Maple

My list of problems solved with Clickable-Calculus syntax-free techniques now numbers 154, spread over eight subject areas. Recently, Maplesoft posted to its website 44 of these problems, along with videos of their point-and-click solutions. Not only do these solutions demonstrate Maple functionalities, but they also have a pedagogic message, that is resequencing skills and concepts. They show how Maple can be used to obtain a solution, then show how Maple can be used to implement the calculations stepwise, a process that injects insight and stresses concept development before it worries about building manipulative skills.

All the 154 Clickable-Calculus examples have been recorded. An additional nine are being added to the Teaching Concepts with Maple section of the Maplesoft website. The initial 44 were distributed across the six subject areas of Differential Calculus, Integral Calculus, Multivariate Calculus, Linear Algebra, Differential Equations, and Vector Calculus. This next ten introduce two new categories, that of Algebra and Precalculus, and Trigonometry. There are two each in these new categories.

The first Algebra/Precalculus problem is a solution of a simple one-variable linear equation; it's solution illustrates both the new Smart Pop-Ups and the older Equation Manipulator. Both of these tools implement a stepwise solution, thereby carrying out the pedagogic paradigm of "resequencing." This paradigm is continued in the second problem in this category, namely, the solution of a system of two linear equations in two unknowns. Here, a graphical solution is investigated, then three different stepwise solutions are given.

The two trig problems are trig equations that are quadratic in a trig function. In the first problem, just one trig function appears; but in the second, two different ones appear. Of course, graphical and numeric solutions come first, but then analytic solutions, and a general solution are also given. Finally, a stepwise solution aided again by Maple's new Smart Pop-Up technology demonstrates the traditional "by-hand" approach found in textbooks.

In differential calculus, we've added a limit problem that illustrates the use of the Limit Methods tutor for obtaining a stepwise solution. In integral calculus, we've added a problem on Riemann sums and the connection between area and antiderivatives. This problem illustrates the Riemann Sum tutor and the RiemannSum command embedded in a task template. In differential equations, we classify an ODE with a task template that implements the DEtools odeadvisor command. In linear algebra, extracting a maximal linearly independent set (i.e., a basis) from a set of vectors is done with a task template that implements the Basis command from the LinearAlgebra package. Finally, in vector calculus, we show how to find a directional derivative stepwise, and with the DirectionalDiff command from the VectorCalculus package.

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