1. An Introduction to MathCAD
Animation, Interpolation and other pretty pictures 1 1

2. Animation Example
Example from our LCR circuit

3. Animation #2 Basics Use FRAME variable
FRAME automatically set by mathCAD for each frame of animation
Select View|Animation… to bring up animation dialog
Give start & end values for FRAME
Select area to animate
Select Animate to produce
Save As… to create .avi file

4. Animation #3 Hints
“Error initialising Video Stream” => Nothing Selected
May want to scale FRAME
Animations can:
Take a long time to create
Produce big files
Windows video player allows thumb bar to step forward & back

5. Animation #4 More Hints Fix scale on graphs
Don’t need to include calculations in animation
Echo FRAME= in shot
If scaling, echo scaled variable
For frequency plots, scale FRAME thus:

6. Vector Field Plots #1 Plot matrix of complex numbers
Each point shown as vector
Plot scaled so that largest vector is gap between points
Useful for:
Electric fields
Magnetic fields
Dynamic Flows
Plotting Gradient of functions

7. Vector Field Plots #2

8. Data Analysis #1 Get data from file
Read data in from datafile
Use either:
Insert|Component|File Read or Write & follow the wizard
READPRN(“filename”)
Reads data from file into vector or matrix
File Read component offers many more file types

9. Data Analysis #2 Select the data we want
Use matrix functions to select data we are interested in
Rows(M) & Cols(M) to get size of data array
Submatrix(M,rs,rf,cs,cf) to select rectangular chunk
M<x> to select column
Csort to sort array
Augment & stack to build arrays

10. Data Analysis #3 Smoothing Data
medsmooth(vy,n) returns vy smoothed with running medians

11. Data Analysis #4 Linear regression
Slope & intercept functions take vectors of X & Y values

12. Data Analysis #5 Interpolation
2 stage process
Fit polynomial through points
cspline – cubic spline
Bspline – B-spline
Interpolate using polynomial obtained in stage 1
interp

13. Cubic Spline fit & Interpolated Fit

14. Function Fitting
Cspline & Bspline fit smooth curve through data points
In physical modelling, we know the shape of the function to fit, just need parameters
Example:
Response of photon counting detector

15. Function Fitting Example #1
Determine parameters a & b

16. Function Fitting Example #2
Rewrite f(x) and derivatives
Replace a,b by u0, u1…
Find partial derivatives of f(x)
Create vector of function & pds

17. Function fitting Example #3
Create vector of guess values
Call genfit to solve
Define function using params

18. Function Fitting Example #4
Plot f(x) against data