<Text-field style="_cstyle39" layout="_pstyle19">Plotting double-gabled roof </Text-field>

Quick Introduction to Maple

(Please, read also New User's Tour (click "Help" and "New User's Tour" ))

Learning basics of Maple is very easy. Every Maple worksheet consists of parts, called execution groups, marked by vertical lines on the left. Some execution groups contain text, like this one. Some, displayed in red with the prompt [> in front, are command lines. In general, you should execute all commands by placing a cursor on the command line and pressing ENTER. For example, the restart; command above clears all prior Maple assignments and starts a fresh Maple session for you. As with every mathematical software, Maple has its own way of entering commands, called syntax. The syntax must be strictly followed.

Basics: precise arithmetics, use of the command evalf to obtain numerical value

The way to enter arithmetical operations is very similar in Maple as it is in most of graphing calculators: +, -, for addition and subtraction, * for multiplication, (don't forget this one!), / for division, ^ for power. For example, if you want to calculate the value of the expression

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

you enter:

(2+3^5)/(7*(31+16));

Execute the command above, by placing the cursor on the red line and pressing ENTER, to see the result, the output, displayed in blue.

Note: Observe that every Maple command has to end with a semicolon! Observe also, that because of the rules of associating operations, you must enclose the denominator in parentheses. This applies to Maple as well as to your graphing calculators.

a:=32/5;

b:=14/3;

a+b;

a*b;

a-b;

12!;

127!;

Pi;

sin(Pi/3);

cos(Pi/4);

sin(1);

evalf(sin(1));

evalf(sin(1),120);

evalf(Pi);

evalf(Pi,340);

evalf(exp(1)); e:=exp(1);

Symbolic Calculations

expand((c+d)^4);

p:=x^2-4*x-5; factor(p);

Solving equations

solve(p,x); solve(p=3,x);

Defining an expression

f:=ln(x^2+sin(x));

Differentiation (finding derivatives)

g:= diff(f,x);

gg:=diff(f,x,x,x);

Derivative of the previous function

diff(%,x);

simplify(%);

Integration of functions

int(sin(x),x);

int(x*ln(x),x);

int(f,x);

int(ln(x+sin(x)),x=2..9);

evalf(%);

Sums

sum(k^2,'k'=1..r);

sum(q^k,k=0..r);

Limits of functions

limit(x*(Pi/2-arctan(x)),x=infinity);

limit(ln(cos(x))/x^2,x=0);

Plotting graphs of functions (2-dimensional plots)

plot(g,x=1..4);

plot({x*sin(x),x^2},x=-1..1);

plot(sin(1/x), x=-0.10..0.10);

Plotting graphs of functions(3-dimensional plots)

plot3d(2*x+y^2-x^3-1,x=-4..4, y=-4..4, axes=box);

plot3d(x^2+y^2, x=-1..1, y=-1..1, axes=normal,style=patchnogrid);

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

plot3d(cos(x^2+y^2), x=-3..3,y=-3..3,style=patchnogrid);

<Text-field style="_cstyle39" layout="_pstyle19">Plotting double-gabled roof </Text-field>

plot3d(1-abs(x),x=-1..1,y=-1..1,axes=box);

plot3d(max(1-abs(x),1-abs(y)),x=-1..1,y=-1..1,axes=box);

The plotting tools: package plots

<Text-field style="_cstyle39" layout="_pstyle19"></Text-field>

with(plots);

Animated graphics

animate3d(cos(t*y*x),t=1..10,x=-1..1,y=-1..1,axes=normal,frames=10);

Implicit plots

implicitplot3d( x^2 + y^2 - z^2 + 1,x=-2..2,y=-2..2, z=-4..4,axes=box);

Space curves (helix)

spacecurve([cos(t),sin(t),t],t=0..20.2,thickness=5,axes=framed);

for k from 1 to 80 do q[k]:=spacecurve([cos(t),sin(t),t],t=0..k*0.2,thickness=5,axes=framed): od:

display([seq(q[k],k=1..80)],insequence=true);

Level sets: contour plots

contourplot(sin(x*y),x=-3..3,y=-3..3);

contourplot(x^4/2-x^2*y^2-6*sin(y),x=-3..3,y=-3..3);

Vector fields

fieldplot3d([-y, x, 0],x=-1..1,y=-1..1,z=-1..1,color=red, axes=boxed);