201-Lect 2 - Objectives MECH201 Understanding what roots...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Week 2 MECH201 Roots of Equations Chapter 5-8 Week 2 Objectives • Understanding what roots problems are and where they occur in engineering and science • Knowing how to determine a root graphically • Knowing how to solve a roots problem using bracketing methods • Knowing how to solve a roots problem with open methods Week 2 What are roots? • The values that make equation equal to zero. ( zeros of equations) • Eg. are the roots of equation a ac b b x 2 4 2 ± = () 0 2 = + + = c bx ax x f Week 2 Solution Methods • Some equations have analytical solutions • But many equations can not be solved directly or analytically • One method is the graphical method to plot the function and determine where it crosses the x- axis, the point of crossing is the root • Although the graphical methods are useful, it is limited because of their lack of precision
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Week 2 Solution Methods • An alternative approach is trial and error method, by guessing a value of x and evaluating whether f( x ) is zero. If not, another guess is repeated until a guess is the root • Such method is inefficient and inadequate of the requirements of engineering practice • For these cases, numerical methods provide efficient means to obtain the answer by employing systematic strategies Week 2 Graphical Methods • Step 1: to obtain f(x i ) for each selected x i • Step 2: to plot the selected points (x i , f(x i )) • Step 3: to derive the point crossing the x-axis, which is the root of the equation NB: Graphical methods can be utilized to obtain rough estimates though they are not very precise. These estimates can be employed as starting guesses for numerical methods Week 2 Eg: to find the root of the following eqn. using graphical method () 40 1 38 667 146843 0 = x . e x . x f Step 1: x f(x) 4 34.115 8 17.653 12 6.067 16 -2.269 20 -8.401 Week 2 Eg: to find the root of the following eqn.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/27/2009 for the course MECH 201 taught by Professor Weihuali during the Three '09 term at University of Wollongong, Australia.

Page1 / 7

201-Lect 2 - Objectives MECH201 Understanding what roots...

This preview shows document pages 1 - 3. Sign up to view the full document.

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