## Additional Clickable Calculus Solutions Posted

Maple

Thirteen Clickable Calculus examples have been added to the Teaching Concepts with Maple section of the Maplesoft web site. The additions include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, and linear algebra. By my count, this means some 97 Clickable Calculus examples are now available.

In the Algebra/Precalculus section, examples of an induction proof, the binomial theorem, and an inverse function have been added. For differential calculus, we've added an example of finding an antiderivative, and two related-rates examples, one of which is a version of the classic "Conical Sand-Pile" problem. For integral calculus, three examples of separable differential equations appear, two of which arise from the standard models: Newton's Law of Cooling, and Logistic Growth.

The three new examples in multivariate calculus (Plane through Three Points, Plane from Point and Normal, and Plane Containing a Direction and Two Points) are taken from the "lines and planes" section that generally opens the typical course in this subject. The solutions given use the expected vector methods, algebraic methods, or a task template. However, in Maple 17 there are new commands for defining and manipulating lines and planes, commands that have been fully integrated into the Context Menu system. For an illustration of how standard exercises from this section of the multivariate calculus course can be solved with these new tools, see the Tips and Techniques article avaialble here in the Maple Application Center.

The final addition, in linear algebra, shows how to simultaneously diagonalize two symmetric real matrices A and B, one of which is positive definite, and then details the connection to the generalized eigenvalue problem . The algorithm used starts with finding a Cholesky decomposition of the positive-definite matrix, and is taken from the text Numerical Analysis, 3rd edition, by Melvin J. Maron and Robert J. Lopez, Wadsworth, 1991. ﻿