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## MATH OF ENGR

by: Daren Beatty Jr.

16

0

3

# MATH OF ENGR ME 17

Daren Beatty Jr.
UCSB
GPA 3.94

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
3
WORDS
KARMA
25 ?

## Popular in Mechanical Engineering

This 3 page Class Notes was uploaded by Daren Beatty Jr. on Thursday October 22, 2015. The Class Notes belongs to ME 17 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/227083/me-17-university-of-california-santa-barbara in Mechanical Engineering at University of California Santa Barbara.

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Date Created: 10/22/15
fx XAZ l Xfzerof 2 Finds the root closest the the initial guess here the guess is 2 l Xfzerof2 X Xfzerofm l Xfzerof0 2 One can define an interval that brackets the root as initial guess X Xfzerof 2 2 The endpoints of the bracket interval return f values of same sign which leads to an error Error using gt lta hrefquotmatlab opentoline39CProgram FilesMATLABR2008atoolboxmatlabfunfunfzerom392930quotgtfzero at 293ltagt The function values at the interval endpoints must differ in sign Here is an example of the different steps taken by the FZERO function e combination of 1 First define an interval where a sign change occurs starting at the nitial guess 2 Use a combination of bissection and inverse quadratic nterpolation ie an open method to find the root o0 gt o0 gt o0 gt optionsoptimset39display3939iter39 x fxfzerox x010 l 5 optionm Search for an interval around 05 containing a sign change Func count a fa b fb Procedure 1 05 0999023 05 0999023 initial interval 3 0485858 0999267 0514142 0998709 search 5 048 099935l 052 0998554 search 7 047l7l6 0999454 0528284 0998307 search 9 046 0999576 054 0997892 search 11 0443431 0999706 0556569 0997148 search 13 042 0999829 058 0995692 search 15 0386863 0999925 0613137 0992491 search 17 034 0999979 066 0984317 search 19 0273726 0999998 0726274 0959167 search 21 018 1 082 0862552 search 23 00474517 1 0952548 0385007 search 25 014 1 114 270722 search Search for a zero in the interval 014 114 Func count x fx Procedure 25 014 1 initial 26 0205272 1 interpolation 27 0672636 0981042 bisection 28 0906318 0626056 bisection 29 102316 0257278 bisection 30 0989128 0103551 interpolation 31 0998894 00110017 interpolation 32 100001 768385e 005 interpolation 33 1 383061e 007 interpolation 34 1 13245e 011 interpolation 35 1 0 interpolation Zero found in the interval 014 11M x 1 fx 0 MATLAB like any software does not always produce a correct answer This comes from the fact that algorithm do not converge to solution In this case it is important to nderstand enough about the underlying algorithms to be able to fix the problem In the following ase changing the initial guess is the fix o C o O rho123mu179e 5D005V40e00151000 RerhoVDmu gf 1sgrtf2log10e37D251Resgrtf fplotg 0008 0081 grid on o 6 The plot of this function g is 3 x x x x 1 x x 001 002 003 004 005 006 007 008 MATLAB can fail fzerog 0008 Exiting fzero aborting search for an interval containing a sign change because complex function value encountered during search Function value at 0000224 is 382705 68l739i Check function or try again with a different starting value ans NaN MATLAB has failed Another guess gives fzerog 03 ans 00290 If we consider polynomial ie a special kind of functions then we an find all the roots using a predefined MATLAB function called ROOTS Define X l al l o O o0

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