


Laboratory Techniques  

An Introduction to MATHCAD 




Review of last week 

Vector and Matrix Maths 

Statistics 

Solving simultaneous equations with matrices 





Processing experimental data with arrays 

Adding Error bars to graphs 

PreProcessing Data 

Convert l to f 

Logarithms for power law 

Extract slope & intercept from data 




Take one or more inputs (parameters) and return
a value or values 

From f(x) toolbar if you don’t know the name 

Afunction(parameters)= 

Avariable:=Afunction(p1,p2,p3…) 

Use the help system/f(x) dialog 





Used for: 

Processing experimental data 

Statistics 

Resolving forces etc in 2D, 3D 

Coordinate transformations 

Simultaneous Equations 

Applying transforms to data 






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 





Same for defining ordinary variable 

Follow : with 

[:::] from toolbar 

<ctrlm> 

InsertMatrix 

Dialog box for rows & columns 






Matrix Multiplication 





Determinant 



Addition of constant 








Add, Multiply & Divide matrices/vectors 

Must have correct numbers of rows & columns 





From f(x) dialog box under “Statistics” 

Averaging 

mean()
‘Average value’ 

median() ‘Half way item’ 

mode()
‘Most common value’ 





Variance & Standard Deviation 

2 forms of each 

Analysis of sample 

Stdev(), Var() 

Analysis of whole population 

stdev(), var() 

Note capitalisation 






Can use matrix maths to solve linear
simultaneous equations 

Arise from: 

Electric Circuits 

Kirchoff’s laws 

Fluid Dynamics 






Kirchoff’s Node Law 

The sum of currents at a node is equal to zero 

Current does not build up at a node 

Kirchoff’s Loop Law 

The sum of potentials around a loop is equal to
zero 






Node Law 

I0I2I1 = 0 

Loop1 

I0R0e0+I2R2=0 

Loop2 

I2R2e1+I1R1=0 






Get rid of I2 & rewrite 



Loop 1 





Loop 2 






Ohms law 



Also works with arrays of resistances &
vectors of voltages & currents 






Loop1 & 

Loop2 from before 





Write in matrix form 




Give values to resistance & voltages 



Form solution step 



