quadrature_trapezoid

quadrature_trapezoid, demonstrates how the integral of a function f(x) can be estimated using the trapezoid rule.

The notes:

• quadrature_trapezoid.pdf
• quadrature_trapezoid.tex

Scripts and functions:

• decrease_h.m, look at the error when a single trapezoid is used, and the interval size decreases.
• hump.m, evaluates the hump() function.
• hump_adapt.m, adaptively estimates the integral of hump() over [0,2].
• hump_int.m, returns the definite integral of hump() over [a,b].
• hump_trap.m, 11 estimates of the integral of hump() over [0,2], using T1, T2, T4, ..., T1024.
• roedder.m, evaluates the roedder() function.
• roedder_int.m, returns the definite integral of roedder() over [0,2pi].
• t2_minus_t1.m, estimates the error in integration by comparing T1 and T2 estimates for the integral of exp(x).
• trap_adapt.m, uses adaptive trapezoidal quadrature.

Text files:

• decrease_h.txt
• hump_adapt.txt
• hump_trap.txt
• hump_trap_pseudocode.txt
• t2_minus_t1.txt
• trap_adapt_pseudocode.txt

Images:

• esin.png, a plot of the esin() function y=exp(x)*sin(x).
• hump.png, a plot of the hump() function.
• pnc_tower.png, the shape of Pittsburgh's PNC tower suggests a trapezoid.