ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 1 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 25 EXCEL Integration

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 2 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Excel Numerical Integration  Game Plan: Divide Unknown Area into Strips (or boxes), and Add Up  Employ Trapezoidal rule with used Slanted-Line tops

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 3 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods  Trapezoidal Elements  By Trapezoid Geometry  Then the Incremental Area

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 4 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Trapezoidal Integration by Excel  Integrate over using Excel  That is, Find  Show Game Plan on Next Slides

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 5 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods The Function Plotted

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 6 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Set Up Integration Strips

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 7 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Integration Equations  dA = [Avg Strip Hgt]*[Strip Width]

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 8 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Integration Result  See next Slide for Graphic  Note the relationship between y(x) and I y (x)  Since is I y (x) is the ANTI-Derivative of y(x), then y(x) is the Derivative of I y (x) Can use y(x) to find Max/Min values of I y (x) Can use y(x) to find Max/Min slopes of I y (x)

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 9 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Maximum Local Slopes Max/Min Local Values

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 10 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Data Acq integration – NO Fcn

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 11 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods 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

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 12 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Time↔DayCode Equivalency

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 13 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods 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

ENGR-25_EXCEL_Integration_Tutorial-Example.pptx 14 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods 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([ ])