Two early attempts at programming Maxima functions. I’d love to hear your comments about how to make these work better. Many thanks to the online community from whom I learned how to get this far!
The script is given at the bottom of this post. Copy and paste into a file (in your working directory) called Riemann.mac, and then load into Maxima using
load(“Riemann.mac”);
/* Two Maxima functions for introductory integral calculus
(c) 2016, themaximalist.org *//* RiemannSum
fn is the function to be integrated on the interval [a,b]
n rectangles
opt specifies:
0: left endpoints
1: midpoints
2: right endpoints
*/RiemannSum(fn,a,b,n,opt):=
block([xx,s],
xx(i,n):= a+(i+opt/2)*(b-a)/n,
s: sum(ev(fn,x=xx(i,n)),i,0,n-1)*(b-a)/n,
float(s))$
/* RiemannRectangles to Draw rectangles
fn is the function to be integrated:
on the interval [a,b]
n rectangles
opt specifies:
0: left endpoints
1: midpoints
2: right endpoints
*/load(draw)%
RiemannRectangles(fn,a,b,n,opt):=
block([xi,xx,rects,wxd],
xi(i,n):= a+i*(b-a)/n,
xx(i,n):= a+(i+opt/2)*(b-a)/n,
rects(n):=makelist(rectangle([xi(k,n),0], [xi(k+1,n),ev(fn,x=xx(k,n))]),k,0,n-1),
wxd(n):=apply(wxdraw2d,
append([xrange=[a-(b-a)/4, b+(b-a)/4],color=blue],
rects(n),
[transparent=true, explicit(fn,x,a, b)]
)
),
wxd(n)
)$
The MaximaList 