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Introduction to MATHCAD: Laboratory Techniques and Data Analysis

This course provides an in-depth introduction to MATHCAD, focusing on laboratory techniques and data analysis. Starting with a review of fundamental concepts in arrays, vectors, and matrices, it progresses to matrix mathematics, statistics, and data plotting. Key topics include data entry, graph formatting, error analysis, and real-world applications such as the Photoelectric Effect. Participants will learn how to preprocess data, apply vector mathematics, and construct models for comparison with experimental data, enhancing their skills in scientific computation and graphical representation.

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Introduction to MATHCAD: Laboratory Techniques and Data Analysis

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  1. PH15720 Laboratory Techniques - An Introduction to MATHCAD

  2. Introduction • Review of Last Week • Arrays, Vectors and Matrices • Simple matrix & vector maths • Statistics • Plotting & analysing data with vectors

  3. Review of Last Week • Entering data with the Input Table • Extracting columns from a matrix • Creating simple X-Y graphs • Formatting graphs • Slope & Intercept

  4. Resistor Example from Lecture 4 #1 Input table as before Extract Voltage to vector & apply units Same for current

  5. Resistor Example from Lecture 4 #2 • Check on values of vectors

  6. Resistor Example from Lecture 4 - Plotting

  7. Error Bars #1 • Add to graph to show uncertainty in y values. • Create vector of ‘High’ values • Create vector of ‘Low’ values • Add as traces to y-axis • Add extra x-axis variables • Format as error bars

  8. Error Bars #2 • Use vector maths to get ‘high’ and ‘low’ vectors Huge error for illustration only

  9. Error Bars #3 • Add to graph

  10. Error Bars #4 • Format traces as Error Error type Hide Arguments&Show Legend

  11. Error Bars – Completed Graph

  12. Pre-Processing Data • Use vector maths to pre-process data before graphing • Use knowledge of physics to get data into a straight line format

  13. Photoelectric Effect #1 • Photoelectrons emitted from metal surface under illumination • Illuminate metal with light of different wavelength • Measure energy of emitted electrons (Stopping Potential) • Keller, Gettys & Skove p976

  14. The Photoelectric effect hv A e- VStop

  15. Photoelectric Effect #2 • Equation given in terms of frequency • Experimental data given in wavelength  convert Planck’s constant StoppingPotential Electronic Charge e Threshold Frequency Applied Frequency

  16. Converting Wavelength to Frequency - n=frequency (Hz) - c= velocity of light (3x108m/s) - l= wavelength (m) - Valid for all electromagnetic radiation

  17. Photoelectric effect #2 • Use resource centre for physical constants • Watch for confusion of e & q • Useful functions (look-up in help system) • slope(vx,vy)  slope of line • intercept(vx,vy)  intercept with axis

  18. Stopping Potential Equation • Vs  Stopping Potential • n  Frequency of radiation • n0 Threshold frequency • h  Planck’s constant • q  Electron Charge

  19. Photoelectric Effect #3 Curves for two different metals shown Slope of lines = h/q Intercept with x-axis (Vs=0) at Threshold Frequency (Different for each metal)

  20. Power Law • Systems in the form:Y=AeBx • Examples: • Cooling • Radioactive Decay • Compound Interest • B is time constant or rate constant

  21. Power Law • Take logs of Y values straight line • intercept gives ln(A) • slope gives B

  22. Power Law Example #1 • Data in input table as before • Extract Columns

  23. Power Law Example #2- Normal Plot Useless – No Information

  24. Power Law Example #3- Format y scale log • Straight line => power law • Need to get slope & intercept

  25. Power Law Example #4 • Take log of y data • Calculate slope & intercept • Display A&B • Create model

  26. Power Law Example #5Compare model vs data

  27. Review of Data Handling#1 • Use of Input Table • Column Extract Operator M<> • Add units if needed • Plot vector vs vector • Add Error bars

  28. Review of Data Handling#2 • Extract Information from data • slope() • intercept() • Pre-processing • Handling power law data • Create model & compare with data

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