Maple via Calculus: A Tutorial Approach by Robert J. Lopez
By Robert J. Lopez
Modern software program instruments like Maple have the capability to change noticeably the way in which arithmetic is taught, realized, and performed. Bringing such instruments into the school room in the course of lectures, assignments, and examinations signifies that new methods oflooking at arithmetic can becomepermanent furniture ofthe curriculum. it really is common entry that would make a software-based method of arithmetic develop into the norm. In 1988, with NSF investment less than an III furnish, I had the chance to deliver Maple into the calculus school room at Rose-Hulman Institute of expertise. considering that then a brand new curriculum according to the supply ofcomputer algebra platforms has developed at RHIT and in my very own classes. This quantity features a list of a few of the insights received into pedagogy utilizing Maple in calculus. The actions and concepts captured in those Maple worksheets mirror thoughts in calculus imple mented in Maple. there's an overt message to the reader that consists of with it an aspect impact. even though, it truly is attainable that for one reader the facet impact is the message and the message is the aspect impact! I had meant to place sooner than my viewers examples extracted from my Maple established curriculum to appeal to a much broader attractiveness ofthe advantages of constructing a working laptop or computer algebra method develop into the foundation of a revised calculus syllabus. through examples I had was hoping to illustrate the "rightness" of utilizing software program instruments for educating and studying calculus.
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8 Unit 12: Teaching the Definite Integral 51 A typical reaction at this point would be the creation of graphs that show 100, 1000, and even 5000 rectangles. Thus, • leftbox(f, x = O.. 8 One good picture is worth a thousand words. This single picture captures the conceptual basis for the definition of the Riemann integral we seek to introduce. But in addition to these pictures, Maple has tools that help in the analytical study of the definite integral as area under a curve. Corresponding to the leftbox ( rightbox ) command is the leftsum ( rightsum) command that will create the analytic representation of the areas of the approximating rectangles.
Thus, • q3 := op(3, yl) i 2 q3 := - 17 J- 25 x 2 + 50 x + 60 We have assigned to the tag q3 a multiple of the square root we need. We can play the nops/op game further if we need to, but here we are going to solve the equation q3 = 0 for x. The constant multipliers in front of the square root will not matter. 843908891 We have found the desired delimiters of the domain of the branches of the implicitly defined function y ( x) . Unit 7: Inverse Functions Here is a lesson designed to illuminate the notion of an inverse function.
Y; ax 2 + bx + c Now for the subtle approach. Recall that the Maple subs command creates a copy of the object into which the substitution is being made. The target expression itself does not change. Hence: 22 • Maple via Calculus: A Thtorial Approach yy := subs(q, y); 16 2 22 yy := - - x - - x 15 15 + -51 5 We made three substitutions into the expression for y. These substitutions are the three rules sitting in the set q. By giving the name yy to the result of the substitution command, we have the desired interpolating parabola tagged as yy and the original parabola (1) is still in its general form.