9780131449237

Calculus Connections

by ; ;
  • ISBN13:

    9780131449237

  • ISBN10:

    0131449230

  • Edition: 1st
  • Format: Paperback
  • Copyright: 1/23/2006
  • Publisher: Pearson

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Supplemental Materials

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Summary

With challenging new standards-based middle school mathematics curricula now in place, future teachers need college-level mathematics instruction that better prepares them for their professional careers. Addresses the importance of learning calculus in preparation for the teaching of middle school mathematics, focusing on concepts and applications to illuminate the connections that exist between college-level calculus and the mathematics taught in todayrs"s middle schools. Examines the unique needs of future teachers in comparison to general calculus books. Initiates new topics with engaging discussion rather than the standard formula-proof-example approach. Stresses the interplay between geometry and calculus, and demonstrates the essential power of calculus for computing areas, lengths, surface areas, and volumes.For current or future mathematics teachers, or anyone interested in learning more about calculus.

Table of Contents

Preface ix
List of Classroom Connections
xv
List of Classroom Discussions
xvi
List of Projects
xix
Sequences and Series
1(58)
Sequences
1(37)
Series
38(21)
Functions, Limits, and Continuity
59(55)
Functions
59(29)
Limits of Functions
88(15)
Continuity
103(11)
Differentiation
114(39)
Average Rates of Change
114(5)
Instantaneous Rates of Change and Slopes of Graphs
119(12)
Motion and Derivatives
131(3)
Rules for Computing Derivatives
134(8)
The Chain Rule
142(11)
More on Differentiation
153(37)
Optimization
153(14)
Curve Sketching
167(9)
Exponential Change
176(14)
Integration
190(22)
Indefinite Integrals
190(9)
Definite Integrals
199(4)
Some Techniques of Integration
203(9)
Applications of Integration to Area
212(61)
Areas of Polygonal Regions
212(5)
Approximate Values for the Area of an Irregular Shape
217(20)
Exact Value of the Area of an Irregular Shape
237(12)
Area of a Disc from Different Points of View
249(9)
Area of a Region Bounded by Two Graphs
258(15)
Further Applications of Integration
273(61)
Lengths of Curves in the Plane
273(13)
Areas of Surfaces of Revolution
286(16)
Volumes of Solids
302(32)
Appendix 334(2)
Answers to Classroom Discussions and Practice Problems 336(89)
Answers to Selected Exercises 425(43)
Photo Credits 468(3)
Index 471

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