With the addition of ten new Clickable-Calculus examples to the Teaching Concepts with Maple section of the Maplesoft website, we've now posted 63 of the 154 solved problems in my data-base of syntax-free calculations. Once again, these examples and associated videos illustrate point-and-click computations, but more important, they embody the pedagogic message of resequencing skills and concepts.
Instead of having students learn and master computational skills that are then used to manipulate and explore concepts in the hope that the concepts will be absorbed, the idea of resequencing is to implant the concept first, using technology to do any "heavy lifting" and to introduce the necessary manipulative skills afterwards, when their role is more readily apparent. The obstacle to this approach to using technology in the classroom would be the need to master the tool first, if the tool were not itself transparent. And that's where "syntax-free" computing comes to the aid of the pedagogical approach of resequencing skills and concepts.
Look for this reorganization in the newest ten examples posted to our website. There are two new Algebra/Precalculus examples, one for solving a quadratic equation, and one for exploring the parameter-dependence of the zeros of a polynomial. Two new examples appear in the Trig section, one being a linear trig equation that has to be converted to a quadratic in order to solve, and the other is an equation that turns out to be an identity.
In differential calculus, there's now an example showing how to apply the limit-definition of the derivative to obtain the derivative of the square-root function, and an example showing how to obtain graphs of a function and its first two derivatives.
In integral calculus, we've added the Riemann-sum calculation of the definite integral of x sin(x), integrated over the interval [a, b]. By forming and evaluating the limit of a Riemann sum, the connection between area under a curve and an antiderivative is illustrated.
We've also added a second problem in the "lines-and-planes" section of the typical multivariate calculus course. This example is that of finding the vector equation for a line between two points. For linear algebra, we've added an example illustrating the meaning and calculation of eigenvalues and eigenvectors.
Finally, in vector calculus, there's now a problem illustrating how to find a scalar potential for a conservative vector field. There's a Context Menu option for this, but the underlying technique of evaluating a line integral is implemented both with Maple's LineInt command and from first principles.