A General Introduction to Maple

Maple is a computer application for advanced mathematics. The way you run Maple depends on the system you are on.  Using Microsoft Windows you click on the Maple icon; it has an integral symbol superimposed on a maple leaf. In the Math L;ab

First do some simple arithmetic:

> 7*(4^3)/9;

448/9

> evalf(7*(4^3)/9); # evalf means give the answer is floating point form, which is computer speak for decimal form.

49.77777778

> 5^77;

661744490042422139897126953655970282852649688720703125

OK, now some algebra:

> factor(x^7-1);

(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)

> expand((x^3+3*x+1)*(x^2-1));

x^5+2*x^3-3*x+x^2-1

Now for a graph. We plot y= x sin (x) from -3 pi to 3 pi.

> plot(x*sin(x),x=-3*Pi..3*Pi,thickness=3,color=black);

[Plot]

Maple can do limis.

> limit(tan(3*x)/sin(4*x),x=0); #The equals sign really means "goes toward".

3/4

> limit(sin(x^3)/x,x=infinity);

0

> limit(exp(1/x),x=0,right); #exp(1/x) means "e to the 1/x" and the limit is "x goes to zero from the right"

infinity

> limit(exp(1/x),x=0,left);

0

Next, some calculus.

> diff(x^3*cos(x^2),x);

3*x^2*cos(x^2)-2*x^4*sin(x^2)

> diff((x+1)/tan(3*x),x);

1/tan(3*x)-(x+1)*(3+3*tan(3*x)^2)/tan(3*x)^2

> diff(x^4-5*x^3+7*x^2+7,x);

4*x^3-15*x^2+14*x

> solve(diff(x^4-5*x^3+7*x^2+7,x)=0,x);

0, 2, 7/4

Later in the course, Chapter 5, we will do integration, which is the inverse operation of differentiation. The command is int.

> int(x*sin(x^2),x);

-1/2*cos(x^2)

> int(x*sin(x^2),x=0..sqrt(Pi));

1

> plot(x*sin(x^2),x=0..7);

[Plot]

Thus, the area under the first hump is exactly 1.