Class08 - Class meeting #8 Monday, Sept 20th GEEN 1300...

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1 GEEN 1300 Introduction to Engineering Computing Class meeting #8 Monday, Sept 20 th circular calculations and the iterative solver solving nonlinear equations live solution using bisection spherical tank problem TABLE function application Spreadsheet Problem Solving 1 Homework #4, due Wednesday Section Test 1, next Monday, Sept 27th, 7–9pm, HUMN 1B50 and RAMY C250 Coverage: Class #1 through #8 today, Labs 1-5 Text, pages 1-274 Section Test 1, next Monday, Sept 27th, 7–9pm, HUMN 1B50 and RAMY C250 Coverage: Class #1 through #8 today, Labs 1-5 Text, pages 1-274 REMINDER Text, pages 1 274 HUMN 1B50 (cap’y 284) Sections 101, 102, 103, 104, 105, 106 (139 students) RAMY C250 (cap’y 204) Sections 107, 109, 110, 111, 112 (109 students) 2 Bring only calculator (spare batteries), two pencils and eraser
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2 What is a circular calculation? Calculation involving one or many formulas Answer “x” Estimate “x” for the solution to be correct, the estimate x ” going into the calculation has to be equal to the answer x ” coming out of the calculation 3 A simple example:  1 x sin x estimate answer This is also called an problem   x gx or a substitution problem or a fixed-point iteration problem Note: by rearranging the above to   x gx 0 we get a standard equation-solving problem 4     f xx g x 0  or an f x0 problem and we use different methods to solve it (later!)
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3 For our simple example,  1 x sin x estimate answer Circular Calculation of x=1/sin(x) Estimate Answer 0.5 2.086 1.149 2.086 1.096 1.124 1.149 1.096 1.000 1.500 2.000 2.500 x value 5 1.109 1.117 1.113 1.115 1.124 1.109 1.117 1.113 0.000 0.500 12345678 try Excel-based solution using formula copying Copy formulas down 6
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4 Excel-based solution using the iterative solver File Button Options Formulas Set up Excel for iterative solving first Default settings 7 Typical settings then click OK Setting up the iterative calculation on the spreadsheet Initial estimate for x g(x) based on what’s in B2 the result of the first try enter a “pointer” formula to 8 cell B3 in place of the initial estimate this “closes the loop” on the circular calculation
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5 as soon as you press Enter, the calculation proceeds by one iteration and “Calculate” is shown on the Status bar to indicate tha the Status bar to indicate that you are in an iterative situation Note: the spreadsheet will not update automatically now you have to force it to re-calculate with Pressing the F9 key a few times will cause the calculation to converge to the correct 9 the F9 [ Calculate ] key answer (approximately) since “estimate” x agrees with “answer” x, the equation is solved, numerically There are (at least) a couple issues here: 1) if you want to reset the calculation to the starting estimate (0 5) and run through it again you have estimate (0.5) and run through it again, you have to replace the pointer formula in B2 with 0.5, and then put the pointer formula back in -- not convenient!
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This note was uploaded on 11/07/2010 for the course CHEN 1300 at Colorado.

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Class08 - Class meeting #8 Monday, Sept 20th GEEN 1300...

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