Maple worksheet to examine (symbolically compute and plot) the relative condition number of some simple single-variable functions. C.G. (9-99) original version C.G. (5-07) .mw version Restart the server. restart; Procedure to compute the relative condition number of f(x), a function or expression. cond := proc ( f, x ) abs( x * diff(f,x) / f ) end;

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Plot f(x) = sin(x). plot( sin(x), x=0..10, title=`sin(x)`, color=red );

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Determine the relative condition number of f(x) = sin(x). 'cond(sin(x),x)' = cond(sin(x),x);

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Plot the relative condition number of f(x) = sin(x) as a function of x. plot( cond(sin(x),x), x=0..10, 0..10, discont=true, title=`cond(sin(x),x)`, color=red );

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Plot f(x) = J0(x) (Bessel function). plot( BesselJ(0,x), x=0..10, title=`BesselJ(0,x)`, color=red );

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

Determine the relative condition number of f(x) = J0(x). 'cond(BesselJ(0,x),x)' = cond(BesselJ(0,x),x);

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Plot the condition number of f(x) = J0(x) as a function of x. plot( cond(BesselJ(0,x),x), x=0..10, 0..10, discont=true, title=`cond(BesselJ(0,x),x)`, color=red );

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The Bernoulli generating function. f := x -> x / ( exp(x) - 1 ) ;

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Plot the Bernoulli generating function. plot( f(x), x=-10..10, y=0..10, discont=true, title=`f(x)`, color=red );

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Determine the relative condition number. 'cond(f(x),x)' = simplify( cond(f(x),x) );

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Plot the condition number. plot( cond(f(x),x), x=-10..10, discont=true, title=`cond(f(x),x)`, color=red );

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