To launch Maple 8 from the NT Labs (340 or 342 DH):

Choose:   Start -> Programs -> Mathematical Applications -> Maple 8 -> Maple 8

Create a new worksheet by clicking on the first item of the toolbar (just below "File").

Once Maple 8 has been started, computations may be executed immediately.  Commands are typed to the right of the prompt;  a semicolon is placed at the end of the command, and then it is evaluated by pressing ENTER.  If a colon is placed at the end of a command, the resulting evaluation is not displayed.
To type comments, begin each line with the symbol #.

You may SAVE your work (once you have an account) by selecting the H drive and choosing the MyHome directory.

(A)   Arithmetic and High-School Algebra.

In each of the following examples, type the given command at the prompt, press ENTER and see what happens.  Note that multiplication is represented using *, and exponentiation by using ^. exp(g(x)) represents e^g(x);  so exp(1) is just the constant e. Pi represents the constant p.    See if you can determine the meaning of the symbol % through an examination of the output.

> 13 + 44;
> 2/3 + 3/5 ;
> 4*9;
> % + 13;
> #  What role does % play here?
> 2* %;
> #  What role does % play here?
> evalf( 1/3 + 1 /4);
> evalf( exp(1) );
> # Explain the difference between exp(1) and evalf(exp(1)) ?
> evalf (Pi*15);
> sin(Pi/6);
> tan(Pi/6);
> evalf(%);   # What is the role of evalf ?

> 3*4^(1/2) + 5;
> simplify(%);   # How does simplify differ from evalf ?

> p := x^2 + 5x + 6;
> factor(p);
> factor (x^6 - 64);
> factor(x^2 - 10*x*y + 21*y^2);
> factor (x^2 + -7x - 44);  # What seems to be wrong here?  Make a correction.
> ifactor(123456);

> arcsin(1/2);  # Is the answer in degrees or in radians?
> arcsec(13);
> evalf(%);

> gcd(45, 933);   # What is the meaning of gcd ?
> lcm(18,34);      #  What is the meaning of lcm?

> convert(72*degrees, radians);
> convert(Pi/12, degrees);   # What is the role of convert ?

> solve (x^2 - 10*x + 21 = 0);
> solve (sin(x) = cos(x));
> solve (x^6 = 2);    # How many of these solutions are real numbers ?
> evalf(%);

> plot ( x * sin(1/x) , x = -0.4 .. 0.4 );
> plot ( x * exp (-x) , x = -1 .. 5 );

> # To display the graphs of two or more functions, we may use braces to signal the beginning and end of our list of functions.
> plot ( {x^2 - x,  6 - x^2}, x = -5 .. 5 );
> plot ({sin(Pi*x), cos(2*Pi*x), 0.15*x}, x = 0..2*Pi);

Exercises:

1.  Solve the equation  x⁴ – 20x³ + 130x² - 300x + 189 = 0.

2.  Sketch the graph of the function y = x cos x over the interval [0, 10].

3.  Sketch the pair of functions y = ln(x) and y = x^1/2 on the same pair of axes over the interval (0,25].

4.  Determine where the two parabolas y = x² - 3x - 4 and y = 1 - 3x² intersect.  (Determine each coordinate to the nearest hundredth.)
Sketch their graphs on the same set of axes.
 
 

Consider a spider traveling in the xy-plane whose position (x,y) (in cm.) at time t (in minutes) is given by x(t) = t² and y(t) = t³/(1+t²).
How can we plot the graph of the trajectory of the spider as time varies from 0 to 13 minutes?

> x := t^2;
> y := t^3/(1+t^2);
> plot ([x, y, t = 0..13]);

Exercises:

1.   Graph the function given parametrically by:   x = 3 cos (s), y = 5 sin(s),  0 < s < 2p.

2.   Graph the cycloid:   x = 3(t - sin t), y = 3(1 - cos t),   0 < t < 25.

The Student package is a collection of subpackages designed to assist with the teaching and learning of standard undergraduate mathematics.  To invoke the Student package in Maple we use:

> with (Student):

Differentiating a function in Maple is relatively straightforward.

> restart;
> with(Student):  # This library is optional for what we are about to do.
> y:=  ln(sin(3*x));
> Diff(y, x);  # This is called pretty printing.
> diff(y, x);   # This actually performs the differentiation. The second variable is just the variable with which differentiation is performed.
>  x :=  s*tan(s)/(1+s^3);
>  diff (x, s);
> diff (sqrt(1+x^3), s);

Computing a definite integral is also easy.

> restart;  # This is very important since we have already assigned an expression to the variable x.
> y := x*ln(x);
> Int(y, x=1..2);  # Again, this is just pretty printing.
> int (y, x=1..2);
> int (y, x);   # This returns an anti-derivative.

Exercises:

1.   Find the area between the two parabolas y = x² - 3x - 4 and y = 1 - 3x² that you graphed in an earlier exercise.

2.   Find an anti-derivative of  x⁴ ln(1+x).

3.   Find the area under the curve x⁴ ln(1+x) between x = 0 and x = 1.
 
 

?f and help(f) give information about the Maple function (or package) f.  Such information will appear in a separate window.  For example, try:

> ? help
> ? plot
> ? radians