Download PDF by R.J. Stroeker, J.F. Kaashoek: Discovering Mathematics with Maple: An interactive

By R.J. Stroeker, J.F. Kaashoek

his e-book grew out of the desire to allow scholars of econometrics get familiar T with the robust suggestions of desktop algebra at an early level of their curriculum. As no textbook on hand on the time met our specifications as to content material and presentation, we had no different selection than to jot down our personal direction fabric. The try-out on a gaggle of eighty first yr scholars was once no longer with out luck, and after including a few useful ameliorations, a similar fabric was once offered to a brand new crew of scholars of comparable measurement the yr after. a few extra alterations have been made, and the ultimate consequence now lies prior to you. operating with desktop algebra programs like Derive, Mathematica, and Maple over a long time confident us of the beneficial clients of laptop algebra as a way of enhancing the student's figuring out of the tough thoughts on which mathematical innovations are frequently dependent. additionally, complicated mathematical ed­ ucation, be it for arithmetic itself or for mathematical facts, operations examine and different branches of utilized arithmetic, can vastly cash in on the big volume of non-trivial mathematical wisdom that's kept in a working laptop or computer algebra method. Admittedly, the very fact continues to be that many a difficult mathematical challenge, reminiscent of fixing a classy non-linear method or acquiring a finite ex­ pression for a a number of parameter crucial, can't simply be dealt with through machine algebra both, if at all.

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Additional info for Discovering Mathematics with Maple: An interactive exploration for mathematicians, engineers and econometricians

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Divide 3175 by 50!. What is the numerator of the resulting (reduced) fraction 7 How many factors 3 does the factorization of this integer contain 7 Use Maple's numer command to obtain the numerator. Then click the right mouse button on this number, after which you can choose the option Integer Factors from the pop-up menu 2 . 2. Determine the time Maple needs to compute 5000!. What takes more time, computing 5000! or 50005000 7 3. (a) Compute log(x) (the logarithm to the base 10) for the numbers x = 56, 123, 5120, and 98765.

But how does this decimal expansion continue? Nobody knows for sure what the billionth decimal digit of 11' is. Nevertheless, it is not a matter of choice, there is only one such digit. Not knowing it is of no great importance, but is does mean that in order to include 11' in our calculations we are forced to make do with only finitely many digits and thus with a inexact, approximate value for 11'. On request, Maple will transform exact values into approximate values, and what is more, we may even choose the number of digits precision Maple should use in its calculations.

In the usual functional terminology, instead of applying the prescription f to x, we have to extract f from the expression f(x). This inverse process therefore has been given the name unapply. > polynomial := unapply(polynomial_expression,x); polynomial := x -+ x7 - x5 +4 The form of the output tells us that here we are dealing with a function prescription. Indeed, we immediately recognize the arrow notation generally used for mathematical functions. The verifications > > type(polynomial_expression,procedure); type(polynomial,procedure); false true 40 Functions and Sequences confirm that polynomiaLexpression is not and polynomial is a procedure.

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