MAPLE~ Lets Learn!

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~MAPLE~

Maple is a symbolic and numeric computing environment, and is also a multi-paradigm programming language.

Developed by Maplesoft, Maple also covers other aspects of technical computing, including visualization, data analysis, matrix computation, and connectivity.

A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation.

Examples of Maple code

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

Integration[edit]

Find

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

.

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

Answer:

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

Determinant

Compute the determinant of a matrix.

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

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

LinearAlgebra:-Determinant(M);

bz-cy+3ay-2az+2xc-3xb

Series expansion

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

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

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

Solve equation numerically[edit]

High order polynomial equation

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

 fsolve(f)

 -1.097486315, -.5226535640, 1.099074017

Solve equation set[edit]

 f := (cos(x+y))^2 + exp(x)*y+cot(x-y)+cosh(z+x) = 0:

 g := x^5 - 8*y = 2:

 h := x+3*y-77*z=55;
                    
 fsolve( {f,g,h} );

 {x = -1.543352313, y = -1.344549481, z = -.7867142955}

Plotting of function of single variable[edit]

Plot $x\cdot \sin(x)$ with $x$ ranging from -10 to 10

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

Plotting of function of two variables[edit]

Plot $x^{2}+y^{2}$ with $x$ and $y$ ranging from -1 to 1

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

Animation of functions[edit]

animation of function of two variables

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);

2D bell solution

animation of functions of three variables

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

3D animation of function

Fly-through animation of 3-D plots.^[12]

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]);

Maple plot 3D fly-through

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