Maple worksheets for Linear Algebra


As part of an ILI grant from the NSF to Saint Louis University, we developed material to extend some of the teaching methods of calculus reform to upper level courses. One of the sub-project is to teach linear algebra in a computer classroom,using the computer whenever it seems appropriate for the material to be taught. We are using the computer algebra system Maple as the base tool on the computer.

Depending on what the instructor thought most effective for a particular class and section of material, the worksheets have been designed in several different models. I will describe them as the classroom activity model, the teacher demonstration model, and the Maple feature demonstration model.

Maple worksheets for Linear Algebra I

The classroom activity model for worksheets -

Classroom Activity worksheets for Linear Algebra I

These worksheets follow, section by section, the material in the text "Linear Algebra, Ideas and Applications" by Richard Penney, published by Wiley Press. The worksheets vary from, a straightforward adaptation of the material in the "On Line" sections of the book to use Maple and a worksheet model, to worksheets that develope supplemental material that the instructor thought appropriate at that point in the course.


The teacher demonstration model for worksheets -

Teacher Demonstration worksheets for Linear Algebra I

The Maple feature demonstration model for worksheets -

Maple feature demonstration worksheets for Linear Algebra I

Maple workshhets for Linear Algebra II

The second course we teach in Linear Algebra is more abstract focusing more heavily on proofs and appropriate inclusion of computer algebra is less clear.

Two worksheets were created for this class using the Maple feature demonstration model. One of them looked at creating matrices with specified Jordan and Rational Blocks, and finding Jordan and Rational bases for a matrix. This was intended to help the students work with nontrivial examples to be able to follow the proofs in the study of canonical forms. The second worksheet of this type looked at the Maple commands for doing Gram Schmidt orthogonalization.

A block of 3 worksheets was developed for the study of orthogonal polynomials as a case study of inner product spaces. It was assumed that the students had already seen inner product spces in the context of Fourier series. The worksheets have the students work through how different inner products produce a different definition of close and what that means in terms of a function space. The first worksheet compares Legandre Polynomial approximation against the more familist Taylor series approximation. The second worksheet compares Chebyshev Polynomial approximation against Legandre Polynomial approximation. The third worksheet worksheet compares Jacobi Polynomial approximations with different weight functions.

Comments and feedback are appreciated. If you find the worksheets useful, please e-mail me at

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Last modified: August 11, 1999