**Part 1: Elementary
Calculations**

Each of the command entry instructions
below is sent to *Maple *for processing by pressing the RETURN or ENTER key
on your keyboard.

1. In the *Maple *worksheet,
type

**2+3 **and then press
RETURN or ENTER. (From now on, we will not add this last part of the
instruction.)

2. Enter

**2^3
**Note where that the cursor remains in the exponent until you move
it.

3.
Enter

**2*(8-2^3)**

**Part 2:** **Variables**

1.
Enter

**x:=3;
y:=2****
**Note where that the semicolon
allows you to put two commands on the same line

2. Enter

**2*x+y**

3. The result of the preceding step
follows from the fact that the variable **x **has been assigned the value
**3 **and the variable **y **has been assigned the value **2**. Check
this by entering** x;
y**

4. Enter the following line. Note that it ends with
a *colon *

5. Enter

**z+y **Note that entering
a line with a colon has the effect as entering it without a colon, except that
nothing is displayed afterwards.

6. Use pencil and paper to decide
what number **xy ^{2} + 3z** represents, and then check your answer by
entering

7. Suppose we want to remove
the identification of **x **with **3**.
Enter

**x:='x'
**Check this by entering

Now remove the identifications of

8. *Maple*
distinguishes between **:=** and **=**. The first is used for definitions. The equals
sign alone is used to enter equations.

Check this by entering

**solve(s^2-s-1=0,s)**

(Here the **s** after the comma in the
command tells *Maple* what to solve for.)

9. Enter

**2+3 **and then

**Part 3:** **Text**

1. You may enter text as you would in any word processor by clicking on the word "Text" on the toolbar (next to the word "Math").

2. You can return to Maple Notation input by clicking on the word "Math".

**Part 4:** **What Maple remembers**

1. Create a new region and
type

**x:=15 **On a new line
type

enter

*Maple ***remembers what has been entered in the order it
was entered. **

- It doesn't matter
what is currently in the worksheet, nor the order things appear in that
worksheet. You may have assigned a value, erased the assigning command line,
and forgotten about it. But
*Maple*remembers. If you use**x**later, assuming it is an unassigned variable, strange things will happen. - If variables are assigned new values, formulas using those variables acquire new values as well.

If you save a
*Maple* file without removing the output, then reload it later, it will
look the same as when you saved it. But *Maple* will not remember any of
the displayed commands. **All of those commands must be reentered before you
are again in the same state as when you saved and closed the
file.**3. Enter

4. Go back up to the line

·
**s:=7; **and change
the

· altered
value to be acknowledged by *Maple*. Similarly, change the value of **t
**to **-1**. Now enter

**z **again.

·
*Maple *remembers what has been entered in the order it was entered.

5. A very useful command is the
*restart* command. If you enter

**restart**

*Maple* clears the memory. It is the same as loading the current worksheet.
All *Maple* commands that you need, including loading
of

packages, must be reentered.

**Part 5:** **Functions**

1. Next we define a function to assign the value
**10 sin x **to each **x**. Enter

**x:='x'
f:=x->10*sin(x)**

and then

2. To obtain
a decimal approximation, enter

**evalf(10*sin(1)) **or
**evalf(%)** ** **The command "evalf" stands for "floating point
evaluation."

3. To be sure that the action of evalf is clear, enter

**2/3
**and then

and then

evalf(pi)

Both "pi" symbols look the same, but only the one obtained with an upper case "P" and a lower-case "i" carries the numerical value.

Now find a decimal approximation to

**Part 6:** **Graphing**

1. In order to
plot **3 sin(2x)** over the interval **[0,2 pi]**.
Enter

**plot(3*sin(2*x),
x=0..2*Pi)**

We can obtain the same result by
defining the function **f **given by **f(x) = 3 sin(2x)** and plotting
**f(x)**. Enter the following:

**f:= x->3*sin(2*x)**

**plot(f(x), x=0..2*Pi)**

2. When the plot appears, use your mouse to "select" it -- you should see a box around the graphic. Experiment with the drag buttons at the corners and sides of the box. Experiment with the icons at the top of the screen to see what they do.

3. Next we plot data given as
ordered pairs. Enter

**data:=[[0,1],[2,2],[4,6],[5,1]]**

Then enter

**plot(data,
style=point)**

Go back and see what happens
if you delete "style=point."

4. Often we wish to view several
graphs at the same time. One way to do this is to enter the desired plots
directly into the plot command.

Enter**
plot([sin(x),cos(x)],x=0..2*Pi, color=[green,blue])**

5. Another way to create multiple plots is
to use the *display* command in the *plots* package. To access this
package click on "Tools" on the top toolbar, then click on "Load Package" then
click on "Plots".

Now enter

**graph1:=plot(sin(x),x=0..2*Pi,color=blue):**

This creates a plot and names it "graph1." Create a second plot by
entering

**graph2:=plot(cos(x),x=0..2*Pi,
color=green):**

To see both plots
together, enter

**display(graph1,graph2)**

6. To plot a curve defined implicitly, like
the unit circle for example, first make sure that you have loaded the
*plots* package (see 5 above)

then on a new line
type **implicitplot(x^2+y^2 = 1, x = -1 .. 1, y = -1 ..
1**).

7. Try ploting x^2-y^2=1 with x =
-3..3 and y = -3..3.

8. In the Maple worksheet, click on the
word ** plots **(following the word loading) to see
many other possible plot commands.

**Part 7:** **Differentiation and
Integration**

1. Define **g** to be the function given
by **g(x) = x ^{2}cos x**.

Check your work by evaluating

2. Now enter

3. If you want to calculate the derivative of an expression that you have not yet entered, just replace

For example, enter

Now insert a literal constant in the expression: Enter

Then change the final

4. Next we calculate indefinite integrals. If necessary, unassign

Then enter

You can check that the result is an antiderivative of

6. Next we calculate definite integrals. To integrate

If you know that all you want is a numerical estimate, you can enter

The significance of the upper-case

8.

Note that there is no space bewtween

3. Enter

4. We may use the solve command to obtain a complete factorization. Enter the following

1. Limits are easy to calculate in
*Maple*. As a test we'll calculate the limit of **sin(x)/x** as **x**
approaches **0**. Enter the
following:

**limit(sin(x)/x, x =
0)**

2. The *Maple* limit command also
calculates limits at infinity. Enter

**limit((1 + x ^{3})/((1 +
x)*(1+2*x^{2})), x = infinity)**

3. The standard limit command will deal with one-sided limits if there is no possibility of confusion. Enter

4. Now
try

**limit(abs(x)/x, x = 0)**

5. Why is this
limit ambiguous? Try**
limit(abs(x)/x, x = 0, right)
**Now replace "right" by
"left."