Lecture_08_Bisection_Method-1

Lecture_08_Bisection_Method-1 - EGR 102 Introduction to...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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)=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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Roots EGR 102 Lecture 8 6
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Graphical Method ± Use a graphical approach to determine the drag coefficient c
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/02/2012 for the course EGR 102 taught by Professor Hinds during the Spring '09 term at Michigan State University.

Page1 / 23

Lecture_08_Bisection_Method-1 - EGR 102 Introduction to...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online