Calculus Connections

by Harcharras, Asma; Mitrea, Dorina; University of Missouri, UMO

• ISBN13: 9780131449237
• ISBN10: 0131449230
• Format: Paperback
• Copyright: 2006-01-23
• Publisher: Pearson

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