HOWTO: Use Maple over a network

1) Login via SSH with your Telecom username and password:

ssh -X [email protected]

2) Setup Maple environment:

SETUP MAPLE17

3a) Launch standard worksheet Maple:

xmaple

3b) Launch classic worksheet Maple:

maple -cw

3c) Launch command line Maple:

maple

HOWTO: Use Maple Keyboard Bindings

Ctrl + B           Cursor Left
Ctrl + F           Cursor Right
Ctrl + A           Move to the Beginning of the Line
Ctrl + E           Move to the End of the Line
Ctrl + W           Move One Word Right
Ctrl + Y           Move One Word Left
Ctrl + ]           Move to Matching Parenthesis, Brace, or Square Bracket
Ctrl + D           Delete (to Right of Cursor), or Exit Maple (if on a Blank Line)
Ctrl + H           Backspace (to Left of Cursor)
Ctrl + X or        Clear the Line
Ctrl + G
Ctrl + K           Clear to the End of Line
Ctrl + U           Undo Changes to the Line
Ctrl + P           Previous Command From the History
Ctrl + N           Next Command From the History
Ctrl + R           Find Matching Command From the History
Ctrl + Space or    Command Completion
Tab
Ctrl + T           Show Completion Matches
Ctrl + C           Interrupt the Currently Executing Command
Ctrl + _           Stop the Currently Executing Command in the Debugger
Ctrl + V           Toggle Insert or Overwrite Mode
Ctrl + L           Redraw the Current Prompt and Any Text Entered

http://www.maplesoft.com/support/help/Maple/view.aspx?path=commandline/reference/shortcutkeys

HOWTO: Use Maple

1) End statement with colon : or semicolon ;

2) Use ^ or ** for exponentiation

3) Use % to operate on the last result or %% to operate on the next-to-last result.

4) Type quit to quit

5) Use evalf(%,3) for evaluation using floating-point arithmetic, where 3—no. of significant digits

6) Help for a particular command ? evalf OR ? plot, color

7) Use := to define variables, e.g.

    A := 5; B := 2;

8) Variable names are case sensitive

9) Set number of significant figures

    Digits := 4;

10) Value of built-in function

    evalf(ln(10), 4);

11) Expression: string of constants, variables, mathematical operators, e.g.

    5*x^2 - 2*y^2 = 3*cos(x*y);

12) Function: relationship for a variable

    z(x,y) = 2*x/y;

13) Use := to define an expression and subs() to substitute a value into it:

    f := x^2;
    subs(x = 5, f).

14) Define function, evaluate function at x = 4:

    g := x -> 1/(x+1);
    g(4);

15) Convert expression into function, evaluate function at x = 5:

    f := unapply(f,x);
    f(5);

16) Convert function back into expression:

    f := f(x);

17) Define equations

    eq1 := 2*x1 - 5*x2 = 12;
    eq2 := 12*x1 + 4*x2 = 17;

18) Solve sets of linear algebraic equations

    sol := solve({eq1, eq2}, {x1,x2});
    sol := fsolve({eq1, eq2}, {x1,x2});

19) Extract solutions

    sol[2]; OR rhs(sol[2]);

20) Specify range(s) for unknown(s) in nonlinear equation(s)

    eq := x = exp(-x);
    sol := fsolve(eq, x, x=0..1);

    f := sin(x+y) - y*exp(x) = 0;
    g := x^2 - y = 2;

    solfg := fsolve({f,g},{x,y},{x = -1..1, y = -2..0});

Use `infinity` OR `-infinity` to specify semi-infinite range limit.

21) Find roots of polynomials

    p := 6*x^4 - 7*x^3 + 6*x^2 - 1 = 0;

    sol := solve(p,x); sol := fsolve(p, x, complex);

22) Imaginary unit is I

23) Access plotting package

    with(plots);

24) Plot tabular data

    T(C)      9.7    20.4    31.0    41.5    51.1
    V(m^3/kg) 108.7   56.4    31.1    18.1    11.5

    VTdata := [ [9.7, 108,7], [20.4, 56.4], [31.0, 31.1], [41.5, 18.1], [51.1, 11.5] ]

    plot(VTdata, T = 0..60, V = 0.120, style = point)

25) Plot two functions

    f := x -> sin(x);
    g := x -> 0.25*x - 1;

    plot( [f(x), g(x)], x=0..4, color=[red,blue], style=[point,line] );

26) Insert text on a plot

    fggraph := plot( [f(x), g(x)], x=0..4, color=[red,blue], style=[point,line] );

    labelf := textplot( [0.8, 0.5, `f(x)`] );
    labelg := textplot( [2, -0.5, `g(x)`], align = {ABOVE, LEFT} );

    display( [fggraph, labelf, labelg] );

27) Unassign a variable k

    k := 'k';

28) Perform algebraic simplification

    k := x*y + y^2;
    p := k/(x+y);

    simplify(p);

29) Differentiate an expression with diff()

    f  := x^3 + 5*exp(-2*x);

    df  := diff(f,x);
    d2f := diff(f,x,x);

    e1 := evalf(subs(x=1,df),  4);
    e2 := evalf(subs(x=1,d2f), 4);

30) Differentiate a function with D()

    g := x -> x^3 + 5*exp(-2*x);

    dg  := D(g);
    d2g := D(D(g));  OR  d2g := D(dg);

    evalf(dg(1),  4);
    evalf(d2g(1), 4);

31) Indefinite integration of an expression with int(f,x)

    f := 3*x^2 - 10*exp(-2*x);

    F := int(f,x);

    evalf(subs(x=1,F), 4);

    diff(F, x);

    F := unapply(F,x);

    D(F);

32) Definite integration of an expression with int(f,x=a..b)

    f := 3*x^2 - 10*exp(-2*x);

    A := int(f, x=0..1);

    evalf(A,4);

33) Numerical integration

    f := exp(-x^3);

    F := int(f, x=0..2);

34) Ordinary differential equations

    // equations
    deqs :=
    diff(Ca(t),t) = -(1/10)*Ca(t),
    diff(Cb(t),t) =  (1/10)*Ca(t) - (2/10)*Cb(t),
    diff(Cc(t),t) =  (2/10)*Cb(t);

    // initial conditions
    inits := Ca(0) = 1, Cb(0) = 0, Cc(0) = 0;

    // list of dependent variable names
    fcns := [Ca(t), Cb(t), Cc(t)];

    // solve equations analytically
    dsolve({deqs, inits}, fcns);

    // create functions for Ca(t), Cb(t) and Cc(t)
    Ca := t -> exp(-1/10*t);
    Cb := t -> exp(-1/10*t) - exp( -1/5*t);
    Cc := t -> 1 - 2*exp(-1/10*t) + exp(-1/5*t);

    // generate a plot of the concentrations vs. time from t=0 to t=40 s
    with(plots);

    P := plot([Ca(t), Cb(t), Cc(t)], t=0..40,
    title = `CONCENTRATION (MOL/L) VS. TIME(SEC)`,
    titlefont = [HELVETICA, BOLD, 14],
    labels = [`t`, `C`],
    style=[point, point, point],
    symbol=[circle, box, diamond],
    color=[red,green,blue]):

    // label curves on the plot
    labela := textplot( [.8, .5, `Ca`] ):
    labelb := textplot( [4, .26, `Cb`] ):
    labelc := textplot( [20, .8, `Cc`] ):

    // display plot with curve labels
    display([P, labela, labelb, labelc]);

    // generate numerical solutions of the equations and plot them
    // turn Ca, Cb and Cc from functions back into variable names
    Ca := 'Ca':  Cb := 'Cb': Cc := 'Cc':

    // add differential equations package
    with(DEtools):

    // create and store separate plots of the dependent variables vs. the independent variable
    Caplot := DEplot( [deqs], fcns, t=0..40, [[inits]], scene=[t,Ca], linecolor=red,   stepsize=0.2, arrows=none ):
    Cbplot := DEplot( [deqs], fcns, t=0..40, [[inits]], scene=[t,Cb], linecolor=green, stepsize=0.2, arrows=none ):
    Ccplot := DEplot( [deqs], fcns, t=0..40, [[inits]], scene=[t,Cc], linecolor=blue,  stepsize=0.2, arrows=none ):

    display( [Caplot, Cbplot, Ccplot, labela, labelb, labelc] );

    // generate and store numerical solutions of the three equations
    soln := dsolve({deqs, inits}, fcns, numeric);

    // display the concentrations at a specified time (t=5), each with four significant figures.
    evalf(soln(5), 4);

    // display a table of concentrations at times 0, 2, 4,..., 20 with four significant figures.
    for k from 0 to 10 do evalf(soln(2*k), 4); od;

http://www4.ncsu.edu/unity/lockers/users/f/felder/public/tutorials/maple1.htm http://www4.ncsu.edu/unity/lockers/users/f/felder/public/tutorials/maple2.htm http://rt.uits.iu.edu/visualization/analytics/math/maple-getting-started.php