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

Graphing in Maple

plot(cos(1/2*x)+sin(2*x), x = 0 .. 4*Pi);

If no range is specified, Maple uses the default range -10..10.

plot(sin(t)/(1 + exp(t)^2), t);

Launch the Interactive Plot Builder. Using the Plot Builder, you can easily customize plots before creating them.

plots[interactive](abs(cosh(t/5) - 2) + sin(t^2)/10);

plot3d((1.3)^x * sin(y), x=-1..2*Pi, y=0..Pi, coords=spherical, style=patch);

plot3d([1,x,y], x=0..2*Pi, y=0..2*Pi, coords=toroidal(10), scaling=constrained);

plot3d(sin(x*y), x=-Pi..Pi, y=-Pi..Pi, style=contour);

In some cases, you can provide variable range endpoints.

plot3d(sin(x+y), x = -1 .. 1, y = -1 .. 1);

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(POLYGONS([[0,0,0],[1,0,0],[1,1,0],[0,1,0]], [[0,0,0],[0,1,0],[0,1,1],[0,0,1]], [[1,0,0],[1,1,0],[1,1,1],[1,0,1]], [[0,0,0],[1,0,0],[1,0,1],[0,0,1]], [[0,1,0],[1,1,0],[1,1,1],[0,1,1]], [[0,0,1],[1,0,1],[1,1,1],[0,1,1]]), LIGHT(0,0,0.0,0.7,0.0), LIGHT(100,45,0.7,0.0,0.0), LIGHT(100,-45,0.0,0.0,0.7), AMBIENTLIGHT(0.4,0.4,0.4), TITLE(CUBE), STYLE(LINE), COLOR(ZHUE));

plot an arrow or a vector

with(plots):

Plot a sequence of related arrows.

arrow([seq(<sin(i), cos(i)*cos(7/23*i), sin(7/23*i)>, i=1..23)], axes=FRAMED);

Plot three points with various shapes.

Plot three points with various shapes.Plot three points with various shapes.

a1 := arrow(<0,0,1>, shape=harpoon): a2 := arrow(<0,1,0>, shape=arrow): a3 := arrow(<1,0,0>, shape=double_arrow): a4 := arrow(<1,1,1>, shape=cylindrical_arrow): display(a1, a2, a3, a4, scaling=CONSTRAINED, axes=FRAMED);

Vector/Gradient, Nabla, Divergent, Curl

What is meant by NABLA? Verify the result by hand.

with(VectorCalculus):

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Nabla(x^2+y^2+z^2 );

SetCoordinates( 'cartesian'[x,y,z] );

F := VectorField( <x^2,y^2,z^2> );

Divergence( F );

Divergence();

Del . F;

Nabla . F;

Laplacian( x^2+y^2+z^2, [x,y,z] );DotProduct(Del, F);

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Divergence( (x,y,z) -> <sin(x),cos(y),tan(z)> );

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2OVElQ1VSTEYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUqdW5kZXJsaW5lR0Y6LyUqc3Vic2NyaXB0R0Y6LyUsc3VwZXJzY3JpcHRHRjovJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGOi8lK2V4ZWN1dGFibGVHRjcvJSlyZWFkb25seUdGOi8lKWNvbXBvc2VkR0Y6LyUqY29udmVydGVkR0Y6LyUraW1zZWxlY3RlZEdGOi8lLHBsYWNlaG9sZGVyR0Y6LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lKm1hdGhjb2xvckdGQy8lL21hdGhiYWNrZ3JvdW5kR0ZGLyUrZm9udGZhbWlseUdGMS8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUpbWF0aHNpemVHRjQtSSNtb0dGJDYzUSI6RicvJSVmb3JtR1EmaW5maXhGJy8lJmZlbmNlR0Y6LyUqc2VwYXJhdG9yR0Y6LyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGJy8lJ3JzcGFjZUdGam8vJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKG1heHNpemVHUSlpbmZpbml0eUYnLyUobWluc2l6ZUdRIjFGJy8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUwZm9udF9zdHlsZV9uYW1lR0ZXLyUlc2l6ZUdGNC8lK2ZvcmVncm91bmRHRkMvJStiYWNrZ3JvdW5kR0ZG

with(linalg):

f := [x^2, x*z, y^2*z]: v := [x, y, z]: curl(f, v);

g := [r, sin(theta), z]: v := [r, theta, z]: curl(g, v, coords=cylindrical);

define the scale factors in cylindrical coordinates

h := [1, r, 1]: curl(g, v, h);

with(VectorCalculus):

SetCoordinates( 'cartesian'[x,y,z] );

F := VectorField( <y,-x,0> );

Curl( F );

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Take a new window and produce the solution and turn in. Do not forget to write your name, class time and date.

Your Name:................... Class time: ........................ date: ..................

Question: 1. Create a box with vertices given as (0,-1, 0), (2,-1,0), (2,1,0), (0,1,0), (0,1,-3), (2,1,-3),

(2,-1, -3), and (0,-1,-3)

Question: 2. For the given vector field F = <x^2*z, x*z, y^2*z> calculate curl F and verify your result by hand.