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: “BASIC TECHNICAL MATHEMATICS with CALCULUS”, 8th edition

by Allyn J. Washington (ISBN: 0-321-13194-0)

Note to student: The CASIO CFX 8950G or any TI series graphic calculator is recommended.

SECTIONS TOPICS SUGGESTED EXERCISES

CHAPTER 25 INTEGRATION (approx. 10 hrs.)

25.1 Antiderivatives p. 735/1-35 odd

25.2 The Indefinite Integral p. 740/1-39 odd

25.3 The Area Under a Curve p. 745/1,5,9,11,15,19

25.4 The Definite Integral p. 748/1,3,5,9,13,17,21,23,25,27,29,33

25.5 Numerical Integration: The Trapezoidal Rule p. 751/1,3,7,11

25.6 Simpson’s Rule p. 755/1,3,7,11,13

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

26.1 Applications of the Indefinite Integral p. 763/1,3,5,7,11,13,15,17,21

26.2 Areas by Integration p. 769/1,3,5,9,13,17,21,23,29,35

26.3 Volumes by Integration p. 774/1,3,5,9,13,17,21,23,27,29

26.4* Centroids p. 780/1,5,9,13,17,21,25

26.6 Other Applications p. 791/1,5,7,13,17

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

28.1 The General Power Formula p. 834/1-31 odd

28.2 The Basic Logarithmic Form p. 837/1-37 odd

28.3 The Exponential Form p. 840/1-17 odd; 25,27,29

28.4 Basic Trigonometric Forms p. 844/1-21 odd; 27,29,31

28.5* Other Trigonometric Forms p. 848/1-27 odd; 31,32,35

28.7 Integration by Parts p. 856/1-25 odd

28.8* Integration by Trigonometric Substitution p. 859/1-19 odd

CHAPTER 30 DIFFERENTIAL EQUATIONS (approx. 7 hrs.)

30.1 Solutions of Differential Equations p. 912/1,5,7,11,21,23

30.2 Separation of Variables p. 916/1-35 odd

30.4 The Linear Differential Equation of the First Order p. 921/1,3,5,9,13,17,21,23,25,27,29,31

30.5 Elementary Applications p. 925/1,13-21 odd; 25,27,35,36

CHAPTER 29 EXPANSION OF FUNCTIONS IN SERIES (approx. 7 hrs.)

29.2 Maclaurin Series p. 883/1,3,4,5,11,17,19

29.4 Computations by Use of Series Expansions p. 891/1,4,5,7,9,13,17

29.5 Taylor Series p. 894/1,5,9,13,17,21

29.6 Introduction to Fourier Series p. 900/1,3,5,7

*Optional

RG(1/2006)