Maple
Maple : . , () (). >.
26 ( A Z z), 10 (0 9) 32 . , , . Maple .
, . ( ) . , , , .
. , .
Maple :
+ - | -> - | |
- - | < - | |
* - | > - | |
/ - | = - | |
**, ^ - | <= - | |
! | >= - | |
. | <> - | |
:= - | or | |
and |
aple . - .
aple . ,
with (name),
name .
, .
( ):
Sin, cos, tan, sec, csc, cot, arcsin, arcos, arctan.., exp...,sqrt
ilog10, ilog - (ilog10(25)=1);
ln, log, log10, sqrt, abs.
:
factorial(n) !;
iquo (a,b) b;
irem (a,b ) b;
igcd(a,b ) - . ;
lcm ;
:
ceil >=x;
floor <=x;
frac ;
trunc , ;
round ;
signum (-1, 1);
aple :
1. ( :=) :
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> m:=sqrt(x^2+y^2);
> x:=3: y:=4: m;
2. C à :
name:=(x,y,) à expr;
:
name(x,y), x,y .
:
> restart;
> x:=o;y:=0;
> m:=(x,y)->sqrt(x^2+y^2);
> m(3,4);
> m(0,1);
> [x,y];
3. C unapply :
name:= unapply(expr, var1, var2,..);
:
> restart;
> fm:=unapply(sqrt(x^2+y^2),x,y);
> m:=fm(3.,4);
, .. evalf ( eval).
: evalf(expr, n) expr , n . n , n=10.
> evalf(m);
> evalf(m,2);
m=
, Digits:
> Digits:=3;evalf(m);
Maple . , , plot plot3d. , , . Maple.
plot.
:
plot(function, variable_x {,variable_y}{option});
function , ;
variable_x , ;
variable_y , ;
option , .
.
:
- numpoints ( =49);
- color ;
- title (, title=string);
- coords , 15 . ;
- axes (frame - , boxed - , normal - , none );
- thickness ;
- xtickmarks, ytickmarks , .. ;
- style (line , point );
- scalling (constrained , unconstrained - );
- size ;
- symbol (box - , cross - , circle - , point , diamond - );
- titlefont ;
- labelfont (labels) ;
- view=[A,B] , , A=[xmin..xmax], B=[ymin..ymax].
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1. sin(x)/x -15..15 (. . 1).
> plot(sin(x)/x, x=-15..15,color=red, title="");
.1. sin(x)/x
2. sin2(x) c , x=-5..5,y=0..0.5, (. . 2).
> fun:=sin(x)^2;
3. sin(x),sin(x)/x, sin(x3/100) (. . 3).
> plot([sin(x),sin(x)/x,sin(x^3/100)],x=10..10, color = [black,blue,red],style=[line, line, point]);
.3.
Maple plot3d. :
plot3d(expr1, x = a..b, y = c..d, p),
plot3d(f, a..b, c..d, p),
plot3d([exprf, exprg, exprh], s = a..b, t = c..d, p),
plot3d([f, g, h], a..b, c..d, p).
p , .
, z(x,y). .
. h2 (. . 4).
> plot3d(h^2,a=-Pi..Pi,h=-5..5, coords=cylindrical, style =patch, color=sin(h));
.4.
, Maple solve, .
solve(eqn, var);
eqn , ;
var .
, .
> y:=x^2+2*x-3;# eqn
> rez:=solve(y,x);# rez.
> x1:= rez [1];# 1
> x2:= rez [2];# 2
> subs(x=x1, y);#
> subs(x=x2, y);#
, NULL. fsolve, .
fsolve(eqn, var);
eqn , ;
var .
> solve(exp(x)+ln(2*x)-4.2*x);
, , , fsolve.
> fsolve(exp(x)+ln(2*x)-4.2*x);
, solve. . , .
> sys:={3*x1-4*x2-x3=10,6*x1-8*x2-3*x3=19,-x1+x2+x3=-3};
> rez:=solve(sys,{x1,x2,x3});
> subs(rez={x1,x2,x3},sys); #
.
Maple :
Int(f,x)
int(f,x) -
Maple
Int(f,x=a..b, continuous) ;
int(f,x=a..b, continuous) - ;
f ,
x , ,
b .
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continuous .
evalf:
evalf(int(f, x=a..b)).
, int infinity.
:
> restart;
> Int(sin(x)/x, x=0..1.)=int(sin(x)/x, x=0..1.);
> Int(x*exp(-x),x=0..infinity)=int(x*exp(-x), x = 0..infinity);
fn(x) =d fn(x)/ d xn . . Maple6 :
diff(a,x1,x2,,xn) diff(a,[x1,x2,,xn])
Diff(a,x1,x2,, xn) Diff(a,[x1,x2,,xn])
a , f(x1, x2,,xn) , .
Diff diff .
diff(f(x),x) f(x) x. n 1, , diff(diff(f(x),x),y). $.diff(f(x), x$4), x, diff(f(x),x,x,x,x).
:
> Diff(a*x^n,x)=diff(a*x^n,x);
> Diff(sin(x),x)=diff(sin(x),x);
> f(x,y):=cos(x)*y^3;
> Diff(f(x,y),x)=diff(f(x,y),x);
> Diff(f(x,y),x$2,y$2)=diff(f(x,y),x$2,y$2);