BRONX COMMUNITY COLLEGE of the City University of New York

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

 

SYLLABUS:            MTH 15-CALCULUS (3 credits, 3 hours)

 

PREREQUISITE:     MTH 14

TEXTBOOK:  ÒBASIC TECHNICAL MATHEMATICS with CALCULUSÓ, 10th edition

                        by Allyn J. Washington  (ISBN-13: 978-0-13-311653-3;  ISBN-10: 0-13-311653-0)

Publisher: Pearson/Prentice Hall

 

Note to student: Any graphic calculator is recommended.

 

 

SECTIONS                            TOPICS                                         SUGGESTED EXERCISES

 

CHAPTER 25 INTEGRATION (approx. 10 hrs.)

25.1      Antiderivatives                                                                   p. 744/1-35 odd

25.2      The Indefinite Integral                                                         p. 748-749/1-39 odd

25.3      The Area Under a Curve                                                      p. 754/1,5,9,11,15,19

25.4      The Definite Integral                                                           p. 757/1,3,5,9,13,17,21,23,25,27,29,33

25.5      Numerical Integration: The Trapezoidal Rule                           p. 761/1,3,7,11

25.6      SimpsonÕs Rule                                                                 p. 764/1,3,7,11,13

 

CHAPTER 26 APPLICATIONS OF INTEGRATION (approx. 8 hrs.)

26.1      Applications of the Indefinite Integral                                     p. 772-773/1-25 odd

26.2      Areas by Integration                                                            p. 777-778/1-29odd; 33,35

26.3      Volumes by Integration                                                       p. 783-784/1,3,5,9,13,17,21,23,27,29,38

26.4*    Centroids                                                                          p. 789-790/1,5,9,13,17,21,25,30

26.6      Other Applications                                                              p. 799/1,5,7,13,17

 

CHAPTER 28 METHODS OF INTEGRATION (approx. 10 hrs.)

28.1      The General Power Formula                                                 p. 842-843/1-31 odd

28.2      The Basic Logarithmic Form                                                p. 846-847/1-37 odd

28.3      The Exponential Form                                                        p. 849-850/1-17 odd; 25-33 odd

28.4      Basic Trigonometric Forms                                                  p. 853/1-21 odd; 27,29,31

28.5*    Other Trigonometric Forms                                                  p. 857/1-27 odd; 31,32,35

28.7      Integration by Parts                                                             p. 865/1-25 odd

28.8*    Integration by Trigonometric Substitution                              p. 868/1-19 odd

 

CHAPTER 30 EXPANSION OF FUNCTIONS IN SERIES (approx. 7 hrs.)

30.2      Maclaurin Series                                                                 p. 912/1,3,4,5,11,17,19

30.4      Computations by Use of Series Expansions                             p. 920/1,4,5,7,9,13,17

30.5      Taylor Series                                                                     p. 923/1,5,9,13,17,21

30.6      Introduction to Fourier Series                                               p. 929/1,3,5,7

 

CHAPTER 31 DIFFERENTIAL EQUATIONS (approx. 7 hrs.)

31.1      Solutions of Differential Equations                                         p. 941/1,5,7;11-23odd

31.2      Separation of Variables                                                        p. 945/1-35 odd

31.4      The Linear Differential Equation of the First Order                    p. 950/1,3,5,9,13,17,21,23,25,27,29,31

31.6      Elementary Applications                                                      p. 956-958/1,13-21 odd; 25,27,35,36

 

 

 

*Optional

RG(1/2006) PY(11/2009) PY(08/2014)