Introduction to Mathcad

1
Introduction to Mathcad
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• Select Mathcad from the Start menu to begin
  execution
• By default, the Mathcad window includes the Menu
  bar and the Standard toolbar
• Select View/Toolbars/Math to add the Math toolbar

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• Clicking on the icons of the Math cause
  additional tool pallets to open
• Click on the Calculator icon
• Note that this is a detachable toolbar or pallet.
  It can be displayed with the other toolbars at
  the top or shown as a separate tool pallet
• The Calculator toolbar is convenient for
  selecting basic math operators
• Click on the icon containing ab to open the
  Greek toolbar or pallet
• The Greek toolbar is useful for entering Greek
  symbols in math and text expressions

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• An important concept in Mathcad is the
  distinction between
• Evaluation or Display operator
• Assignment operator
• move the cursor to the desired location and
  left-click to move the red insertion point cross
• type the characters25
• note the blue backwards L which marks the
  insertion point in the equation
• The key causes the expression on the left to be
  evaluated and with the result displayed to the
  right of the symbol

5

• Click below the first equation to move the red
  insertion point
• Type the charactersa34
• Note that typing a semicolon causes the entry of
  the combination which is the Assignment
  operator
• The expression on the right of the combination
  is evaluated and assigned to the variable named
  to the left of the
• Move the red insertion point down and
  typea
• The expression to the left of the is just the
  variable a which is evaluated with the result
  displayed to the right of the

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• Summary
• pressing the key causes the insertion of the
  Evaluation or Display operator the expression
  to the left of the is evaluated and displayed
  to the right of the
• pressing the key causes the insertion of the
  Assignment operator the expression to the right
  of the is evaluated and assigned to the
  variable named to left of the
• move the display expression above and to the
  right of the assignment operation
• Mathcad expressions are evaluated from the
  top-down

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• Mathcad allows the entry of parameters that
  include units.
• The unit systems used in a single expression can
  be mixed as shown with the combination of ft and
  cm
• The result is shown in Mathcads default internal
  unit system, SI in this case
• The small black square at right is a place holder
  where an alternate unit can be entered change
  the units to inches as shown

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• Mathcad will not allow inconsistent units in a
  single expression
• As shown, it is not legal to and feet and seconds
• As you have noticed, an expression shown in red
  indicates an error
• Clicking on the expression causes an error
  explanation to appear (some are more useful than
  others)

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• Type the expression a 2 5
• Note that the blue insertion point cursor
  includes a vertical and horizontal line segment
• The vertical segment indicates the point of
  insertion for the next character or operator
• The horizontal bar indicates the part of the
  expression that will affected by the next
  operation
• With the blue insertion point around the 5 press
  the space bar several times to change the length
  of the horizontal blue bar
• Pressing the / key with the 5 selected yields 4.5
• Pressing the / key with 25 selected yields 3.5

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• Enter a 2 5
• Press the space bar to select 25
• Click on the () tool in the Calculator tool
  pallet
• Press the space bar to select (25)
• Press the Insert key to flop the insertion
  point to the other side
• Press the key to indicate that we want to
  multiply the expression in parentheses
• Enter an 8 in the placeholder

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• We will calculate the volume of a cylindrical
  tank and its weight when filled with water
• Define the variables h and d for the height and
  diameter as shown
• Calculate the cross-sectional area (note that the
  value of pi can be obtained from the Greek symbol
  pallet)
• After entering the exponent 2, press the space
  bar to select d2
• Then, divide by 4 to complete the expression
• Display the cross-sectional area
• Calculate and display the volume
• Note that the units are correctly determined

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• Set the value of the density (note that the Greek
  character rho is available on the symbol pallet)
• Calculate the weight of the tank
• Like pi, the value of g is predefined in Mathcad
• The weight is easily shown in Newtons and pounds
  force.

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• Functions are defined by entering the function
  name followed by parentheses enclosing the
  function arguments
• The equation for the function is entered on the
  right side of the assignment operator
• Once defined, the function can be evaluated for
  any combination of meaningful parameters (i.e.,
  negative values of height dont make sense)
• The parameters entered for a function evaluation
  must include units
• Additional functions can use previously defined
  functions

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• We will now plot the variation of tank volume
  with diameter
• We will need to create a Range Variable for the
  plot. Click on the Vector and Matrix icon in the
  Toolbar
• To generate a range of values of diameter, define
  D with the first value in the desired range,
  followed by a comma and the second value in the
  desired sequence
• Click on the Range Variable tool in the Matrix
  tool pallet
• Enter the final value in the desired range

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• Display the variable D to verify that a sequence
  or range of values from 1 m to 4 m has been
  created.

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• Click on the Graph icon of the toolbar to open
  the Graph tool pallet
• Click on the X-Y Plot icon to open a plot form
• Enter the range variable D as the independent
  plot parameter
• Enter the volume function as the dependent
  parameter.
• The volume is evaluated at a constant height of
  2m and the range of diameter values
• The range on the axes can be changed by clicking
  on the plot and entering new values at the ends
  of the axes