Lecture Module 1 - Introduction New

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ENGINEERING MATHEMATICS 4ENGINEERING MATHEMATICS 4

BDA34003

Lecture Module 1: Introduction

Waluyo Adi [email protected]


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BDA34003 Engineering Mathematics 4Waluyo Adi Siswanto ([email protected]

!

Course Objective

The main objective of learning Engineering Math 4is to provide students with the tools ofNUMERICAL METHODS NUMERICAL METHODS .

Engineering Math 4 umerical Methods

!umerical "nal#sis$


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Leari! Outco"es

"t the end of the course studentsshould be able to:

A""ly the #nowledge o$ di$$erentiation andintegration and standard numerical analysis tosol%e mathematical "ro&lems. ('3 )*+,

-nde"endently "roceed to li$e long learning inim"ro%ing the #nowledge. (A! )*+


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#$at %ou ca &o'( problem illustrations )

%ou can anal#&e this problem' and man# others

x

" ( ) * E

1o

) 1.1+4o

)1.1+4o

) 1.1,+1o

) 1.,+1o

)

-., -., -., -., -.,

1o

)

∂T

∂ t =0./

∂!

T

∂ x!

Aa(%sis Resu(ts


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#$at %ou ca &o'( problem illustrations )

%ou can prepare programming codes

function[L,U,d,x]=doolittle(A,B)

[m n]=size(A);if (m ~= n )disp ( 'LR2 eo! "#tix must $e s%u#e' );etun;end;L=zeos(m,m);U=zeos(m,m);& LU ecomposition (L**L+ "+*)

fo i=-!m fo .=-!i/- L(i,.)=A(i,.); fo 0=-!./- L(i,.)= L(i,.)/L(i,0)1U(0,.); end L(i,.) = L(i,.)U(.,.); end fo .=i!m U(i,.) = A(i,.);

fo 0=-!i/- U(i,.)= U(i,.)/L(i,0)1U(0,.); end endendfo i=-!m L(i,i)=-;+nd

& 3o4#d su$stitution 'Ld=$' to sol5e dd=zeos(m,-);d(-)=B(-)L(-,-);fo i=2!m d(i)=/L(i,-)1d(-); fo .=2!i/- d(i)=d(i)/L(i,.)1d(.); end; d(i)=(B(i)6d(i))L(i,i);end;

& B#c4#d su$stitution 'Ux=d' to sol5e xx=zeos(m,-);x(m)=d(m)U(m,m);i=m/-;%=7;48ile (i~= 7) x(i)=/U(i,m)1x(m); %=i6-; 48ile (%~=m) x(i)=x(i)/U(i,%)1x(%); %=%6-; end; x(i)=(d(i)6x(i))U(i,i); i=i/-;end;


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Re)ereces

(1) D. V. Griffiths, I. M. Smith. 2006. Numerical methods for enineers, 2th!dition. "oca #aton, $%& 'haman *all.

(2) +. N. Sharma. 200. Numerical methods for enineers and scientists,-anourne& /lha Science International.

() +aan iusalaas. 200. Numerical methods in enineerin 3ith M/4%/",'amride& 'amride 5niersit7 -ress.

() +ohn *. Mathe3s, urtis D. $in8. 200. Numerical methods usinM/4%/", th !dition. 5S 5er Saddle #ier, N+& -earson !ducation.

() %aurene $ausett. 2002. Numerical methods usin Math'/D, 5erSaddle #ier, Ne3 +erse7.

(6) Steen '. 'hara, #a7mond -. 'anale. 2002. Numerical methods forenineers& 3ith soft3are and rorammin alications, th !dition.

(9) Nafisah Md amaruddin, et. al. 200:. Numerical Method. -usat-ena;ian Sains, 54*M.

(:) 4a7 im Gai8. 200. *o3 to use 'alculator 'asio f.

(?) 4a7 im Gai8, %im ian "oon and #osmila /dul ahar. 2011. NumericalMethods usin 'asio f


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Mat$e"atica( Too(s)or Nu"erica( Co"*utatios

(1) SMath, htt&@@en.smath.info@forum@

(2) $reeMat, htt&@@freemat.sourcefore.net@

() Sci%a, htt&@@333.scila.or@

() >ctae, htt&@@333.nu.or@soft3are@octae@

() !uler, htt&@@euler.sourcefore.net@ (6) 'alfem, htt&@@sourcefore.net@ro;ects@calfem@

ree /oftware 0 open source software:

(1) Mathcad, htt&@@333.tc.com@roduct@mathcad@ (2) Matla, htt&@@333.math3or8s.com@roducts@matla@

() Male, htt&@@333.malesoft.com@roducts@Male@

() Mathematica, htt&@@333.3olfram.com@mathematica@

roprietar# /oftware !license re2uired$:

http://en.smath.info/forum/http://freemat.sourceforge.net/http://www.scilab.org/http://www.gnu.org/software/octave/http://euler.sourceforge.net/http://sourceforge.net/projects/calfem/http://www.ptc.com/product/mathcad/http://www.mathworks.com/products/matlab/http://www.maplesoft.com/products/Maple/http://www.wolfram.com/mathematica/http://www.wolfram.com/mathematica/http://www.maplesoft.com/products/Maple/http://www.mathworks.com/products/matlab/http://www.ptc.com/product/mathcad/http://sourceforge.net/projects/calfem/http://euler.sourceforge.net/http://www.gnu.org/software/octave/http://www.scilab.org/http://freemat.sourceforge.net/http://en.smath.info/forum/


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Subject De(iver%

Lecturi!

E+*(aii! t$eories, "et$o&s a& u&ersta&i! re(ate& to t$eto*ics-

Tutori!

Discussi! sa"*(e *rob(e"s re(ate& to t$e to*ics


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Assess"et Sc$e"e

/tudents attendance 3

ui& 0"ssignment !1-5$

roject !1-5$

Test !T1: 165 T,: 165$

inal E7amination !6-5$

3 "ttendance must not less than .0/


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art 1

1) Introduction to Numerical Analysis andError

2) Nonlinear Equations

3) Systems of Linear Equations

4) Interpolation

5) Numerical Differentiation


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art 2

) Numerical Inte!ration

") Ei!en #alues and Ei!en #ectors

$) %rdinary Differential Equations&) 'artial Differential Equations


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Lecture Ti"e Tab(es

lease refer to#our time tables


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INTRODCTIONINTRODCTION


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&ersta&i! Error Rou&o)) Error

Rou&o))Rou&o)) errors arise when numbers having limited significant figures are usedto represent e7act numbers.

There are two techni2ues : C$o**i!o)) and Rou&i!o)) !the most common8$

In general engineering applications Rou&i! tec$i5ue is a(6a%s use&


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&ersta&i! Error Trucatio Error

TrucatioTrucatio errors arise when appro7imations are used to represent e7act numbers.

See t$e &i))erece 7See t$e &i))erece 7


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&ersta&i! Error Error Aa(%sis

"bsolute error 9

elative error 9∣ Exact − Approximation ∣

∣ Exact ∣

∣ Exact − Approximation ∣

In mechanical engineering' for e7ample

elative Error 9

∣ Measured result −Simulation result ∣

∣ Measured result ∣


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Stu&et Activit%Stu&et Activit%


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rob(e" 1A1

E7periment /imulation result

6-;

6-;

/ensor reading,--.6< Ma

numerical result1+? Ma

a$ E7press the numerical result in , decimal places !6$% 2 8 &iscuss 8$b$ @hat is the relative error of the simulation result to the e7perimental result


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Lecture Module 1 - Introduction New

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