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Department of Mathematics and Mathematical Computer Science

Occasional Maple Worksheets for Calc II

(For Maple 9.5)

In trying 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 constraints.

At Saint 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.

Nevertheless, 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.

A second 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.

With that 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 worksheet.
  • 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 worksheet.
  • 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 power series.
  • 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.

The 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 substantial revision.

Comments and feedback are appreciated. If you find the worksheets useful, please e-mail me at
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Last updated 11/21/05

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