PH15010

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PH15010

• Laboratory Techniques -
• An Introduction to MATHCAD

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Introduction

• Review of last week
• Vector and Matrix Maths
• Statistics
• Solving simultaneous equations with matrices

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Review of Last Week

• Processing experimental data with arrays
• Adding Error bars to graphs
• Pre-Processing Data
• Convert l to f
• Logarithms for power law
• Extract slope intercept from data

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Functions Reviewed

• Take one or more inputs (parameters) and return a
  value or values
• From f(x) toolbar if you dont know the name
• Afunction(parameters)
• AvariableAfunction(p1,p2,p3)
• Use the help system/f(x) dialog

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Matrix Vector Maths

• Used for
• Processing experimental data
• Statistics
• Resolving forces etc in 2D, 3D
• Co-ordinate transformations
• Simultaneous Equations
• Applying transforms to data

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Creating Arrays in MathCAD

• 2 ways of entering arrays
• Input Table (already encountered)
• Spreadsheet type entry
• Expand to fit data available
• Insert Matrix Dialog box
• Array of placeholders
• Good if you know how many elements in
  matrix/vector

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Creating an array with InsertMatrix

• Same for defining ordinary variable
• Follow with
• from toolbar
• ltctrl-mgt
• InsertMatrix
• Dialog box for rows columns

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Creating arrays with InsertMatrix
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Matrix Maths 1
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Matrix Maths 2(Symbolically)

• Matrix Multiplication
• Determinant
• Addition of constant

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Matrix Vector Maths

• Add, Multiply Divide matrices/vectors
• Must have correct numbers of rows columns

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Addressing Arrays with Indices

• Index addressing allows access to individual
  elements of array
• Examine Set elements
• Indices start at 0
• Indices use key
• 2D matrices use two indices for row, column
  selection

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Indices 1 Vector Example

• Simple 2 element vector
• Examine elements
• Set element 0
• Result of setting

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Indices 2Matrix Example

• Sample matrix
• Examine elements
• Subscript too big
• Set element
• Result

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Accessing Parts Of Arrays

• Index addressing single element ?
• Column Extract operator Mltgt ?
• Submatrix() function
• Transposing matrices

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The submatrix() function
Define a matrix
Use submatrix() to extract part of the array
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Transpose Rows Columns

• Uses MT operator
• From matrix toolbar

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Other matrix functions1. Information

• Return information about
• Size of matrix
• rows(M), cols(M), last(V), length(V)
• Contents of matrix
• min(A), max(A)
• ?V

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Other matrix functions2. Manipulation

• Create new arrays
• Put 2 arrays together
• stack(A1,A2)
• augment(A1,A2)
• Sorting
• sort(V), reverse(A)
• rsort(M,r), csort(M,c)

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Statistical Functionson Vectors 1

• From f(x) dialog box under Statistics
• Averaging
• mean() Average value
• median() Half way item
• mode() Most common value

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Statistical Functionson Vectors 2

• Variance Standard Deviation
• 2 forms of each
• Analysis of sample
• Stdev(), Var()
• Analysis of whole population
• stdev(), var()
• Note capitalisation

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Vectorise Operator 1

• From matrix toolbar
• Forces evaluation on element by element basis
• Overrides normal matrix maths
• dot product
• Determinant M
• Powers Mx

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Vectorise Operator 2

• Dot product
• With vectorise operator

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Range Variables

• Take on a series of values
• Define using semicolon

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Range Variables 2

• Restrictions on where used
• illegal context error message
• Useful for filling arrays

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Filling Arrays using RVs

• Define RV
• Use RV in array index expression

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Processing Arrays using RVs

• Use RV in expressions to create output array from
  input array

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Range Variables with different step sizes

• Can create RVs with different step sizes.
• Enter first 2 values separated by comma ,
  before typing

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Summation 1

• Summation operator on matrix palette
• Sum of all elements in a vector

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Summation 2

• Operators on Calculus palette
• Do summation on any expression
• 2 forms
• Plain gt defines local RV
• Range Variable gt uses existing RV

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Summation 3

• Sum of first 5 integers
• Sum of elements 20-30 of vector Counts

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Summation 4Reciprocals of factorials

• 2 terms
• 4 terms
• 9 terms

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Data Files

• Used Input table to put data into MathCAD by
  hand.
• Can use Import on input table to get from a file
  (makes a copy)
• Select table right-click
• Also can link to data file with File Read
  Component (preferred)

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Reading Data Files 1

• File Read Component
• Reads from datafile ? array
• Text files
• Numbers separated by comma or tab
• Other formats supported

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Reading Data Files 2

• InsertComponentFile Read or Write
• Wizard
• (Select file type)
• Browse for file
• Finish
• Give name for array

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Reading Data Files 3

• Example

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This weeks worksheet

• Arrays Indices
• Columns (Revision)
• Submatrix() function
• Other array functions
• Reading data from file