines and Planes                        871/ 1 – 43 odd

Review                                                            882/ 1 – 20 odd

(OVER)

Vector Functions

13.1     Vector Functions and Space Curves               893/ 1 – 20 odd

13.2     Derivatives and Integrals of Vector

Functions                                                        900/ 1 – 27 odd

13.3     Arc Length and Curvature                              908/ 1 – 33 odd

Review                                                            922/ 1 – 13 odd

Partial Derivatives

14.1     Functions of Several Variables                        939/ 3 – 27 odd

14.2     Limits and Continuity                                                950/ 1 – 37 odd

14.3     Partial Derivatives                                          964/ 11 – 40 odd, 45 – 70 odd

14.4     Tangent Planes and Linear

Approximations                                              974/ 1 – 23 odd

14.5     The Chain Rule                                               983/ 1 – 34 odd

14.6     Directional Derivatives and the Gradient

Vector                                                             997/ 7 – 33 odd

14.7     Maximum and Minimum Values                    1007/ 1 – 20 odd, 27 – 35 odd

Review                                                            1022/ 1 – 49 odd

Multiple Integrals

15.1     Double Integrals over Rectangles                    1039/ 1 – 25 odd, 39, 40

15.2     Double Integrals over General Regions           1048/ 1 – 32 odd, 39, 40

15.3     Double Integrals in Polar Coordinates            1054/ 1 – 27 odd

15.6     Triple Integrals                                               1077/ 1 – 23 odd

Review                                                            1102/ 3 – 8 odd, 9, 19, 21 – 40 odd

08/ 08/ 16 (JP)