MAPLE commands - Quick Reference Guide - By OM, 12/02
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COMMAND                    EXPLANATION
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## general 

> restart;                 # good to have this at the top of worksheet; 
> with(student);           # adds extra functionality (recommended)
> f:=x->x^2;               # define a function f(x)
> g:=x->evalf(x^3);        # define a function f(x), force it to give decimal result
> evalf(%)                 # evaluate previous output in decimal form
> diff(sin(x),x);          # derivative of sin(x) with respect to x
> diff(f(t),t);            # derivative of f(t) with respect to t
> int(f(x),x=1..2);        # integrate f(x) for x between 1 and 2.
> Int(f(x),x=1..2);        # display the integral of f(x) for x between 1 and 2.
> Pi ;                     # the number 3.1415...Note the it begins with capital P.
> exp(2.5);                # exponential function evaluated at 2.5
> ln(2.5);                 # the natural logarithm of 2.5
> p := x^2 - 2*x;          # store the expression x^2-2*x under the name "p"
> subs(x=3,p);             # substitute x=3 into expression p

# plotting functions and points

> with(plots);                                   # adds functionality for plotting (recommended)
> plot(f(x),x=-1..1,y=0..2,scaling=constrained); # plot f(x) with same scaling in x and y axes. 
> plot(f(x),x=-1..1,y=0..2,axes=boxed);          # a plot of f(x) in boxed form. 
> plot([f(x),g(x)],x=0..2);                      # plot f(x) and g(x) for x between 0 and 2.
> mypts:=[seq([n,10*n-n^2],n=0..10)];            # define a list of points
> plot(mypts,x=0..10,style=point,symbol=circle); # plot the points above

## solving equations

> solve( cos(x)+y = 9, x );    # solve an equation for x
> solve( {x^2*y^2=0, x-y=1} ); # solve a system of equations for x,y
> fsolve(x^3-2*x+1,x,-1..1);   # numerically solve x^3-2*x+1 = 0  for x between -1 and 1

## differential equations

> with(DEtools):                                # loads diff eqns package
> de1 := diff(x(t),t) = 3*x(t)*(1-x(t)/300);    # assigns a differential equation to a name
> DEplot(de1,x(t),t=0..3,x=0..400);             # slope field plot of diff eqn "de1"
> DEplot(de1,x(t),t=0..3,x=0..400,[[x(0)=50]]); # slope field plot and solution through (0,50)
> dsolve({de1,x(0)=50},x(t));                   # solves the differential eqn "de1"

## curve fitting

> with(stats):                               # loads package for curve fitting
> xvals := [-2.,-1.,0.,1.,2.];               # data needed for fit command
> yvals := [-3,0,1,0,-3];                    # more data needed for fit command
> fit[leastsquare[[x,y], y=a*x^2+b*x+c]]( [xvals,yvals]);    # fit a parabola