Tales of History and Imagination

Calculus Explorations Powered by Technology

Published by Houghton Mifflin; co-author Mike Caraco. You may order a book or request an examination copy; the ISBN number is 0-618-24751-3.

LABS

Lab 1: The Quadratic Family of Functions
Lab 2: Mathematical Muscle: Dominant Functions, The Rule of Three, and the Restaurant at the End of the Universe
Lab 3: Thomas Malthus' "Utterly Dismal Theorem" and the Hungry Nation of Farlandia
Lab 4: Galileo's Ramps; Pretty Polynomial Patterns
Lab 5: Slippery Slopes
Lab 6: Around in Circles: Claudius Ptolemy's Planetary Epicycles
Lab 7: The Marquis de L'Hopital and His (?) Rule
Lab 8: Boxed In: Pepto-Cola's Secret Formula
Lab 9: Newton's Method at Work
Lab 10: Newton's Method at Play: Complex Calculus and Fractals
Lab 11: Pierre de Fermat and the Area Problem
Lab 12: Taking Chances with Normality
Lab 13: In the Area: Improving on Riemann Sums
Lab 14: Continuity Meets Chaos: Differential Equations, Euler's Method, and Population Growth
Lab 15: Johannes Kepler and the Wine Merchant
Lab 16: Riemann Sums and the Greek Paradoxes
Lab 17: Music to the Ears: Fourier Series and Michelson's Discordant Note
Lab 18: How Long is a Coastline? A Series of Series

TECHNOLOGY GUIDE

The technology guide is not merely a set of instructions. We believe that technology should play only a supporting role to the real business: calculus and its uses. We have based the technology section on two scenarios:

The Keeling curve of carbon dioxide concentration in the atmosphere
The real flight of a soccer ball, considering air resistance

After one-page introductions to both scenarios, we describe how to perform various tasks relevant to calculus, in each case using one or the other scenario as the context. Carrying through an actual substantial example of the use of a particular technology to accomplish a real task seems to us the most motivated and concrete approach to teaching technology. Tell us what you think!

On This Site:

An email newsgroup for instructors, which will contain my suggested solutions to all lab questions, and provide a forum for discussion. If you are an instructor and wish to join the list, send me an email. I will need verification that you are not a student trying to access the solutions!
Specialized software (Geometer's Sketchpad animations, Microsoft Excel sheets, a couple of programs) to support several of the labs.
Links to all supported software and all links appearing in the book.
A description of the spirit in which the labs were written. See below!

Supported Software

The manual contains (calculus-specific and lab-specific) instructions for the following software formats:

Mathematica (multi-platform)
Maple (multi-platform)
Graphmatica (shareware; Windows only)
TI-83 Plus, TI-86, TI-89, TI-92 Plus graphing calculators (see Texas Instruments' graphing calculator web site

For those of you looking for an alternative to Graphmatica for the Macintosh, we highly recommend Curvus Pro.

The Spirit of the Labs (written for the first edition, 1996)

Computer-based laboratories are becoming standard in introductory calculus. Our take on these laboratories concentrates on certain pedagogical goals:

Mathematics emerges from, and interacts with, substantial physical context.
Mathematical knowledge is built by exploration leading gradually to greater precision, and eventually formalism - but only as the last step.
Higher-level problem-solving skills are primary; technical facility is only secondary.
Conversational student-friendly language helps to build mathematical concepts from the student's existing reasoning skills. There is no need to build an "algorithmic processing centre" to handle mathematics in our students' minds.
Historical and cultural episodes enliven the subject, provide different approaches to the discipline, and help integrate mathematical knowledge with the academic spectrum.

Click here for a detailed description of our pedagogical motivations.

To Request an Examination Copy:

Use this link to go to the Houghton Mifflin page for the Ostebee/Zorn calculus book. Our book is listed as "Technology Projects and Lab Manual" among the supplements.

Price: ???

ISBN # 0-618-24751-3

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Last updated: August 27, 2004