of Mathematics and Mathematical Computer
Maple Worksheets for Calc II
to appropriately incorporate technology into the teaching
of mathematics, there are a number of reasonable strategies. The best
strategy for any given school and sequence of courses will depend on
factors specific to the situation including a description of a
typical student, the technological support available, and financial
Louis University, we are using graphing calculators as
the primary technology incorporated into teaching our main calculus
sequence. The easy arguments for graphing calculators are that they
are relatively inexpensive (about the cost of a standard calculus
textbook), moderately easy to learn to use, and are in the students'
hands so that the students have the same set of tools available in
class, for homework, and during quizzes and tests. Hopefully they
will understand that the tools are tools for doing mathematics rather
than tools for working in mathematics classes. Quite simply, we felt
that graphing calculators made the best fit for the needs of the
calculus students we have.
as the students move through the calculus sequence
there are topics where a computer algebra system is much more
effective than a graphing calculator. These topics include symbolic
integration, power series, and numerical solutions to differential
equations. A computer algebra system like Maple can be used
effectively for these topics.
One of the
drawbacks of a program as powerful as Maple is that the
difficulties of learning Maple and learning to use a computer need to
be consciously factored in when planning the course. One pedagogical
strategy is to make using Maple a routine part of the course and
consistently teach use of the program along with the mathematics.
This strategy is not feasible if computer algebra is a secondary
technology that is used only on occasion.
strategy (and the one I have used) is to introduce Maple
through carefully designed worksheets. The worksheets are set up so
that the first time through a student can get through the worksheet
by hitting enter repeatedly. The worksheets include a significant
amount of exploratory text. The exercises tend to ask to student to
repeat the examples from the worksheets with minor modification. I
use the template model because I want them to use the power of the
Maple to look at problems where I could not expect them to produce
the code, but I can expect them to copy and modify a code template,
focusing on the results.
long winded introduction, here are some worksheets I
produced for topics in calculus II. I find it is best to take the
class to the lab for a worksheet, assigning the students to finish it
on their own time. A zipped
archive of all the worksheets is available.
- The preliminary worksheet - Just
Enough Maple- is designed to cover the skills the students need to
run the worksheets and answer the exercises they contain. This
worksheet covers those pesky skills, like copying, pasting, saving, and
printing, that get in the way of getting started on a computer
- The first worksheet -
Integration check - is designed to walk the students through the
process of using Maple to do symbolic integration. This worksheet is
tied to the book we use, giving exercises that refer back to specific
pages. Unless you use Ostebee and Zorn, you will want to modify this
- The second worksheet - Numeric
Integration - explores the various ways of approximating an
integral with a Riemann sum rule. The student package with Maple
produces pretty pictures of the graph and sum.
- The third worksheet - Error
Bounds for Numeric Integration - Explores the error bounds for the
various means of numeric integration. This involves looking at bounds
for the first four derivatives of a function. There is also Key for Error Bounds for Numeric
Integration, a version of this worksheet with the answers filled in.
- The fourth worksheet -
Animating Taylor Series - is probably the most impressive for
using Maple as a teaching tool. It gives code to animate a series of
Taylor series wrapping down to a function. It makes it much easier to
discuss series as polynomial approximations of functions and to discuss
the interval of convergence of a series.
- The fifth worksheet - Working
with Power Series as Functions - shows how to use Maple to work
with a power series that is defined with sigma notation. It is
noteworthy that Maple can produce closed form equivalents for many
- The two worksheets are of a different nature. They are
intended for use by the instructor, rather than by the class. They are
intended to give templates for producing nice graphics that can be
useful for quizzes and tests. Thus although I use other software for
the introduction to differential equations that is part of calc II, I
have a Maple worksheet for producing slope field
diagrams for quizzes and tests. Similarly, there is a Maple
worksheet for producing graphs of
surfaces of revolution.
worksheets were originally written for Maple V R4 on the
Macintosh platform. They were updated to be compatible with Maple
9.5, but no major conceptual ravision was made.
A revision for Maple 10 is in the works. It should be more
and feedback are appreciated. If you find the worksheets
useful, please e-mail me at firstname.lastname@example.org.
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Last updated 11/21/05