An Interactive, Online, Single-Variable Calculus Text

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An Interactive, Online, Single-Variable Calculus
Text http//www.math.duke.edu/education/calculuste
xt
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Background Project CALC

• Calculus As a Laboratory Course
• Funded by NSF, 1988-1995
• First edition textbook/lab materials published by
  Houghton Mifflin (D. C. Heath), 1996
• Online lab modules developed as the Connected
  Curriculum Project, 1993-2001
• Materials still in use at some colleges

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Project CALC Awards
Also named A Program That Works by Project
Kaleidoscope, 1993
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Philosophy
Central idea of calculus
(differential),
(integral), using very small runs. The
derivative is developed by zooming in to a very
small run. The integral is developed as
solution to an initial value problem
via Eulers Method.
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Features of the Text

• guided discovery learning
• real-world applications as motivators
• making connections topics are not isolated
• writing as window into students thinking
• high expectations of students
• emphasis on students checking their own work

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The Second Edition

• Our desires
• Make the text flexible, hyperlinked, interactive,
  richly illustrated, and available at low cost
• Demonstrate feasibility of an online text
• Support NSF grant to MAA for the Online Books
  Project
• Objective Redesign and redevelop the textbook
  entirely online
• Publication MAA will publish the online text in
  2010 (available free for AY 09-10)

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Issues

• Navigation
• Directory and file structure
• Design
• Illustrations
• Interactivity
• Technical requirements
• Presentation of mathematics

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Presentation of Mathematics

• XHTML files for main body of text
• HTML files for front page, tables of contents,
  pop-ups
• MathML formulas, created by WebEQ, in main pages
• asciiMathML formulas in pop-ups and in main pages
• Flash applets, javascript pop-ups, and Maple,
  Mathcad, and Mathematica CAS files for
  interactions

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Table of Contents

1. Relationships
2. Models of GrowthRates of Change
3. Initial Value Problems
4. Differential Calculus and its Uses
5. Modeling with Differential Equations

1. Antidifferentiation
2. The Fundamental Theorem of Calculus
3. Integral Calculusand its Uses
4. Probability and Integration
5. Polynomial and SeriesRepresentations ofFunctions

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Sample Pages

• Front Page
• Chapter Tables of Contents (Ch. 4)
• Chapter openers - About this Chapter (4.0)
• Text pages (4.4.1)
• Activity including Flash applet (2.4.3)
• Activity including CAS files (6.2.1)

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Sample Pages

• Checkpoints (6.1.2)
• Exercises (5.1)
• WeBWorK Exercises (4.5)
• Making connections (6.3.4)
• Chapter Summary (Ch. 3)
• Projects (Ch. 4)
• Projects (Ch. 7)

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Previews of Coming Attractions

• Routine exercises in WeBWorK
• Instructors Guide by Sr. Barbara Reynolds
• All mathematical diagrams in consistent style in
  SVG, Troy Henderson
• Sections on use/misuse of CAS and on convergence
  of series to the right function
• More projects
• Enrichment material (applications, theory)

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Classroom Test Sites
Class tested at Hood College, 2006-2009
New test sites, 2008-09
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Online PREP Workshop

• Title Calculus Online and Interactive
• Dates June 22-26, 2009
• Presenters
• Lang Moore and David Smith, Duke University
• Kimberly Tysdal, Hood College
• Maria Andersen, Muskegon Community College
• Mike Gage, University of Rochester
• Workshop web page http//www.math.duke.edu/educat
  ion/prep09/

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An Interactive, Online, Single-Variable Calculus
Text http//www.math.duke.edu/education/calculuste
xt