An Online Calculus Text for the iPadhttps://www.math.duke.edu/education/calculustext-rev11/

04/21/23 An Online Calculus Text for the iPad 2

Philosophy

riseslope

run

rise slope run

( ),dy

f xdx

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 Euler’s Method.

( ) 0,y a

04/21/23 An Online Calculus Text for the iPad 3

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

04/21/23 An Online Calculus Text for the iPad 4

Table of Contents

1. Relationships2. Models of Growth:

Rates of Change3. Initial Value Problems4. Differential Calculus

and its Uses5. Modeling with

Differential Equations

6. Antidifferentiation7. The Fundamental

Theorem of Calculus8. Integral Calculus

and its Uses9. Probability and

Integration10.Polynomial and Series

Representations ofFunctions

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Classroom AdoptionsClass tested at 2006-2013

Now with all students using iPads

Additional sites, 2008-2013

04/21/23 An Online Calculus Text for the iPad 6

Adaptation for iPad from online text at http://calculuscourse.maa.org/

Replaced all XHTML pages with HTML

Replaced all asciiMathML with MathJax

Replaced asciiMathML popup calculator with pure javascript + MathJax version(thanks to Peter Jipsen)

Replaced all Maple, Mathematica, Mathcad, and Flash interactions with Sage interact cells (thanks to Jason Grout, John Travis, Karl-Dieter Crisman, Dan Drake, Ira Hanson …)

04/21/23 An Online Calculus Text for the iPad 7

An Online Calculus Text for the iPad

https://www.math.duke.edu/education/calculustext-rev11/