Maple via Calculus: A Tutorial Approach by Robert J. Lopez PDF

By Robert J. Lopez

Modern software program instruments like Maple have the aptitude to change notably the best way arithmetic is taught, realized, and performed. Bringing such instruments into the study room in the course of lectures, assignments, and examinations implies that new methods oflooking at arithmetic can becomepermanent furniture ofthe curriculum. it's common entry that might make a software-based method of arithmetic turn into the norm. In 1988, with NSF investment lower than an III supply, I had the chance to deliver Maple into the calculus school room at Rose-Hulman Institute of know-how. when you consider that then a brand new curriculum according to the provision ofcomputer algebra structures has advanced at RHIT and in my very own classes. This quantity encompasses a checklist of a few of the insights won into pedagogy utilizing Maple in calculus. The actions and ideas captured in those Maple worksheets mirror thoughts in calculus imple­ mented in Maple. there's an overt message to the reader that includes with it a facet influence. although, it's attainable that for one reader the aspect impact is the message and the message is the part impression! I had meant to place prior to my viewers examples extracted from my Maple dependent curriculum to appeal to a much wider popularity ofthe merits of constructing a working laptop or computer algebra approach develop into the foundation of a revised calculus syllabus. by way of examples I had was hoping to illustrate the "rightness" of utilizing software program instruments for educating and studying calculus.

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Extra resources for Maple via Calculus: A Tutorial Approach

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5 ° 0",5 From the graph we see that f (x) is not a monotone function. To "invert" f (x), we will have to select a monotone portion and work with that new function. For simplicity, let's choose the branch for which x is nonnegative. If f (x) is the function with ordered pairs (x, f (x) ), then the inverse function has ordered pairs (J (x), x). We can exploit this relationship and parametrically plot both f (x) and its inverse 9 (x) before doing any of the algebra needed for actually finding 9 (x).

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. Ping y and yy to verify these claims: • y; • yy; 16 2 22 51 --x --x+15 15 5 Unit 5: Conic Through Five Points Five points determine a conic. If you pick five points in the plane, what is the resulting conic that interpolates those points? The general form of the quadratic expression that determines a conic is ax 2 + bxy + cy2 + dx + ey + I = (2) 0 There are 6 constants, not 5.

X + x-I )2 -1 + x x 2 + x-I 1 F3:= - 2 - x+5 1 F4:=- F2:= x-3 The astute reader will notice, perhaps, that the quadratic factor in the example above is actually factorable over the reals. Indeed, • solve(x~2 + x - 1, X); 1 1 1 1 --+-vs ----VS 2 2 ' 2 2 This raises a question among Electrical Engineers, for example, who prefer that partial fraction decompositions be performed over the complex field so that all factors are linear! Can Maple be induced to factor a polynomial into linear factors over the complex number field?

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