<Text-field style="_cstyle259" layout="Heading 2"><Font bold="true" size="16">First Things First</Font></Text-field>

<Text-field style="Heading 2" layout="Heading 2">Lessons</Text-field>

<Text-field style="Heading 3" layout="Heading 3">Arithmetic</Text-field>

<Text-field style="Heading 4" layout="Heading 4">Discussion</Text-field>

Maple is an example of a computer algebra system. One feature of the system is that it can be used as a very smart calculator. In particular, you can use Maple to add, subtract, multiply, and divide numbers or expressions. These primary arithmetic operations are represented in Maple by the following symbols:

+ (addition), - (subtraction), * (multiplication), / (division), ^ (exponentiation).

If you ever need additional information regarding a Maple command, you can gain access to a help window by entering the command preceded by a question mark (and not followed by a semicolon). For example, if you enter ?+, a help window for the Maple operation of addition will open. Try entering the next command.

Here are some examples which illustrate the basic mathematical operations in Maple.

Addition. To add the numbers 1 through 10:

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

Subtraction. To subtract 10 and 5 from 53:

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

Multiplication. To multiply the numbers 54, 55, and 56:

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

Division. To divide 108 by 435:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2OVEhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSp1bmRlcmxpbmVHRjcvJSpzdWJzY3JpcHRHRjcvJSxzdXBlcnNjcmlwdEdGNy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y3LyUrZXhlY3V0YWJsZUdGOi8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjcvJSpjb252ZXJ0ZWRHRjcvJStpbXNlbGVjdGVkR0Y3LyUscGxhY2Vob2xkZXJHRjcvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUqbWF0aGNvbG9yR0ZDLyUvbWF0aGJhY2tncm91bmRHRkYvJStmb250ZmFtaWx5R0YxLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lKW1hdGhzaXplR0Y0

Exponentiation. To raise 12 to the 5th power:

12^5;

Important: Use only parentheses to enclose groups of operations. Maple will NOT recognize square brackets or curly braces for this purpose. The following example illustrates this.

5^(2*[3+4]);

To find the decimal representation of a number, the command evalf can be used. The default number of digits provided is 10.

evalf(1/3);

To obtain more or less than 10 digits, the desired number of digits must be specified. The following gives the decimal representation of 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 out to 20 digits. Note that Maple recognizes 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 as Pi.

evalf(Pi,20);

<Text-field style="Heading 4" layout="Heading 4">Exercises</Text-field>

1. Subtract 3 from the sum of 5 and 4, then multiply the result by 2. Your answer should be 12.

2. Find the smallest integer 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 such that 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 is greater than 1000000. (Hint: Just guess and check different values for n. Maple allows full screen editing -- you can change part of an earlier guess and reenter the command.)

3. Calculate the 10-digit decimal representation of the following number: 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.

(Hint: you must tell Maple to multiply: e.g., it won't understand (52)(63) as multiplication. Enter 52*63 instead.)

<Text-field style="Heading 3" layout="Heading 3">Defining Variables and Functions</Text-field>

<Text-field style="Heading 4" layout="Heading 4">Discussion</Text-field>

To assign a variable to represent a particular numerical value or a function in Maple, you must use the "colon-equals" notation :=.

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

These commands indicate that the variable "A" has been assigned the value 5. It will then have this value throughout the session until A is assigned another value or its value is "unassigned". What should the result of the following command be?

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

The following command "unassigns" the value of A. Note the use of single quotes (') in the command.

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

Now what do you expect the result of the following command to be?

4*A+12;

There are two ways to define a function in Maple. One way is to define the function as an expression. For example, the function 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 can be defined as an expression by typing f:=x^2. (Note the use of the carot -- above the 6 -- to create superscripts. Use the right arrow key or your mouse to get back to normal text.)

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;

When a function is defined this way, to evaluate the function at a specific input you must use the Maple subs ("substitute'') procedure. This is illustrated in the next command.

subs(x=5,f);

WARNING: For a function defined as an expression, the standard functional notation, such as f(5), is not understood by Maple and results in nonsense. For example:

In this course, we will usually use functions (rather than expressions). To let Maple know you are working with a function, the notation is a little different. Think of the example below as saying that the function named f consists of taking the input x and "sending it to" the output x^2. (We type in f:=x->x^2.) The arrow is made up of a hyphen and a greater-than symbol.)

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNigtSSNtaUdGJTY5USJmRigvJSdmYW1pbHlHUStNb25vc3BhY2VkRigvJSVzaXplR1EjMTJGKC8lJWJvbGRHUSV0cnVlRigvJSdpdGFsaWNHUSZmYWxzZUYoLyUqdW5kZXJsaW5lR0Y7LyUqc3Vic2NyaXB0R0Y7LyUsc3VwZXJzY3JpcHRHRjsvJStmb3JlZ3JvdW5kR1EqWzI1NSwwLDBdRigvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYoLyUnb3BhcXVlR0Y7LyUrZXhlY3V0YWJsZUdGOC8lKXJlYWRvbmx5R0Y7LyUpY29tcG9zZWRHRjsvJSpjb252ZXJ0ZWRHRjsvJStpbXNlbGVjdGVkR0Y7LyUscGxhY2Vob2xkZXJHRjsvJTBmb250X3N0eWxlX25hbWVHUSxNYXBsZX5JbnB1dEYoLyUqbWF0aGNvbG9yR0ZELyUvbWF0aGJhY2tncm91bmRHRkcvJStmb250ZmFtaWx5R0YyLyUsbWF0aHZhcmlhbnRHUSVib2xkRigvJSltYXRoc2l6ZUdGNS1JI21vR0YlNjNRIzo9RigvJSVmb3JtR1EmaW5maXhGKC8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGKC8lJ3JzcGFjZUdGW3AvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdRIjFGKC8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUwZm9udF9zdHlsZV9uYW1lR0ZYLyUlc2l6ZUdGNS8lK2ZvcmVncm91bmRHRkQvJStiYWNrZ3JvdW5kR0ZHLUYtNjlRInhGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1GX282M1EtJlJpZ2h0QXJyb3c7RihGYm9GZW9GZ28vRmpvUTBtZWRpdW1tYXRoc3BhY2VGKC9GXXBGXXJGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtSSVtc3VwR0YlNiVGZnEtSSNtbkdGJTY5USIyRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYoLUZfbzYzUSI7RihGYm9GZW8vRmhvRjgvRmpvUSQwZW1GKEZccEZecEZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcTcjQyQ+SSJmR0YoZio2I0kieEdGKEYoNiRJKW9wZXJhdG9yR0YoSSZhcnJvd0dGKEYoKiQpRmVzIiIjIiIiRihGKEYoRlx0

f(x);

f(5);

What symbol (or combination of symbols) separates the input from the output when defining a function?

<Text-field style="Heading 4" layout="Heading 4">Exercises</Text-field>

1. Define the function 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. Use trial and error to find an approximate root of F. (Hint: Try evaluating F at various values between 0 and 1.)

2. Define the variable NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiMtSSNtaUdGJTY5USJBRigvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRjgvJSpzdWJzY3JpcHRHRjgvJSxzdXBlcnNjcmlwdEdGOC8lK2ZvcmVncm91bmRHUSpbMCwwLDIwNF1GKC8lK2JhY2tncm91bmRHUShbMCwwLDBdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjgvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZWN0ZWRHRjgvJSxwbGFjZWhvbGRlckdGOC8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk1hdGhfNEYoLyUqbWF0aGNvbG9yR0ZELyUvbWF0aGJhY2tncm91bmRHRkcvJStmb250ZmFtaWx5R0YyLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKC8lKW1hdGhzaXplR0Y1NyM2IyUiQUc= to be the expression 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. Then use subs to evalute 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 at NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiktSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRLFsxNTMsMCwxNTNdRigvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYoLyUnb3BhcXVlR0Y4LyUrZXhlY3V0YWJsZUdGOC8lKXJlYWRvbmx5R0Y4LyUpY29tcG9zZWRHRjgvJSpjb252ZXJ0ZWRHRjgvJStpbXNlbGVjdGVkR0Y4LyUscGxhY2Vob2xkZXJHRjgvJTBmb250X3N0eWxlX25hbWVHUSoyRH5NYXRoXzdGKC8lKm1hdGhjb2xvckdGRC8lL21hdGhiYWNrZ3JvdW5kR0ZHLyUrZm9udGZhbWlseUdGMi8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigvJSltYXRoc2l6ZUdGNS1GJDYlLUYtNjlRInhGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1JI21vR0YlNjNRIj1GKC8lJWZvcm1HUSZpbmZpeEYoLyUmZmVuY2VHRjgvJSpzZXBhcmF0b3JHRjgvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYoLyUncnNwYWNlR0ZgcC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJTBmb250X3N0eWxlX25hbWVHRlgvJSVzaXplR0Y1LyUrZm9yZWdyb3VuZEdGRC8lK2JhY2tncm91bmRHRkctSSNtbkdGJTY5USIwRihGMEYzRjYvRjpGOEY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ24vRmpuUSdub3JtYWxGKEZcby1GZG82M1EiLEYoRmdvRmpvL0ZdcEY7L0ZfcFEkMGVtRigvRmJwUTN2ZXJ5dGhpY2ttYXRoc3BhY2VGKEZjcEZlcEZncEZqcEZdcUZfcUZhcUZjcUZlcUZncUZpcS1GXHI2OUZccUYwRjNGNkZfckY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GYHJGXG9GYnItRiQ2JC1GZG82M1EqJnVtaW51czA7RigvRmhvUSdwcmVmaXhGKEZqb0ZccEZmci9GYnBGZ3JGY3BGZXBGZ3BGanBGXXFGX3FGYXFGY3FGZXFGZ3FGaXFGanJGLDcjNiUvJSJ4RyIiISIiIiwkRmlzISIi.

<Text-field style="Heading 3" layout="Heading 3">Algebra</Text-field>

<Text-field style="Heading 4" layout="Heading 4">Discussion</Text-field>

One of the great benefits of a computer algebra system like Maple is that it allows one to manipulate entire algebraic expressions in the same way that a calculator manipulates numbers. Some of the related Maple commands are:

simplify - simplifies an algebraic expression

expand - expands (multiplies out) an expression

factor - factors an expression

solve - solves a system of equations for a set of unknowns.

Remember you can use Help whenever you need additional information regarding a particular command. We now illustrate these commands.

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

Here's an example that asks Maple to solve a system of two equations in two unknowns.

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

Observe how braces "{" and "}" were used in the preceding Maple input. Maple understands items enclosed in braces to be a set, and yields output which is also in the form of a set.

<Text-field style="Heading 4" layout="Heading 4">Exercises</Text-field>

1. Factor the polynomial 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.

2. Solve the following system of equations for x and y:

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, 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

<Text-field style="Heading 3" layout="Heading 3">Two-Dimensional Plots</Text-field>

<Text-field style="Heading 4" layout="Heading 4">Discussion</Text-field>

To plot the graph of a function of one variable in Maple, the procedure plot can be used. A function f defined on an interval 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 can be plotted over this interval by entering

plot(f(x), x = a..b,options)

We will now illustrate these commands with some examples involving the function 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. In Maple, raising the number 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 to a power is obtained by using the built-in function exp(). Entering e^2 for 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 will not work, rather, you must enter exp(2). Notice also that Maple recognizes the sine function as sin().

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;

The following command plots this function over the interval [-10, 10]. This is the default interval that Maple will use if you do not specify values for the input variable.

The next command plots the same curve but shows only the part where x is between 0 and 3. Notice that Maple decides for you which ouput values to display to make a good picture.

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

You can specify which values you would like to see for both the x and y axes.

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

The plot command will be used extensively in Calculus I.

<Text-field style="Heading 4" layout="Heading 4">Exercises</Text-field>

1. Plot the graph of 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 over the interval [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]. Recall that Maple understands "Pi" to be 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.

2. Plot the graph of 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 over the interval [-12,12], with the y-axis values from -2 to 2.