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Slightly Inclusive
Calculus Resources
Contents
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Description.
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Course Design.
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Lectures.
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Labs.
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Archive of the whole site.
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Future Plans.
This site contains both print and Braille/Nemeth versions of lectures, labs,
and other materials I prepared for a first semester calculus class in
Spring, 2001. Because one of the students in that class happened to be
blind, I ended up preparing several hundred pages of course materials in
print and in Braille, and making them available to the students. As often
seems to happen, what started out as an accommodation to the special needs of
one student turned out to be a useful resource for all the students. The
purpose of this site is to share the materials I prepared and my experiences
in the class with others. Possible audiences and uses include
- Students or faculty looking for a concise summary of the high points of
a first semester calculus course, either in print or in Braille format.
These folks can take a look at what's on this site and see if it provides a
useful second opinion to their current texts.
- Other faculty who find themselves in my position of trying to teach
effectively to an audience including blind or visually impaired students.
For these people, I'll try to share briefly what I learned about this, with the
warning that I'm not an expert at all.
- The material at this site can be freely used and modified by anyone
wishing to use the same tools I used. If, like me, you suddenly find
yourself needing to prepare a lot of course material in Braille, then you
might be able to save some labor by using or modifying something here.
I'm still gathering the material for this site; I hope to have it in fairly
finished form by the end of August, 2002.
Currently available files are listed below. If you're confused by your
choices, take a look at the
discussion of file formats.
This document is a discussion of the course and
of how I modified it to work for a mixed audience of sighted and blind
students. It includes information on technologies available for sighted and
blind mathematicians to exchange text and figures, and it ends with a few
links to sites and people I found helpful.
This really amounts to a short book on the basics of calculus. I've
divided it into 8 sections. The order of the material is based on the text
we were using, Larson, Hostetler and Edwards' Calculus With Analytic
Geometry.
- Preliminaries. This is just here for completeness. It's my
course syllabus and some comments on academic integrity at Earlham.
Braille,
PDF,
LaTeX,
LaTex without figures.
- Introduction. This lays out the basic ideas of calculus, and
reviews algebraic and trigonometric background.
Braille,
PDF,
LaTeX,
LaTex without figures.
- Limits. The first basic idea of the calculus.
Braille,
PDF,
LaTeX,
LaTex without figures.
- Derivatives. The tool that lets one compute slopes.
Braille,
PDF,
LaTeX,
LaTex without figures.
- Graphing. How to use derivatives as a tool in plotting functions.
Braille,
PDF,
LaTeX,
LaTex without figures.
Also included in this section is a
Maple worksheet showing how
changing one's window on a complicated function changes one's interpretation
of that function.
- Integrals. The tool that lets one find the areas under curves.
Braille,
PDF,
LaTeX,
LaTex without figures.
- Logs and Exponential Functions. Using all our tools on a new
class of functions, and how integrals can actually help us to define logs
and exponential functions.
Braille,
PDF,
LaTeX,
LaTex without figures.
- What's Next? A teaser showing the idea of Taylor series, and why
you might want to keep doing math.
Braille,
PDF,
LaTeX,
LaTex without figures.
We had roughly weekly lab sessions aimed at helping students discover as
much of calculus as possible by themselves.
- Introduction to Maple.
Braille,
PDF,
LaTeX,
LaTeX without figures.
There's also a Maple worksheet,
Tim's Maple Intro.
- Limits. An introduction to the modern notion of limits, and an
investigation of how Archimedes used a related idea to approximate pi.
Braille,
PDF,
LaTeX,
LaTeX without figures.
- Tangents. How one might use limits to compute the slopes of
tangent lines to curves.
Braille,
PDF,
LaTeX,
LaTeX without figures.
- Products and Quotients. What are their derivatives?
Braille,
PDF,
LaTeX,
LaTeX without figures.
- Compositions of Functions. What are their derivatives?
Braille,
PDF,
LaTeX,
LaTeX without figures.
- Newton's Method. Using derivatives to approximate the roots of
equations.
Braille,
PDF,
LaTeX,
LaTeX without figures.
- Regression. How derivatives help us fit lines and curves to data.
Braille,
PDF,
LaTeX,
LaTeX without figures.
- Area Functions. Conjecturing and understanding the Fundamental
Theorem of Calculus.
Braille,
PDF,
LaTeX,
LaTeX without figures.
- Approximating Areas. Using rectangles and trapezoids to
approximate the areas under curves, and discovering Simpson's Rule.
Braille,
PDF,
LaTeX,
LaTeX without figures.
This lab also included a
Maple Worksheet.
Finally, for anyone really wishing to use this material in a class, I have an
archive in .tar.gz format containing
this entire site. This has not only the files listed above, but also
- Snapshots of all the figures in .wmf and .eps format.
- The Maple worksheets used to prepare those figures I couldn't make
within Scientific Notebook (i.e., those needing to combine text and
graphics).
For the moment, that's all I have. Other material I prepared as part of
the class included
- Solutions to all the labs.
- Homework problems and their solutions.
- Tests and their solutions.
Some of this material went away as a result of ill-conceived system
maintenance on my part. I hope to get the rest up here soon. Anyone
needing this material before it makes it to this site should
contact me.
I'm putting this site up as it is and am going on vacation; but when I
get back, I want to look at how I can make it work well both for sighted and
blind users. I'm not a web designer; I hope people with suggestions on how
to make this page work better for all its target audiences will
send me mail.
Another place I need advice is whether there is a good way to make the
figures in these notes available over the web to blind users. Are there
graphics formats that people can use to read plots of curves, and things of
that sort? If so, then I'd like to make the plots here accessible to
people. Could anyone knowing about this please
write me with
advice?
I hope it's obvious that any other comments and suggestions are welcome.
I'm offering this material freely in the hope that it may help someone else;
I'd be more than happy to make whatever modifications I can to make it more
useful.
Tim McLarnan,
Tremewan Professor of Mathematics
Earlham College,
Richmond, IN 47374 USA
Write me
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