1

 Laboratory Techniques 
 An Introduction to MATHCAD

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 The if() function
 Complex Numbers
 Symbolic Algebra

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 if(condition,Tval,Fval)
 condition evaluated
 True (¹0) è returns Tval
 False (=0) è
returns Fval

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 From evaluation palette
 = (bold, logical equals) <ctrl =>
 > greater than
 < less than
 ³ greater than
or equal to
 £ less than or
equal to
 ¹ Not equal to

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 False = 0
 True = 1 (or ¹0)
 Use multiplication for AND
 Use addition for OR
 (x>5)•(x<8)
 (x<3)+(x>16)

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 Different equations inside and outside conductor
 Inside:
 Outside:

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 Combine two equations using if() function

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 Handled same as other numbers
 Full range of complex maths
 Put i (or j) directly after complex number
 Enter i as 1i
 Use x to get modulus
 Use arg() to get argument
 Avoid using i as variable when using complex numbers

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 Principle roots found
 Need to get other roots by hand or by using polyroots()

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 Manipulate equations rather than numbers
 Symbolic Palette
 Evaluate ®
 Simplify
simplify ®
 Expand
expand,n ®
 Substitute substitute, n= n ®
 Solve solve, n ®

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 Not covered in depth here
 Handout gives resource centre references
 Worth a look

15

 From example sheet  solve
using mathCAD
 A manufacturer of tin cans wishes to maximise the volume contained in a
can, whilst minimising the amount of metal used to construct the can.
Show that, for given amount of metal, the volume of a can is maximised
when the radius is half the height.

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 Assume Area of tin constant
 Obtain expression for Volume in terms of Area and radius
 Find dVol/dr
 dVol/dr will be 0 at max volume so use this to find r
 Substitute to find r in terms of h

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 Need to find when dVol/dr=0
 Write down expressions for Volume & Area
 Use bold, logical equals sign

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 Copy & Paste expression for Area & solve for h

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 Copy & paste expression for Vol
 Substitute expression for h

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 Use symbolic differentiation to find dVol/dr
 This will be 0 at maximum

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 Solve for dVol/dr = 0 to find r
 2 solutions, copy +ve

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 Have expression for r in terms of Area
 Substitute expression for Area
 Now have expression for r in terms of r and h

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 Take expression for r in terms of r and h
 Add r=
 Solve for r to get answer

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 Modelling a discontinuous universe with the if() function
 Complex Numbers
 Symbolic Algebra

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 Next Week
 In class
 Processing experimental data

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 Comment & Explain
 Get paper size right (A4)
 Layout/Page breaks
 Use MathCAD 8 format
 Name/UserID on Header/Footer
 Attempt everything
