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Lecture_08_Bisection_Method-1

Lecture_08_Bisection_Method-1 - EGR 102 Introduction to...

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EGR 102 Introduction to Engineering Modeling Bracketing Methods hapter .1- .4 Chapter 5.1 5.4 EGR 102 Lecture 8 1 Figures from: “Applied Numerical Methods with MATLAB,” Steven Chapra, McGraw Hill
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Objectives ± Understand what roots problems are and where they occur in engineering and science. ± Know how to determine a root graphically. ± Know how to solve a roots problem with the bisection method. EGR 102 Lecture 8 2
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Roots ± “Roots” problems occur when some function f can be written in terms of one or more dependent variables x, where the solutions to f(x)=0yields the solution to the problem. ± These problems often occur when a design problem presents an implicit equation for a quired parameter required parameter. EGR 102 Lecture 8 3
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Roots ac b b x c bx ax 4 0 2 2 = = + + m a 2 n ? 0 2 3 4 5 = = + + + + + x f ex dx cx bx ax ? 0 sin = = + x x x EGR 102 Lecture 8 4
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Roots ± Roots of an equation: alues of x that make ) = 0 ± Values of x that make ƒ(x) = 0 ± Also called “zeros” of the equation EGR 102 Lecture 8 5
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Roots EGR 102 Lecture 8 6
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Graphical Methods A simple method for obtaining an estimate of the root of the equation =0 is to make a plot of the function f(x)0 is to make a plot of the function and observe where it crosses the x-axis. Graphing the function can also indicate here roots may be and where some where roots may be and where some root-finding methods may fail: a) Same sign, no roots ifferent sign one root b) Different sign, one root c) Same sign, two roots d) Different sign, three roots EGR 102 Lecture 8 7
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Graphical Method ± Use a graphical approach to determine the drag coefficient c
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Lecture_08_Bisection_Method-1 - EGR 102 Introduction to...

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