AUTOMATED LEARNING ASSISTANT FOR VECTOR CALCULUS: INTEGRATION OVER PLANAR

Abstract

This paper presents a computer learning assistant ILMEV (Interactive Learning -Mathematica Enhanced Vector calculus), that helps students understand the theory and applications of integration in vector calculus. No Computer Algebra System (CAS) has algorithms powerful enough to automatically solve all but the most elementary problems of this type that appear in textbooks. To overcome this, we implemented ILMEV, which can compute closed form solutions to many two dimensional textbook examples without substantial user intervention. ILMEV succeeds because it contains simplified Cylindrical Algebraic Decomposition(CAD) algorithms for reducing the integrals appearing in vector calculus to sums of iterated integrals which Mathematica can then compute. The typical presentation of this material in textbooks was reorganized and a model was created to make it suitable for developing ILMEV. The important educational guiding principles (interactivity, visualization, experimentation, White and Black Box Principle, multiple representations and step-by-step technique (with some explanations)), and an easy to use interface were also incorporated in ILMEV.

Keywords

• d: computer algebra
• vector calculus
• cylindrical algebraic decomposition algorithm (cad)
• computer algebra system pedagogical guiding principl