Chapter 8
Calculating in Mathcad
Defining and Evaluating Variables
Defining and Evaluating Functions
Units and Dimensions
Working with Results
Controlling Calculation
Error Messages
Defining and Evaluating Variables
Variables allow you to define values to be used to evaluate expressions and solve equations.
Defining a Variable
A variable definition defines the value of a variable everywhere below and to the right of the definition. To define a variable:
1. Type the variable name.
2.Press the colon [:] key, or click 
on the Calculator toolbar. The definition symbol (:=) appears with a blank placeholder to the right.
3.Type an expression to complete the definition. This expression can include numbers and any previously defined variables and functions.
The left-hand side of a “:=” can contain any of the following:
• A simple variable name like x.
• A subscripted variable name like vi.
• A matrix whose elements are either of the above. For example, |
x |
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y1 |
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allows you to define several variables at once: each element on the right-hand side is assigned simultaneously to the corresponding element on the left-hand side.
•A function name with an argument list of simple variable names. For example, f(x, y, z). Names are described further in the next section.
•A superscripted (column) matrix name like M 1 .
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Names
A name in Mathcad is simply a sequence of characters you type referring to a variable or function used in computations.
Built-in Names
Mathcad’s built-in names include built-in variables and built-in functions.
•Some predefined or built-in variables either have a conventional value, like π (3.14159…) or e (2.71828…), or are used as system variables to control how Mathcad performs calculations. (See “Built-in Variables” on page 81.)
•In addition to these predefined variables, Mathcad treats the names of all built-in units as predefined variables. For example, Mathcad recognizes the name “A” as the ampere, “m” as the meter, “s” as the second, and so on. Choose Unit from the
Insert menu or click |
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on the Standard toolbar to see Mathcad’s predefined |
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units. (See “Units and |
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Dimensions” on page 90.) |
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• Choose Function from the Insert menu or click |
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on the Standard toolbar to |
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see Mathcad’s built-in functions. |
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User-defined Variable and Function Names
Names in Mathcad can contain any of the following characters:
•Uppercase and lowercase letters.
•The digits 0 through 9, although they cannot start a name.
•The underscore [_].
•The prime symbol [']. Note that this is not the same as an apostrophe. You can press [Ctrl] [F7] to insert it.
•The percent symbol [%].
•Greek letters. To insert a Greek letter, click a button on the Greek toolbar or type the equivalent Roman letter and press [Ctrl] G. (See “Greek Letters” on page 26.)
• The infinity symbol [∞]. Insert it by clicking |
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on the Calculus toolbar or by |
typing [Ctrl] [Shift] Z. |
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•The following are examples of valid names:
alpha |
b |
xyz700 |
A1_B2_C3_D4%%% |
F1' |
a%%x |
Note Mathcad distinguishes between uppercase and lowercase letters. For example, diam is a different variable from DIAM. Mathcad also distinguishes between names in different fonts, as discussed in “Math Styles” on page 35. Thus, Diam is also a different variable from Diam.
Online Help See “Variable and Function Names” in online Help for restrictions and other details for names in Mathcad.
Defining and Evaluating Variables / 81
Literal Subscripts
If you include a period in a variable name, Mathcad displays whatever follows the period as a subscript. You can use these literal subscripts to create variables with names like velinit and uair.
To create a literal subscript:
1. Type the text that appears before the subscript.
2. Type a period [.] followed by text that is to become the subscript.
Tip Do not confuse literal subscripts with array subscripts, which you generate with the left bracket
key [[] or by clicking 
on the Matrix toolbar. They appear similar, but behave quite differently in computations. A literal subscript is simply a cosmetic part of a variable name. An array subscript represents a reference to an array element. When you click on a name with a literal subscript, a period [.] displays in front of the subscript. See Chapter 5, “Range Variables and Arrays.”
Built-in Variables
Some built-in variables have conventional values, like π and e, and some are system variables that control how Mathcad works.
Note Mathcad treats the names of all built-in units as predefined variables. See “Units and Dimensions” on page 90.
Although Mathcad’s predefined variables already have values when you start Mathcad, you can still redefine them. For example, if you want to use a variable called e with a value other than the one Mathcad provides, enter a new definition, like e := 2. The variable e takes on the new value everywhere in the worksheet below and to the right of the new definition. Or create a global definition for the variable as described in “Global Definitions” on page 83.
Note Mathcad’s predefined variables are defined for all fonts, sizes, and styles. This means that if you redefine e as described above, you can still use e, for example, as the base for natural logarithms.
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You can modify some of Mathcad’s built-in variables without having to explicitly define them in your worksheet. To do so, choose Worksheet Options from the Tools menu, and click the Built-In Variables tab.
You can enter new values for any of these variables. Then choose Calculate > Worksheet from the Tools menu to ensure that all existing equations use the new values.
The numbers in brackets to the right of the variable names represent the default values for those variables.
Evaluating Expressions Numerically
To evaluate an expression numerically:
1.Type an expression containing any valid combination of numbers, variables, and functions. Any variables or functions should be defined earlier in the worksheet.
2.Press the “=” key or click 
on the Calculator toolbar. Mathcad computes the value of the expression and shows it after the equal sign.
Tip Whenever you evaluate an expression, Mathcad shows a final placeholder at the end of the equation. This placeholder is for unit conversions, as explained in “Working with Results” on page 93. As soon as you click outside the region, Mathcad hides the placeholder.
Figure 8-1 shows some results calculated from preceding variable definitions.
How Mathcad Scans a Worksheet
Mathcad scans a worksheet from left to right and top to bottom. This means that a variable or function definition involving a “:=” affects everything below and to the right of it.