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Appendix
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Section A2: Arithmetic Calculations
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Introduction


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Table A2.1 demonstrates how to implement the arithmetic operations of addition, subtraction, multiplication, division, and exponentiation in Maple. A number of the examples in the table have been computed "live" by means of the Context Panel option "Evaluate and Display Inline." This option evaluates the live math, and places the evaluation inline and to the right.

Addition

$2\+3$ = ${5}$${}$

Subtraction

$73$ = ${4}$${}$

Multiplication
(Math mode)

$2\cdot 3$ = ${6}$ (The explicit asterisk appears as the centered dot.)
$xy$ (The space character is interpreted as the multiplication operator.)

Multiplication
(Text mode)

${6}$

Division (Math mode)

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$\frac{2}{3}$ (The slash "/" automatically sets the fraction with numerator and denominator.)

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$2\/3$ (This style of setting a fraction is called "shilling" and is set by preceding the forward slash "/" with the backward slash "\", which serves as an escape character.)


Exponentiation
(Math mode)

${x}^{2}$ (Attempting to insert the caret ^ for exponentiation simply raises the cursor.)

Exponentiation
(Text mode)

${{x}}^{{2}}$

The Exponential $e$
(Math mode)

${\ⅇ}^{x}$
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Select the $\ⅇ$ from a palette (Constants and Symbols, or Common Symbols) or type the character "e" and bring up the commandcompletion table (Figure A2.1) from which the exponential $e$ can be selected. Command completion can be selected from the Tools menu, or implemented by pressing the Escape key (Esc).


Figure A2.1 The commandcompletion table for "e"




The Exponential $e$
(Text mode)

${\ⅇ}$
${{\ⅇ}}^{{x}}$

Table A2.1 Arithmetic operators in Maple



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Tables such as Table A2.1 are used extensively in this work to organize the onscreen display of calculations. A default setting for tables is to add expression labels automatically for each displayed calculation. It is possible to change this default so that no equation labels are displayed within a table.
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Enter some live math and press the Enter key.
Note the display of the expression label.


$x\+y$



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Launch Table Properties from the Format menu.

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In the Table Properties dialog, uncheck
"Show expression labels"
See Figure A2.1.


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Figure A2.1 Lower part of Table Properties dialog




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Enter some live math and press the Enter key.
Note the suppression of the expression label.


$x\+y$
${x}{\+}{y}$





Examples


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Example A2.1

Evaluate $\frac{2}{3}\+\frac{5}{7}$ both exactly and as a floatingpoint (decimal) number.

Example A2.2

Evaluate ${\left(2\+4\right)}^{2}\left(31\right)$.

Example A2.3

Determine if ${2}^{9}1$ is a composite number or a prime. If it is composite, find its integer factors.

Example A2.4

Explore each of the following: $\sqrt{2}\/3$, 5, ${e}^{3}$, $\mathrm{ln}\left(4\right)$, ${\mathrm{log}}_{2}\left(8\right)$.

Example A2.5

Find exact and floatingpoint (decimal) values for each of the following:
$\mathrm{sin}\left(\mathrm{\π}\/4\right)$, $\mathrm{cos}\left(1\right)$, $\mathrm{tan}\left(\mathrm{\π}\/12\right)$, ${\mathrm{sec}}^{1}\left(2\/\sqrt{3}\right)$



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