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Lecture_08_Bisection_Method

# Lecture_08_Bisection_Method - EGR 102 Introduction to...

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1 EGR 102 Lecture 8 1 EGR 102 Introduction to Engineering Modeling Bracketing Methods Chapter 5.2 & 5.4 Figures from: “Applied Numerical Methods with MATLAB,” Steven Chapra, McGraw Hill 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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2 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)=0 yields the solution to the problem. These problems often occur when a design problem presents an implicit equation for a required parameter. EGR 102 Lecture 8 3 EGR 102 Lecture 8 4 Roots a ac b b x c bx ax 2 4 0 2 2 ? 0 sin ? 0 2 3 4 5 x x x x f ex dx cx bx ax
3 EGR 102 Lecture 8 5 Roots of an equation: Values of x that make ƒ (x) = 0 Also called “zeros” of the equation Roots EGR 102 Lecture 8 6 Roots

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4 Graphical Methods A simple method for obtaining an estimate of the root of the equation 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 where roots may be and where some root-finding methods may fail: a) Same sign, no roots b) Different sign, one root c) Same sign, two roots d) Different sign, three roots EGR 102 Lecture 8 7 EGR 102 Lecture 8 8 Graphical Method
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Lecture_08_Bisection_Method - EGR 102 Introduction to...

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