Computer Algebra and Interpolation: a Lesson Plan

Polynomial interpolation and related numerical analysis questions are used to take users of computer algebra systems from issuing one-liners to writing more complex programs. An alternate use of the outlined lessons is to introduce students to interpolation and acquaint them with splines and numerical differentiation. Constructive symbolic derivations of formulae for polynomial interpolants are presented. Numerical differentiation formulae are derived using them. Necessary background material is introduced. The examples and assignments can be done using any general purpose symbolic manipulator; complete codes using the computer algebra system AXIOM are given.