Page 810 - Advanced_Engineering_Mathematics o'neil

790 APPENDIX A A MAPLE Primer

This will return the decimal 26.82836630. As another example,
evalf(cos(3) + sin(3));
will return the decimal value -.8488724885 of cos(3) + sin(3).
To solve an algebraic equation, use the solve command. For example,
∗
solve(x∧2+2 x - 1=0,x);
√ √
2
will return the roots −1 + 2 and −1 − 2of x + 2x − 1 = 0. This solve command includes
a designation of x as the variable for which to solve—an essential piece of information for the
program. Of course, other symbols than x can be used in the equation and the instruction. For
the solutions in decimal form, use
evalf(solve(x∧2+2 x - 1=0,x);
∗
which will return the decimal values 0.414213562 and −2.414213562 of these roots. As another
example, enter
evalf(solve(cos(t) - t = 0,t));
to obtain the approximate solution 0.7390851332 of cos(t) − t = 0.
To solve a system of equations, enter the system in curly brackets in the solve command. For
example,
∗
solve({x - 2 * y=4,5 x + y = -3},{x,y});
gives the solution x =−2/11, y =−23/11. Again, note the designation of x and y as the variables
for which solutions are wanted.
In order to define a function, say f (x) = x sin(5x) − 3x, enter
∗
∗
∗
f:=x→x sin(5 x) - 3 x;
This names the function f and the variable x. The arrow must be typed into MAPLE as a dash
followed by a “greater than” symbol. If we want to evaluate this function at a point, say π/4,
type
f(Pi/4);
√
to obtain the value −π 2/8 − 3π/4.
To plot a graph of f , say on the interval [−1,3], enter
plot(f(x), x=-1..3);
If we wish, we can enter a function directly into the plot command without prior definition.
For example,
∗
∗
plot(x cos(3 x) - exp(x), x=-1..1);
x
will graph x cos(3x) − e for −1 ≤ x ≤ 1.
To plot several graphs of functions that have been defined, enter, for example,
plot({f(x),g(x),h(x)},x=a..b);
We can arrange for all the graphs to be in one color, say black, by
plot({f(x),g(x),h(x)},x=a..b,color=black);
Sometimes we want to enter a function having jump discontinuities. This is done by
specifying the value of the function on successive intervals. For example, to define
⎧
⎪x for x < −1
⎪
⎪
cos(3x) for −1 < x < 4
⎨
s(x) =
⎪x 2 for 4 < x < 9
⎪
⎪
sin(4x) for x > 9
⎩
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October 14, 2010 15:43 THM/NEIL Page-790 27410_24_appA_p789-800