Electronic Proceedings of the Seventh Annual International Conference on Technology in Collegiate MathematicsOrlando, Florida, November 1720, 1994Paper C025
Modified Integration with MAPLE 
WeiChi Yang
Department of Mathematics & Statistics
Radford University
Radford, VA 24142
USA
Phone: (540) 8315232
Fax: (540) 8316452
wyang@mathstat.ms.runet.edu
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It has been known that computer algebra system such as Maple can be used to
help students learning and researchers making new mathematical conjectures.
In this paper, I will demonstrate how we could make use the symbolic and
numeric computation capacity of Maple and infinite matrices to integrate
a monotone function with singularity such as f(x) =1/sqrt(x) if x is not
equal to 0 and f(0) = 0. Traditional methods such as Riemann sum, trapezoid,
and Simpson's rules usually divide interval into equally spaced
subintervals. But for a function such as f it is more efficient to divide
the interval [0,1] unevenly, say smaller to the left than to the right,
because the function is steeper to the left. We shall also look at the
case when a function is highly oscillating, such as f(x) = (1/x)*sin(1/x)
for x is in (0,1], and f(0) = 0. We will see how the infinite matrices
together with the trapezoidal rule are implemented in Maple without using
the method of transformation.
Being the chair of the international program committee, I will also
preview the First Asian Technology Conference in Mathematics, Singapore,
December 1821, 1995.
Keyword(s): Maple, calculus, integrals