arithmetic

arithmetic, shows how arithmetic on a computer can break many mathematical rules.

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1070_2019/arithmetic/arithmetic.html

The notes:

• arithmetic.pdf
• arithmetic.tex

Scripts:

• cos_taylor.m, evaluates the Taylor series for cos(x).
• cos_taylor_test.m, compares the Taylor series for cos(x) to cos(x) itself.
• patriot.m, looks at how a small error in the Patriot missile eventually becomes a big one.
• pi_series1.m, evaluates a series for pi.
• pi_series2.m, evaluates a series for pi until better accuracy than 22/7 is achieved.
• pi_series3.m, evaluates a series for pi until better accuracy than 355/113 is achieved.
• plot_poly.m, plots three versions of the same formula: p1(x) = x^7-7x^6+21x^5-35x^4+35x^3-21x^2+7x-1; p2(x) = ((((((x-7)*x+21)*x-35)*x+35)*x-21)*x+7)*x-1; p3(x) = (x-1)^7.
• rule_breakers.m, quickly calculates some numbers that characterize limits of computational accuracy.
• tan_difference.m, tries to estimate the derivative of tan(x) using an ever decreasing finite difference stepsize.

Text:

• patriot.txt
• pi_series1.txt
• pi_series2.txt
• pi_series3.txt
• rule_breakers.txt
• tan_difference.txt

Images:

• cos_taylor_test.png, a Taylor series for cos(x) fails for large x.
• plot_poly.png, three ways to evaluate the same polynomial give different results.
• tan_difference.png, how the error in a difference estimate for the derivative of the tangent function blows up.
• trident.png, a Trident missile fails its test.