CS 123 - Computation Lab III - Spring 2008

Department of Computer Science
College of Engineering
Drexel University

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Maple Command Summary

Summary of Maple operations and Commands
CS 123 - Drexel University
Spring 2008

Key Topics Skills to Master Maple Commands Examples of Use
General Use Open, create, and save a Maple worksheet. (see File menu) File/Open
File/New/Worksheet Mode
Insert and delete execution groups. (see Insert & Edit menus) Insert/Execution Group/Before Cursor
Insert/Execution Group/After Cursor
Edit/Delete Element
Use the Maple help system. (see Help menu)
Help/Maple Help
? <command> ?solve
Use special characters. ; (end of command) 2+3;
: (suppress output) 2*3:
% (previous result) %;
# (comment) 3! = 3*2*1;  # Factorials are fun!
Reset all variables. Should be use at top of every program restart restart;
Variables vs. Names Assign a value to a variable. <var> := <value>; x := 0;
Unassign a variable. <var> := '<var>'; x := 'x';
Understand how Maple evaluates variables and names. eval a := 2;  b := 1;  a*x + b;
eval(%, x=0);
Printing Print a decimal integer  printf(%d, <var>); x := 12:
printf("There are %d zeroes", x);
Print a floating-point number in scientific notation printf(%e, <var>); x := 12.3:
printf("%e is the answer", x);
Print a fixed-point number printf(%f, <var>); x := 12.3:
printf("%f", x);
Print a string printf(%s, <var>); s := "Fred!":
printf("First name is: %s", s);
Solving Equations Create and solve single equations, or expressions solve solve(a*x + b = 0, x);
solve(3*y^2 + y/b, y);
Create and solve systems of equations. solve solve({x+y=2, x-y=1}, {x,y});
Numerically solve one or more equations fsolve fsolve(sin(x) = x/2, x=1..3);
Plotting Create 2-D plots of simple expressions. plot plot(x+1, x=0..5);
Load the plots package (and other Maple packages). with with(plots);
Plot a list of  points in the plane. plots[pointplot] P1 := [1,2];  P2 := [3,4];
L := [P1,P2];  pointplot(L);
Plot a curve using an implicit equation. plots[implicitplot] with(plots):
eq := y - x = 1;
implicitplot(eq, x=0..5, y=1..6);
Display multiple plots simultaneously. plots[display]
plot1 := plot(x+1, x=0..5);
plot2 := pointplot(L);
Calculate the arclength (the perimeter of a semi-circle) arclength with(Student[Calculus1]):
ArcLength(sqrt(1-x^2), x=-1..1);


Student[Calculus1] [ArcLength]   (sqrt(1-x^2), x=-1..1);
Animate Generate an 2-D animation animate(plot,..)
animate( plot, [A*x^2,x=-4..4], A=-3..3 );
Generate an 3-D animation animate(plot3d,...) plots[animate]( plot3d, [A*(x^2+y^2),x=-3..3,y=-3..3], A=-2..2);
Conditional Statements Understand and write Maple expressions which evaluate to true or false.
(see ?boolean help page)
i = 1;
j <= 2;
(0 < x) and (x <= 1);
x := Pi;
type(x, realcons);
Understand and write "if" statements, including those with "elif" and "else" clauses. if y := -1;
if y = 0 then
elif y > 0 then
end if;
Write simple "for" loops with a fixed number of iterations. for for i from 1 to 10 do
  printf("%d^2 = %d\n", i, i^2);
end do;
Write nested "for" loops, including those with a variable number of iterations. for for i from 1 to 5 do
  for j from i+1 to 5 do
    print(i < j);
  end do;
end do;
Write a "for" loop to build up a sequence. for
L := [];
for i from 1 to 10 do
   L := [op(L), i^2];
end do;
Write simple "while" loops with a fixed numer of iterations while i := 1;
while i <= 10 do
   printf("%d^2 = %d\n", i, i^2);
   i := i + 1:
end do:
Implicit LoopsApply a function to every element of a list, producing another listmapL2 :=map( (x) -> x^2, [1.1, 2.3, 3.5]);
Sum together things referenced by the range of values of a variable.sumL := [1.7, -3.9, 4.5];
sum(L[i], i=i = 1..nops(L));
Random Numbers Create a random number generator in Maple. rand coin := rand(0..1);
flip := coin();

die := rand(1..6);
toss := die();
Generate a list of random numbers using a sequence. seq tosses := [seq(coin(), i=1..100)];
Generate a list of random numbers using a loop. for tosses := [];
for i from 1 to 100 do
  tosses := [op(tosses), coin()];
end do:  # suppress loop output
Calculus Commands Define a function with 2 variables ->
f := (x) -> 2*x;
f := (x,y) -> 2*x + 3*y;
Find the partial derivative diff(expr, variable) diff(2*x^2 + 3*x, x);
ONLY returns the symbolic(unevaluated)  expression for the partial derivative Diff(expr, variable) Diff(2*x^2 + 3*x, x);
Compute indefinite integrals int(expr, variable) int(sin(x), x);
Compute definite integrals int(expr , variable = low .. high) int(sin(x), x=0..Pi);
ONLY returns the symbolic (unevaluated) expression for the integralInt(expr, variable)

Int(expr , variable = low .. high)
Int(sin(x), x);

Int(sin(x), x=0..Pi);
Find the minimum value of a function minimize(expr, var=a..b); minimize(sin(x), x=0..Pi);
Find the maximum value of a function maximize(expr, var=a..b); maximize(sin(x), x=0..Pi);
Find a local minimum for for an expression in a interval with(Optimization);
NLPSolve(expr, var = a..b);
NLPSolve(x*(5-x), x=0..6);
Various useful commands Convert exact results to floating point numbers evalf evalf(Pi);
Returns a decimal approximation using 20 significant digits. evalf evalf(Pi, 20);
Write a piecewise function piecewise piecewise(x>0, x, -0);

piecewise( x <-0, 0, x<=1, .5,
Simplify the format of an expression simplify simplify(4^(1/2)+3);
Convert an expression to factored normal form normal normal((x^2-y^2)/(x-y)^3);
Expand the numerator and denominator  (to partially simplify) normal(..,expanded) normal(1/x+x/(x+1),expanded);
Math functions Return the minimum of a sequence of numbers. min min(2, 3, 3.7);
Return the maximum value max max(2, 3, -47);
Return the absolute value abs abs(-3); 
Calculate the value of e to the power of x exp exp(1); # returns e
Find the natural logarithm (lnx) log log(20);
Find the common logarithm log10 log10(1000); # return 3
Trigonometric functions
(see ?trig, ?invtrig help pages)
sin(x), cos(x), tan(x), sec(x)
csc(x), cot(x), sinh(x), cosh(x)   tanh(x), sech(x), csch(x), coth(x),
arcsin(x), arccos(x), arctan(x),
arccsc(x), arcsec(x), arcccot(x),
arcsinh(x), arccosh(x), arctanh(x),
arcsech(x), arccsch(x), arccoth(x),
Compute the square root sqrt sqrt(16);
Compute powersa^b5^3, 5^(1/3), 7^(-2), 3.5^b
Summation (definite or symbolic)sum( expr, var = low .. high);sum( i, i=1..10);

sum( i^2, i=1..n);
Products (definite or symbolic)product( expr, var = low .. high);product( i, i=100..200);

Computation Lab | Department of Computer Science | College of Engineering | Drexel University

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