The Calculus Collection: A Resource for AP and Beyond

Portada
Caren L. Diefenderfer, Roger B. Nelsen
MAA, 18 de febr. 2010 - 507 pàgines
0 Ressenyes
The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.The MAA has twice previously issued a calculus reader, collecting articles on calculus from its journals: Selected Papers in Calculus, published in 1969 and reprinted as Part I of A Century of Calculus, and Part II published in 1992. In a sense The Calculus Collection is the third volume in that series, but different in that it is a collection chosen for its usefulness to those who teach first-year calculus in high schools as well as colleges and universities.
 

Què opinen els usuaris - Escriviu una ressenya

No hem trobat cap ressenya als llocs habituals.

Continguts

Graphs of Rational Functions for Computer Assisted Calculus
76
The Derivative from Fermat
94
Careers in Mathematics 2nd edition edited by Andrew Sterrett
101
Derivatives Without Limits
106
Rolle over LagrangeAnother Shot at the Mean Value Theorem
118
A Note on the Derivative of a Composite Function
124
Do Dogs Know Calculus?
125
Do Dogs Know Bifurcations?
133
The Indeterminate Form 0
245
A Useful Notation for Rules of Differentiation
257
SelfIntegrating Polynomials
308
Sums and Differences vs Integrals and Derivatives
314
How Do You Slice the Bread?
322
Disks Shells and Integrals of Inverse Functions
328
Gabriels Wedding Cake
334
A Paradoxical Paint Pail
341

The Story of Related Rates
139
vii
140
The Falling Ladder Paradox
149
How Not to Land at Lake Tahoe
175
To Build a Better Box
182
The Curious 13
189
A Dozen Minima for a Parabola
200
Constrained Optimization and Implicit Differentiation
208
Roast or Light a Fire?
217
Descartes Tangent Lines
223
Differentiate Early Differentiate Often
230
LHopitals Rule Via Integration
238
Finding Curves with Computable Arc Length
350
xii
398
The Trapezoidal Rule for Increasing Functions
443
Pictures Suggest How to Improve Elementary Numeric Integration
449
The Geometric Series in Calculus
456
A Visual Approach to Geometric Series
462
What Did He Do Besides Cry Eureka? Sherman Stein
466
Proof Without Words
469
On Rearrangements of the Alternating Harmonic Series
476
A Differentiation Test for Absolute Convergence
482
Copyright

Frases i termes més freqüents

Quant a l’autor (2010)

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).

Informació bibliogràfica