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Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege

Engineering 25. EXCEL Integration. Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. Game Plan: Divide Unknown Area into Strips (or boxes), and Add Up. Excel Numerical Integration. Employ Trapezoidal rule with used Slanted-Line tops. Trapezoidal Elements

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Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege

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  1. Engineering 25 EXCELIntegration Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. Game Plan: Divide Unknown Area into Strips (or boxes), and Add Up Excel Numerical Integration • Employ Trapezoidal rule with used Slanted-Line tops

  3. Trapezoidal Elements • By Trapezoid Geometry • Then the Incremental Area

  4. Trapezoidal Integration by Excel • Integrate over 1.7-4.3 using Excel • That is, Find • Show Game Plan on Next Slides

  5. The Function Plotted

  6. Set Up Integration Strips

  7. Integration Equations • dA = [Avg Strip Hgt]*[Strip Width] Time For Live Demo

  8. Integration Result • See next Slide for Graphic • Note the relationship between y(x) and Iy(x) • Since is Iy(x) is the ANTI-Derivative of y(x), then y(x) is the Derivative of Iy(x) • Can use y(x) to find Max/Min values of Iy(x) • Can use y(x) to find Max/Min slopes of Iy(x)

  9. Max/MinLocal Values MaximumLocal Slopes

  10. Data Acq integration – NO Fcn

  11. Time in Excel  DAYS • Regardless of how TIME is DISPLAYED in a spreadsheet table, Excel ENCODES time in DAYS • Any “time” format can be converted to Fractional Days using either of • reFORMAT the current Cell • Copy-n-Paste VALUES into a number-formatted cell • Excel uses this “Day Code” to Add and/or Subtract Dates & Times

  12. Time↔DayCode Equivalency Time For Live Demo

  13. Excel HELP on DATE Codes • In Excel the “Date Codes Start at the “zero hour” of the year 1900 • See Excel help for more information • Remember all Times & Dates are internally stored as DAYS

  14. MATLAB Code % Bruce Mayer, PE * 07Dec09 % ENGR36 * EXCEL integration Prob % file = Excel_Integ_Stem_0912.m % % Set up WhtBd Graphic to show % integration Strips % x = [1.7:.05:4.3] y = 8*exp(-0.2*x).*sin(9*x.^0.63) + log(sqrt(7*x)) stem(x,y), grid, axis([1.6 4.4 -3.5 7])

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