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The Calculus Collection


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Table of Contents

Part I. Functions, Graphs and Limits; Part II. Derivatives; Part III. Integrals; Part IV. Polynomial Approximations and Series; Part V. Appendixes.

Promotional Information

A collection of articles introducing the core ideas of calculus. A resource for teachers of secondary school and undergraduate students.

About the Author

Caren L. Diefenderfer (AB Dartmouth College, MA, Ph.D. University of California at Santa Barbara) is Professor of Mathematics at Hollins University. Caren has been active with the AP Calculus Program for over 20 years and served as Chief Reader for AP Calculus from 2004-2007. She has been a leader with MAA efforts on Quantitative Reasoning and is currently the Chair of the MAA's Special Interest Group for the Teaching of Advanced High School Mathematics (SIGMAA TAHSM). Roger B. Nelsen (BA DePauw University, Ph.D. Duke University) is Professor Emeritus of Mathematics at Lewis and Clark College. Roger has been an AP Calculus Reader for many years and has authored or co-authored four books for the MAA: Proofs Without Words: Exercises in Visual Thinking (1993); Proofs Without Words II: More Exercises in Visual Thinking (2000); Math Made Visual: Creating Images for Understanding Mathematics (with Claudi Alsina, 2006); and When Less Is More: Visualizing Basic Inequalities (with Claudi Alsina, 2009).


This book is a collection of 123 selected articles...published originally in one of the periodicals of the Mathematical Association of America...With the help of an Advisory Panel of six veteran high school teachers with the nationwide Advanced Placement Program of the USA, these publications were compiled to provide a useful resource for everyone who teaches calculus...the various articles collected in the present book provide a wealth of interesting new viewpoints, didactical insights, methodological variants, inspiring examples and applications, entertaining depictions, and motivating pedagogical tricks. No doubt, every calculus teacher can profit a great deal from this multifarious collection of articles on teaching elementary calculus, each of which is evidently written with gripping enthusiasm, pedagogical experience and cultural sensitiveness."" - Zentrallblatt Math

""This book is a collection of published articles about calculus and the staple problem is the theme for many of them. For example, the falling ladder problem is the point of several of them and the goal is to provide insight to and poke a little fun at these staples. In that respect, the book is a welcome relief for it gives the reader an opportunity to look at these problems in a fresh light. The point is made that at this time in the United States, the high school AP calculus students form the largest market for calculus instruction. That is why the book is targeted at the teaching of calculus at the AP level, although that is a bit disingenuous. It is stated that AP calculus should be the same as college calculus yet the book is aimed at the AP ""level."" That marketing ploy aside, this book contains a large number of nuggets that can be used to enliven and strengthen the teaching of calculus, independent of the where and the level."" - Charles Ashbacher

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