Maple

Procedur

myfac := proc(n::nonnegint)
  local out, i;
  out := 1;
  for i from 2 to n do
      out := out * i
  end do;
  out
end proc;

Funktion

myfac := n -> product( i, i=1..n );

Integration

${\displaystyle \int \cos \left({\frac {x}{a}}\right)dx}$.

int(cos(x/a), x);

Resultat:

${\displaystyle a\sin \left({\frac {x}{a}}\right)}$

Determinant

M:= Matrix([[1,2,3], [a,b,c], [x,y,z]]);

${\displaystyle {\begin{bmatrix}1&2&3\\a&b&c\\x&y&z\end{bmatrix}}}$

LinearAlgebra:-Determinant(M);

Resultat:

${\displaystyle bz-cy+3ay-2az+2xc-3xb}$

Serie expansion

series(tanh(x),x=0,15)

Resultat:

${\displaystyle x-{\frac {1}{3}}\,x^{3}+{\frac {2}{15}}\,x^{5}-{\frac {17}{315}}\,x^{7}}$

${\displaystyle +{\frac {62}{2835}}\,x^{9}-{\frac {1382}{155925}}\,x^{11}+{\frac {21844}{6081075}}\,x^{13}+O(x^{15})}$

Lös ekvation numeriskt

f := x^53-88*x^5-3*x-5 = 0
fsolve(f)

Resultat:

-1.097486315, -.5226535640, 1.099074017

Visualisering av en enkel variabel funktion

plot(x*sin(x),x=-10..10);

Visualisering av en funktion av två variabler

plot3d(2-x-(y^2-x^2)^0.5), x=0..1, y=0..1);

Animation

${\displaystyle f:=2\cdot k^{2}/\cosh(k\cdot (x-4\cdot k^{2}\cdot t))^{2}}$

plots:-animate(subs(k = .5, f), x=-30..30, t=-10..10, numpoints=200, frames=50, color=red, thickness=3);

plots:-animate3d(cos(t*x)*sin(3*t*y), x=-Pi..Pi, y=-Pi..Pi, t=1..2);

M := Matrix([[400,400,200], [100,100,-400], [1,1,1]], datatype=float[8]):
plot3d(1, x=0..2*Pi, y=0..Pi, axes=none, coords=spherical, viewpoint=[path=M]);

Laplace transform

f := (1+A*t+B*t^2)*exp(c*t);

${\displaystyle (1+A\cdot t+B\cdot t^{2})\cdot e^{c\cdot t}}$

inttrans:-laplace(f, t, s);

Resultat:

${\displaystyle {\frac {1}{s-c}}+{\frac {A}{(s-c)^{2}}}+{\frac {2B}{(s-c)^{3}}}}$

inttrans:-invlaplace(1/(s-a),s,x)

Resultat:

${\displaystyle e^{ax}}$

Fourier transform

inttrans:-fourier(sin(x),x,w)

Resultat:

${\displaystyle \mathrm {I} \pi \,(\mathrm {Dirac} (w+1)-\mathrm {Dirac} (w-1))}$

Noter