Chapter Simpson s 1/3 Rule of Integration. ( x)
|
|
|
- Phoebe Beasley
- 6 years ago
- Views:
Transcription
1 Cpter 7. Smpso s / Rule o Itegrto Ater redg ts pter, you sould e le to. derve te ormul or Smpso s / rule o tegrto,. use Smpso s / rule t to solve tegrls,. develop te ormul or multple-segmet Smpso s / rule o tegrto,. use multple-segmet Smpso s / rule o tegrto to solve tegrls, d. derve te true error ormul or multple-segmet Smpso s / rule. Wt s tegrto? Itegrto s te proess o mesurg te re uder uto plotted o grp. Wy would we wt to tegrte uto? Amog te most ommo emples re dg te veloty o ody rom elerto uto, d dsplemet o ody rom veloty uto. Trougout my egeerg elds, tere re wt sometmes seems lke outless ppltos or tegrl lulus. You red out some o tese ppltos Cpters 7.A-7.G. Sometmes, te evluto o epressos volvg tese tegrls eome dutg, ot determte. For ts reso, wde vrety o umerl metods s ee developed to smply te tegrl. Here, we wll dsuss Smpso s / rule o tegrl ppromto, w mproves upo te ury o te trpezodl rule. Here, we wll dsuss te Smpso s / rule o ppromtg tegrls o te orm were I d s lled te tegrd, lower lmt o tegrto upper lmt o tegrto Smpso s / Rule Te trpezodl rule ws sed o ppromtg te tegrd y rst order polyoml, d te tegrtg te polyoml over tervl o tegrto. Smpso s / rule s 7..
2 7.. Cpter 7. eteso o Trpezodl rule were te tegrd s ppromted y seod order polyoml. Fgure Itegrto o uto Metod : Hee I d d were s seod order polyoml gve y. Coose,,,, d, s te tree pots o te uto to evlute, d. Solvg te ove tree equtos or ukows,, d gve
3 Smpso s / Rule o Itegrto 7.. Te d I d Susttutg vlues o, d gve d Se or Smpso / rule, te tervl [ ], s roke to segmets, te segmet wdt Hee te Smpso s / rule s gve y d Se te ove orm s / ts ormul, t s lled Smpso s / rule. Metod : Smpso s / rule lso e derved y ppromtg y seod order polyoml usg Newto s dvded deree polyoml s were
4 7.. Cpter 7. Itegrtg Newto s dvded deree polyoml gves us d d d Susttutg vlues o,, d to ts equto yelds te sme result s eore d Metod : Oe ould eve use te Lgrge polyoml to derve Smpso s ormul. Note y metod o tree-pot qudrt terpolto e used to ompls ts tsk. I ts se, te terpoltg uto eomes Itegrtg ts uto gets
5 Smpso s / Rule o Itegrto 7.. d Beleve t or ot, smplyg d torg ts lrge epresso yelds you te sme result s eore d. Metod : Smpso s / rule lso e derved y te metod o oeets. Assume d Let te rgt-d sde e et epresso or te tegrls, d, d d d. Ts mples tt te rgt d sde wll e et epressos or tegrls o y ler omto o te tree tegrls or geerl seod order polyoml. Now d
6 7.. Cpter 7. d d Solvg te ove tree equtos or, d gve Ts gves d Te tegrl rom te rst metod d d e vewed s te re uder te seod order polyoml, wle te equto rom Metod d e vewed s te sum o te res o tree retgles. Emple Te dste overed y roket meters rom 8 t s to t s s gve y l dt t t Use Smpso s / rule to d te ppromte vlue o. Fd te true error, t E. Fd te solute reltve true error, t.
7 Smpso s / Rule o Itegrto 7..7 Soluto 8 9 t l 9. 8t t 8 l m 8 l m 9 l m 9 8 [ 8 9 ] [ ].7 m Te et vlue o te ove tegrl s l 9.8t dt t 8. m So te true error s E t True Vlue Appromte Vlue m Te solute reltve true error s True Error t True Vlue.8.
8 7..8 Cpter 7..9% Multple-segmet Smpso s / Rule Just lke multple-segmet trpezodl rule, oe sudvde te tervl [ ], to segmets d pply Smpso s / rule repetedly over every two segmets. Note tt eeds to e eve. Dvde tervl [ ], to equl segmets, so tt te segmet wdt s gve y. Now d d were d d d d d... Apply Smpso s /rd Rule over e tervl,... d Se...,,, te... d { } { } [ ]......
9 Smpso s / Rule o Itegrto 7..9 odd eve Emple d odd eve Use -segmet Smpso s / rule to ppromte te dste overed y roket meters rom t 8 s to t s s gve y l 9.8t dt t 8 Use our segmet Smpso s /rd Rule to estmte. Fd te true error, E t or prt. Fd te solute reltve true error, t or prt. Soluto: Usg segmet Smpso s / rule, t t t odd eve 8 8. t l 9. 8t t t So t 8 8 l m 8 t 8..
10 7.. Cpter 7.. l 9.8..m. t l m 9 t 9... l m. t t l m t t t odd eve 8 8 t t odd eve [ 8 t t t ] [ ] m Te et vlue o te ove tegrl s [ ] l 9.8t dt t 8. m So te true error s True Vlue Appromte Vlue E t E t... m t
11 Smpso s / Rule o Itegrto 7.. Te solute reltve true error s True Error t True Vlue...7% Tle Vlues o Smpso s / rule or Emple wt multple-segmets Appromte Vlue Et t %.7%.%.%.% Error Multple-segmet Smpso s / rule Te true error sgle pplto o Smpso s /rd Rule s gve y E t, < < 88 I multple-segmet Smpso s / rule, te error s te sum o te errors e pplto o Smpso s / rule. Te error te segmets Smpso s /rd Rule s gve y E, < < 88 9 E, < < 88 9 : E, < < 88 9 : Te te true error epresso stds or te ourt dervtve o te uto.
12 7.. Cpter 7., 88 < < E 9 E < <, 88 Hee, te totl error te multple-segmet Smpso s / rule s 9 E t E 9 9, 8 Te term s ppromte verge vlue o < <,. Hee 8 E t were INTEGRATION Top Smpso s / rule Summry Tetook otes o Smpso s / rule Mjor Geerl Egeerg Autors Autr Kw, Mel Ketelts
13 Smpso s / Rule o Itegrto 7.. Dte Deemer, 7 We Ste ttp://umerlmetods.eg.us.edu
Mathematically, integration is just finding the area under a curve from one point to another. It is b
Numerl Metods or Eg [ENGR 9] [Lyes KADEM 7] CHAPTER VI Numerl Itegrto Tops - Rem sums - Trpezodl rule - Smpso s rule - Rrdso s etrpolto - Guss qudrture rule Mtemtlly, tegrto s just dg te re uder urve rom
Chapter Simpson s 1/3 Rule of Integration. ( x)
Cper 7. Smpso s / Rule o Iegro Aer redg s per, you sould e le o. derve e ormul or Smpso s / rule o egro,. use Smpso s / rule o solve egrls,. develop e ormul or mulple-segme Smpso s / rule o egro,. use
Numerical Differentiation and Integration
Numerl Deretto d Itegrto Overvew Numerl Deretto Newto-Cotes Itegrto Formuls Trpezodl rule Smpso s Rules Guss Qudrture Cheyshev s ormul Numerl Deretto Forwrd te dvded deree Bkwrd te dvded deree Ceter te
Chapter 12-b Integral Calculus - Extra
C - Itegrl Clulus Cpter - Itegrl Clulus - Etr Is Newto Toms Smpso BONUS Itroduto to Numerl Itegrto C - Itegrl Clulus Numerl Itegrto Ide s to do tegrl smll prts, lke te wy we preseted tegrto: summto. Numerl
Chapter Trapezoidal Rule of Integration
Cper 7 Trpezodl Rule o Iegro Aer redg s per, you sould e le o: derve e rpezodl rule o egro, use e rpezodl rule o egro o solve prolems, derve e mulple-segme rpezodl rule o egro, 4 use e mulple-segme rpezodl
MTH 146 Class 7 Notes
7.7- Approxmte Itegrto Motvto: MTH 46 Clss 7 Notes I secto 7.5 we lered tht some defte tegrls, lke x e dx, cot e wrtte terms of elemetry fuctos. So, good questo to sk would e: How c oe clculte somethg
3/20/2013. Splines There are cases where polynomial interpolation is bad overshoot oscillations. Examplef x. Interpolation at -4,-3,-2,-1,0,1,2,3,4
// Sples There re ses where polyoml terpolto s d overshoot oslltos Emple l s Iterpolto t -,-,-,-,,,,,.... - - - Ide ehd sples use lower order polyomls to oet susets o dt pots mke oetos etwee djet sples
CS321. Introduction to Numerical Methods
CS Itroducto to Numercl Metods Lecture Revew Proessor Ju Zg Deprtmet o Computer Scece Uversty o Ketucky Legto, KY 6 6 Mrc 7, Number Coverso A geerl umber sould be coverted teger prt d rctol prt seprtely
Chapter Gauss-Seidel Method
Chpter 04.08 Guss-Sedel Method After redg ths hpter, you should be ble to:. solve set of equtos usg the Guss-Sedel method,. reogze the dvtges d ptflls of the Guss-Sedel method, d. determe uder wht odtos
In Calculus I you learned an approximation method using a Riemann sum. Recall that the Riemann sum is
Mth Sprg 08 L Approxmtg Dete Itegrls I Itroducto We hve studed severl methods tht llow us to d the exct vlues o dete tegrls However, there re some cses whch t s ot possle to evlute dete tegrl exctly I
CS321. Numerical Analysis
CS Numercl Alyss Lecture 4 Numercl Itegrto Proessor Ju Zg Deprtmet o Computer Scece Uversty o Ketucky Legto, KY 456 6 Octoer 6, 5 Dete Itegrl A dete tegrl s tervl or tegrto. For ed tegrto tervl, te result
Simpson s 1/3 rd Rule of Integration
Simpso s 1/3 rd Rule o Itegrtio Mjor: All Egieerig Mjors Authors: Autr Kw, Chrlie Brker Trsormig Numericl Methods Eductio or STEM Udergrdutes 1/10/010 1 Simpso s 1/3 rd Rule o Itegrtio Wht is Itegrtio?
Numerical differentiation (Finite difference)
MA umercl Alyss Week 4 To tk d wrte portle progrms we eed strct model of ter computtol evromet. Ftful models do est ut tey revel tt evromet to e too dverse forcg portle progrmmers to lot eve te smplest
under the curve in the first quadrant.
NOTES 5: INTEGRALS Nme: Dte: Perod: LESSON 5. AREAS AND DISTANCES Are uder the curve Are uder f( ), ove the -s, o the dom., Prctce Prolems:. f ( ). Fd the re uder the fucto, ove the - s, etwee,.. f ( )
UNIVERSITI KEBANGSAAN MALAYSIA PEPERIKSAAN AKHIR SEMESTER I SESI AKADEMIK 2007/2008 IJAZAH SARJANAMUDA DENGAN KEPUJIAN NOVEMBER 2007 MASA : 3 JAM
UNIVERSITI KEBANGSAAN MALAYSIA PEPERIKSAAN AKHIR SEMESTER I SESI AKADEMIK 7/8 IJAZAH SARJANAMUDA DENGAN KEPUJIAN NOVEMBER 7 MASA : 3 JAM KOD KURSUS : KKKQ33/KKKF33 TAJUK : PENGIRAAN BERANGKA ARAHAN :.
Numerical Analysis Topic 4: Least Squares Curve Fitting
Numerl Alss Top 4: Lest Squres Curve Fttg Red Chpter 7 of the tetook Alss_Numerk Motvto Gve set of epermetl dt: 3 5. 5.9 6.3 The reltoshp etwee d m ot e ler. Fd futo f tht est ft the dt 3 Alss_Numerk Motvto
Numerical Methods. Lecture 5. Numerical integration. dr hab. inż. Katarzyna Zakrzewska, prof. AGH. Numerical Methods lecture 5 1
Numeril Methods Leture 5. Numeril itegrtio dr h. iż. Ktrzy Zkrzewsk, pro. AGH Numeril Methods leture 5 Outlie Trpezoidl rule Multi-segmet trpezoidl rule Rihrdso etrpoltio Romerg's method Simpso's rule
Chapter Gauss Quadrature Rule of Integration
Chpter 7. Guss Qudrture Rule o Integrtion Ater reding this hpter, you should e le to:. derive the Guss qudrture method or integrtion nd e le to use it to solve prolems, nd. use Guss qudrture method to
12 Iterative Methods. Linear Systems: Gauss-Seidel Nonlinear Systems Case Study: Chemical Reactions
HK Km Slghtly moded //9 /8/6 Frstly wrtte t Mrch 5 Itertve Methods er Systems: Guss-Sedel Noler Systems Cse Study: Chemcl Rectos Itertve or ppromte methods or systems o equtos cosst o guessg vlue d the
INTERPOLATION(2) ELM1222 Numerical Analysis. ELM1222 Numerical Analysis Dr Muharrem Mercimek
ELM Numerl Alss Dr Murrem Merme INTEROLATION ELM Numerl Alss Some of te otets re dopted from Luree V. Fusett Appled Numerl Alss usg MATLAB. rete Hll I. 999 ELM Numerl Alss Dr Murrem Merme Tod s leture
Chapter Runge-Kutta 2nd Order Method for Ordinary Differential Equations
Cter. Runge-Kutt nd Order Metod or Ordnr Derentl Eutons Ater redng ts cter ou sould be ble to:. understnd te Runge-Kutt nd order metod or ordnr derentl eutons nd ow to use t to solve roblems. Wt s te Runge-Kutt
DATA FITTING. Intensive Computation 2013/2014. Annalisa Massini
DATA FITTING Itesve Computto 3/4 Als Mss Dt fttg Dt fttg cocers the problem of fttg dscrete dt to obt termedte estmtes. There re two geerl pproches two curve fttg: Iterpolto Dt s ver precse. The strteg
this is the indefinite integral Since integration is the reverse of differentiation we can check the previous by [ ]
![this is the indefinite integral Since integration is the reverse of differentiation we can check the previous by [ ]](/thumbs/78/76749440.jpg "this is the indefinite integral Since integration is the reverse of differentiation we can check the previous by [ ]")
Atervtves The Itegrl Atervtves Ojectve: Use efte tegrl otto for tervtves. Use sc tegrto rules to f tervtves. Aother mportt questo clculus s gve ervtve f the fucto tht t cme from. Ths s the process kow
Integration by Parts for D K
Itertol OPEN ACCESS Jourl Of Moder Egeerg Reserc IJMER Itegrto y Prts for D K Itegrl T K Gr, S Ry 2 Deprtmet of Mtemtcs, Rgutpur College, Rgutpur-72333, Purul, West Begl, Id 2 Deprtmet of Mtemtcs, Ss Bv,
Trapezoidal Rule of Integration
Trpezoidl Rule o Itegrtio Civil Egieerig Mjors Authors: Autr Kw, Chrlie Brker http://umericlmethods.eg.us.edu Trsormig Numericl Methods Eductio or STEM Udergrdutes /0/00 http://umericlmethods.eg.us.edu
Area and the Definite Integral. Area under Curve. The Partition. y f (x) We want to find the area under f (x) on [ a, b ]
![Area and the Definite Integral. Area under Curve. The Partition. y f (x) We want to find the area under f (x) on [ a, b ]](/thumbs/83/87614710.jpg "Area and the Definite Integral. Area under Curve. The Partition. y f (x) We want to find the area under f (x) on [ a, b ]")
Are d the Defte Itegrl 1 Are uder Curve We wt to fd the re uder f (x) o [, ] y f (x) x The Prtto We eg y prttog the tervl [, ] to smller su-tervls x 0 x 1 x x - x -1 x 1 The Bsc Ide We the crete rectgles
Module 2: Introduction to Numerical Analysis
CY00 Itroducto to Computtol Chemtr Autum 00-0 Module : Itroducto to umercl Al Am of the preet module. Itroducto to c umercl l. Developg mple progrm to mplemet the umercl method opc of teret. Iterpolto:
Trapezoidal Rule of Integration
Trpezoidl Rule o Itegrtio Mjor: All Egieerig Mjors Authors: Autr Kw, Chrlie Brker Trsormig Numericl Methods Eductio or STEM Udergrdutes /0/200 Trpezoidl Rule o Itegrtio Wht is Itegrtio Itegrtio: The process
Chapter 2 Intro to Math Techniques for Quantum Mechanics
Wter 3 Chem 356: Itroductory Qutum Mechcs Chpter Itro to Mth Techques for Qutum Mechcs... Itro to dfferetl equtos... Boudry Codtos... 5 Prtl dfferetl equtos d seprto of vrbles... 5 Itroducto to Sttstcs...
19 22 Evaluate the integral by interpreting it in terms of areas. (1 x ) dx. y Write the given sum or difference as a single integral in
SECTION. THE DEFINITE INTEGRAL. THE DEFINITE INTEGRAL A Clck here for swers. S Clck here for solutos. Use the Mdpot Rule wth the gve vlue of to pproxmte the tegrl. Roud the swer to four decml plces. 9
20 23 Evaluate the integral by interpreting it in terms of areas. (1 x ) dx. y 2 2
SECTION 5. THE DEFINITE INTEGRAL 5. THE DEFINITE INTEGRAL A Clck here for swers. S Clck here for solutos. 7 Use the Mdpot Rule wth the gve vlue of to pproxmte the tegrl. Roud the swer to four decml plces.
Numerical Analysis Third Class Chemical Engineering Department University of Technology Assoc. Prof. Dr. Zaidoon Mohsin shakor
Numercl Alss Thrd Clss Chemcl Egeerg Deprtmet Uverst o Techolog Assoc. Pro. Dr. Zdoo Mohs shkor Itroducto to Numercl Alss U. Alss versus Numercl Alss The word lss mthemtcs usull mes who to solve problem
14.2 Line Integrals. determines a partition P of the curve by points Pi ( xi, y
4. Le Itegrls I ths secto we defe tegrl tht s smlr to sgle tegrl except tht sted of tegrtg over tervl [ ] we tegrte over curve. Such tegrls re clled le tegrls lthough curve tegrls would e etter termology.
FORMULAE FOR FINITE DIFFERENCE APPROXIMATIONS, QUADRATURE AND LINEAR MULTISTEP METHODS
Jourl o Mtemtcl Sceces: Advces d Alctos Volume Number - Pges -9 FRMULAE FR FINITE DIFFERENCE APPRXIMATINS QUADRATURE AND LINEAR MULTISTEP METHDS RAMESH KUMAR MUTHUMALAI Dertmet o Mtemtcs D G Vsv College
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson
CHAPTER 6 CURVE FITTINGS
CHAPTER 6 CURVE FITTINGS Chpter 6 : TOPIC COVERS CURVE FITTINGS Lest-Squre Regresso - Ler Regresso - Poloml Regresso Iterpolto - Newto s Dvded-Derece Iterpoltg Polomls - Lgrge Iterpoltg Polomls - Sple
Matrix. Definition 1... a1 ... (i) where a. are real numbers. for i 1, 2,, m and j = 1, 2,, n (iii) A is called a square matrix if m n.
Mtrx Defto () s lled order of m mtrx, umer of rows ( 橫行 ) umer of olums ( 直列 ) m m m where j re rel umers () B j j for,,, m d j =,,, () s lled squre mtrx f m (v) s lled zero mtrx f (v) s lled detty mtrx
Differential Entropy 吳家麟教授
Deretl Etropy 吳家麟教授 Deto Let be rdom vrble wt cumultve dstrbuto ucto I F s cotuous te r.v. s sd to be cotuous. Let = F we te dervtve s deed. I te s clled te pd or. Te set were > 0 s clled te support set
Section 5.1/5.2: Areas and Distances the Definite Integral
Scto./.: Ars d Dstcs th Dt Itgrl Sgm Notto Prctc HW rom Stwrt Ttook ot to hd p. #,, 9 p. 6 #,, 9- odd, - odd Th sum o trms,,, s wrtt s, whr th d o summto Empl : Fd th sum. Soluto: Th Dt Itgrl Suppos w
The definite Riemann integral
Roberto s Notes o Itegrl Clculus Chpter 4: Defte tegrls d the FTC Secto 4 The defte Rem tegrl Wht you eed to kow lredy: How to ppromte the re uder curve by usg Rem sums. Wht you c ler here: How to use
ZETA REGULARIZATION METHOD APPLIED TO THE CALCULATION OF DIVERGENT DIVERGENT INTEGRALS
ZETA REGULARIZATION METOD APPLIED TO TE CALCULATION OF DIVERGENT DIVERGENT INTEGRALS Jose Jver Grc Moret Grdute studet of Physcs t the UPV/EU (Uversty of Bsque coutry) I Sold Stte Physcs Addres: Prctctes
Regression. By Jugal Kalita Based on Chapter 17 of Chapra and Canale, Numerical Methods for Engineers
Regresso By Jugl Klt Bsed o Chpter 7 of Chpr d Cle, Numercl Methods for Egeers Regresso Descrbes techques to ft curves (curve fttg) to dscrete dt to obt termedte estmtes. There re two geerl pproches two
1 4 6 is symmetric 3 SPECIAL MATRICES 3.1 SYMMETRIC MATRICES. Defn: A matrix A is symmetric if and only if A = A, i.e., a ij =a ji i, j. Example 3.1.
SPECIAL MATRICES SYMMETRIC MATRICES Def: A mtr A s symmetr f d oly f A A, e,, Emple A s symmetr Def: A mtr A s skew symmetr f d oly f A A, e,, Emple A s skew symmetr Remrks: If A s symmetr or skew symmetr,
МИНИСТЕРСТВО ОБРАЗОВАНИЯ И НАУКИ РОССИЙСКОЙ ФЕДЕРАЦИИ. Численные методы. Учебно-методическое пособие
МИНИСТЕРСТВО ОБРАЗОВАНИЯ И НАУКИ РОССИЙСКОЙ ФЕДЕРАЦИИ Нижегородский государственный университет им. Н.И. Лобачевского Численные методы К.А.Баркалов Учебно-методическое пособие Рекомендовано методической
Outline. Finite Difference Grids. Numerical Analysis. Finite Difference Grids II. Finite Difference Grids III
Itrodcto to Nmercl Alyss Mrc, 9 Nmercl Metods or PDEs Lrry Cretto Meccl Egeerg 5B Semr Egeerg Alyss Mrc, 9 Otle Revew mdterm soltos Revew bsc mterl o mercl clcls Expressos or dervtves, error d error order
ITERATIVE METHODS FOR SOLVING SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS
Numercl Alyss for Egeers Germ Jord Uversty ITERATIVE METHODS FOR SOLVING SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS Numercl soluto of lrge systems of ler lgerc equtos usg drect methods such s Mtr Iverse, Guss
PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation
PGE 30: Formulato ad Soluto Geosystems Egeerg Dr. Balhoff Iterpolato Numercal Methods wth MATLAB, Recktewald, Chapter 0 ad Numercal Methods for Egeers, Chapra ad Caale, 5 th Ed., Part Fve, Chapter 8 ad
Advanced Algorithmic Problem Solving Le 3 Arithmetic. Fredrik Heintz Dept of Computer and Information Science Linköping University
Advced Algorthmc Prolem Solvg Le Arthmetc Fredrk Hetz Dept of Computer d Iformto Scece Lköpg Uversty Overvew Arthmetc Iteger multplcto Krtsu s lgorthm Multplcto of polyomls Fst Fourer Trsform Systems of
GENERALIZED OPERATIONAL RELATIONS AND PROPERTIES OF FRACTIONAL HANKEL TRANSFORM
S. Res. Chem. Commu.: (3 8-88 ISSN 77-669 GENERLIZED OPERTIONL RELTIONS ND PROPERTIES OF FRCTIONL NKEL TRNSFORM R. D. TYWDE *. S. GUDDE d V. N. MLLE b Pro. Rm Meghe Isttute o Teholog & Reserh Bder MRVTI
CURVE FITTING LEAST SQUARES METHOD
Nuercl Alss for Egeers Ger Jord Uverst CURVE FITTING Although, the for of fucto represetg phscl sste s kow, the fucto tself ot be kow. Therefore, t s frequetl desred to ft curve to set of dt pots the ssued
Numerical Integration
Numericl tegrtio Newto-Cotes Numericl tegrtio Scheme Replce complicted uctio or tulted dt with some pproimtig uctio tht is esy to itegrte d d 3-7 Roerto Muscedere The itegrtio o some uctios c e very esy
Mathematics HL and further mathematics HL formula booklet
Dplom Progrmme Mthemtcs HL d further mthemtcs HL formul boolet For use durg the course d the emtos Frst emtos 04 Publshed Jue 0 Itertol Bcclurete Orgzto 0 5048 Mthemtcs HL d further mthemtcs formul boolet
Soo King Lim Figure 1: Figure 2: Figure 3: Figure 4: Figure 5: Figure 6: Figure 7: Figure 8: Figure 9: Figure 10: Figure 11:
Soo Kg Lm 1.0 Nested Fctorl Desg... 1.1 Two-Fctor Nested Desg... 1.1.1 Alss of Vrce... Exmple 1... 5 1.1. Stggered Nested Desg for Equlzg Degree of Freedom... 7 1.1. Three-Fctor Nested Desg... 8 1.1..1
Strategies for the AP Calculus Exam
Strteges for the AP Clculus Em Strteges for the AP Clculus Em Strtegy : Kow Your Stuff Ths my seem ovous ut t ees to e metoe. No mout of cochg wll help you o the em f you o t kow the mterl. Here s lst
Mathematics HL and further mathematics HL formula booklet
Dplom Progrmme Mthemtcs HL d further mthemtcs HL formul boolet For use durg the course d the emtos Frst emtos 04 Edted 05 (verso ) Itertol Bcclurete Orgzto 0 5048 Cotets Pror lerg Core 3 Topc : Algebr
PowerPoints organized by Dr. Michael R. Gustafson II, Duke University Revised by Prof. Jang, CAU
Part 4 Capter 6 Sple ad Peewe Iterpolato PowerPot orgazed y Dr. Mael R. Gutao II Duke Uverty Reved y Pro. Jag CAU All mage opyrgt Te MGraw-Hll Compae I. Permo requred or reproduto or dplay. Capter Ojetve
Numerical Solution of Higher Order Linear Fredholm Integro Differential Equations.
Amerc Jorl of Egeerg Reserch (AJER) 04 Amerc Jorl of Egeerg Reserch (AJER) e-iss : 30-0847 p-iss : 30-0936 Volme-03, Isse-08, pp-43-47 www.jer.org Reserch Pper Ope Access mercl Solto of Hgher Order Ler
Roberto s Notes on Integral Calculus Chapter 4: Definite integrals and the FTC Section 2. Riemann sums
Roerto s Notes o Itegrl Clculus Chpter 4: Defte tegrls d the FTC Secto 2 Rem sums Wht you eed to kow lredy: The defto of re for rectgle. Rememer tht our curret prolem s how to compute the re of ple rego
ENGI 4430 Numerical Integration Page 5-01
ENGI 443 Numercal Itegrato Page 5-5. Numercal Itegrato I some o our prevous work, (most otaly the evaluato o arc legth), t has ee dcult or mpossle to d the dete tegral. Varous symolc algera ad calculus
General Method for Calculating Chemical Equilibrium Composition
AE 6766/Setzma Sprg 004 Geeral Metod for Calculatg Cemcal Equlbrum Composto For gve tal codtos (e.g., for gve reactats, coose te speces to be cluded te products. As a example, for combusto of ydroge wt
The z-transform. LTI System description. Prof. Siripong Potisuk
The -Trsform Prof. Srpog Potsuk LTI System descrpto Prevous bss fucto: ut smple or DT mpulse The put sequece s represeted s ler combto of shfted DT mpulses. The respose s gve by covoluto sum of the put
PROBLEM SET #4 SOLUTIONS by Robert A. DiStasio Jr.
PROBLM ST # SOLUTIONS y Roert. DStso Jr. Q. Prove tht the MP eergy s sze-osstet for two ftely seprted losed shell frgmets. The MP orrelto eergy s gve the sp-ortl ss s: vrt vrt MP orr Δ. or two moleulr
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
PAIR OF STRAIGHT LINES. will satisfy L1 L2 0, and thus L1 L. 0 represent? It is obvious that any point lying on L 1
LOCUS 33 Seto - 3 PAIR OF STRAIGHT LINES Cosder two les L L Wht do ou thk wll L L represet? It s ovous tht pot lg o L d L wll stsf L L, d thus L L represets the set of pots osttutg oth the les,.e., L L
Gauss Quadrature Rule of Integration
Guss Qudrture Rule o Integrtion Mjor: All Engineering Mjors Authors: Autr Kw, Chrlie Brker http://numerilmethods.eng.us.edu Trnsorming Numeril Methods Edution or STEM Undergrdutes /0/00 http://numerilmethods.eng.us.edu
Diagonally Implicit Runge-Kutta Nystrom General Method Order Five for Solving Second Order IVPs
WSEAS TRANSACTIONS o MATHEMATICS Fudzh Isml Dgoll Implt Ruge-Kutt Nstrom Geerl Method Order Fve for Solvg Seod Order IVPs FUDZIAH ISMAIL Deprtmet of Mthemts Uverst Putr Mls Serdg Selgor MALAYSIA fudzh@mth.upm.edu.m
ORDINARY DIFFERENTIAL EQUATIONS
6 ORDINARY DIFFERENTIAL EQUATIONS Introducton Runge-Kutt Metods Mult-step Metods Sstem o Equtons Boundr Vlue Problems Crcterstc Vlue Problems Cpter 6 Ordnr Derentl Equtons / 6. Introducton In mn engneerng
Chapter 5. Curve fitting
Chapter 5 Curve ttg Assgmet please use ecell Gve the data elow use least squares regresso to t a a straght le a power equato c a saturato-growthrate equato ad d a paraola. Fd the r value ad justy whch
TEACHERS ASSESS STUDENT S MATHEMATICAL CREATIVITY COMPETENCE IN HIGH SCHOOL
Jourl o See d rs Yer 5, No., pp. 5-, 5 ORIGINL PPER TECHERS SSESS STUDENT S MTHEMTICL CRETIVITY COMPETENCE IN HIGH SCHOOL TRN TRUNG TINH Musrp reeved: 9..5; eped pper:..5; Pulsed ole:..5. sr. ssessme s
Chapter Unary Matrix Operations
Chpter 04.04 Ury trx Opertos After redg ths chpter, you should be ble to:. kow wht ury opertos mes,. fd the trspose of squre mtrx d t s reltoshp to symmetrc mtrces,. fd the trce of mtrx, d 4. fd the ermt
Introduction to Numerical Integration Part II
Introducton to umercl Integrton Prt II CS 75/Mth 75 Brn T. Smth, UM, CS Dept. Sprng, 998 4/9/998 qud_ Intro to Gussn Qudrture s eore, the generl tretment chnges the ntegrton prolem to ndng the ntegrl w
i+1 by A and imposes Ax
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 09.9 NUMERICAL FLUID MECHANICS FALL 009 Mody, October 9, 009 QUIZ : SOLUTIONS Notes: ) Multple solutos
Lecture 3-4 Solutions of System of Linear Equations
Lecture - Solutos of System of Ler Equtos Numerc Ler Alger Revew of vectorsd mtrces System of Ler Equtos Guss Elmto (drect solver) LU Decomposto Guss-Sedel method (tertve solver) VECTORS,,, colum vector
PubH 7405: REGRESSION ANALYSIS REGRESSION IN MATRIX TERMS
PubH 745: REGRESSION ANALSIS REGRESSION IN MATRIX TERMS A mtr s dspl of umbers or umercl quttes ld out rectgulr rr of rows d colums. The rr, or two-w tble of umbers, could be rectgulr or squre could be
MATLAB PROGRAM FOR THE NUMERICAL SOLUTION OF DUHAMEL CONVOLUTION INTEGRAL
Bullet of te Trslv Uversty of Brşov Vol 5 (54-1 Seres 1: Specl Issue No 1 MATLAB PROGRAM FOR THE NUMERICAL SOLUTION OF DUHAMEL CONVOLUTION INTEGRAL M BOTIŞ 1 Astrct: I te ler lyss of structures troug modl
148 CIVIL ENGINEERING
STRUTUR NYSS fluee es fo Bems d Tusses fluee le sows te vto of effet (eto, se d momet ems, foe tuss) used movg ut lod oss te stutue. fluee le s used to deteme te posto of movele set of lods tt uses te
SOLUTION OF TWO DIMENSIONAL FRACTIONAL ORDER VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
Jourl of Al-Nhr Uversty Vol. (4), Deeber, 009,.85-89 See SOLUTION OF TWO DIMENSIONAL FRACTIONAL ORDER VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS Mh A. Mohed * d Fdhel S. Fdhel ** * Dertet of Mthets, Ib-Al-Hth
COMPLEX NUMBERS AND DE MOIVRE S THEOREM
COMPLEX NUMBERS AND DE MOIVRE S THEOREM OBJECTIVE PROBLEMS. s equl to b d. 9 9 b 9 9 d. The mgr prt of s 5 5 b 5. If m, the the lest tegrl vlue of m s b 8 5. The vlue of 5... s f s eve, f s odd b f s eve,
Chapter 2 Intro to Math Techniques for Quantum Mechanics
Fll 4 Chem 356: Itroductory Qutum Mechcs Chpter Itro to Mth Techques for Qutum Mechcs... Itro to dfferetl equtos... Boudry Codtos... 5 Prtl dfferetl equtos d seprto of vrbles... 5 Itroducto to Sttstcs...
Systems of second order ordinary differential equations
Ffth order dgolly mplct Ruge-Kutt Nystrom geerl method solvg secod Order IVPs Fudzh Isml Astrct A dgolly mplct Ruge-Kutt-Nystróm Geerl (SDIRKNG) method of ffth order wth explct frst stge for the tegrto
Lecture 26 Finite Differences and Boundary Value Problems
4//3 Leture 6 Fnte erenes and Boundar Value Problems Numeral derentaton A nte derene s an appromaton o a dervatve - eample erved rom Talor seres 3 O! Negletng all terms ger tan rst order O O Tat s te orward
NATIONAL OPEN UNIVERSITY OF NIGERIA COURSE CODE : MTH 307 COURSE TITLE: NUMERICAL ANALYSIS II
NATIONAL OPEN UNIVERSITY OF NIGERIA COURSE CODE : MTH 7 COURSE TITLE: NUMERICAL ANALYSIS II Corse Code: MTH 7: Corse Ttle: NUMERICAL ANALYSIS II Corse Developer/Wrter: Corse Edtor: Progrmme Leder: Corse
Chapter Direct Method of Interpolation More Examples Civil Engineering
Chpter 5. Direct Method of Interpoltion More Exmples Civil Engineering Exmple o mximie ctch of bss in lke, it is suggested to throw the line to the depth of the thermocline. he chrcteristic feture of this
Differentiation and Numerical Integral of the Cubic Spline Interpolation
JOURNAL OF COMPUTER VOL. NO. OCTOBER 7 Deretto d Nuercl Itegrl o te Cuc ple Iterpolto g Go cool o Coputer cece d Tecolog Jgsu Uverst o cece d Tecolog Zejg C El: go_sg@otl.co Zue Zg d Cuge Co Ke Lortor
CHAPTER 4 RADICAL EXPRESSIONS
6 CHAPTER RADICAL EXPRESSIONS. The th Root of a Real Number A real umber a s called the th root of a real umber b f Thus, for example: s a square root of sce. s also a square root of sce ( ). s a cube
Interpolation. 1. What is interpolation?
Iterpoltio. Wht is iterpoltio? A uctio is ote give ol t discrete poits such s:.... How does oe id the vlue o t other vlue o? Well cotiuous uctio m e used to represet the + dt vlues with pssig through the
4. Runge-Kutta Formula For Differential Equations. A. Euler Formula B. Runge-Kutta Formula C. An Example for Fourth-Order Runge-Kutta Formula
NCTU Deprme o Elecrcl d Compuer Egeerg Seor Course By Pro. Yo-Pg Ce. Ruge-Ku Formul For Derel Equos A. Euler Formul B. Ruge-Ku Formul C. A Emple or Four-Order Ruge-Ku Formul
02/15/04 INTERESTING FINITE AND INFINITE PRODUCTS FROM SIMPLE ALGEBRAIC IDENTITIES
0/5/04 ITERESTIG FIITE AD IFIITE PRODUCTS FROM SIMPLE ALGEBRAIC IDETITIES Thomas J Osler Mathematcs Departmet Rowa Uversty Glassboro J 0808 Osler@rowaedu Itroducto The dfferece of two squares, y = + y
Numerical Integration - (4.3)
Numericl Itegrtio - (.). Te Degree of Accurcy of Qudrture Formul: Te degree of ccurcy of qudrture formul Qf is te lrgest positive iteger suc tt x k dx Qx k, k,,,...,. Exmple fxdx 9 f f,,. Fid te degree
Spectrum Estimation by Several Interpolation Methods
IJCSNS Itertol Jourl o Computer Scece d Network Securty VOL.6 No.A Februry 006 05 Spectrum Estmto by Severl Iterpolto Metods Mbu Isr Oym Ntol College o Tecology Oym-S Tocg 33-0806 JAPAN Summry I ts pper
Some Unbiased Classes of Estimators of Finite Population Mean
Itertol Jourl O Mtemtcs Ad ttstcs Iveto (IJMI) E-IN: 3 4767 P-IN: 3-4759 Www.Ijms.Org Volume Issue 09 etember. 04 PP-3-37 ome Ubsed lsses o Estmtors o Fte Poulto Me Prvee Kumr Msr d s Bus. Dertmet o ttstcs,
Analytical Approach for the Solution of Thermodynamic Identities with Relativistic General Equation of State in a Mixture of Gases
Itertol Jourl of Advced Reserch Physcl Scece (IJARPS) Volume, Issue 5, September 204, PP 6-0 ISSN 2349-7874 (Prt) & ISSN 2349-7882 (Ole) www.rcourls.org Alytcl Approch for the Soluto of Thermodymc Idettes
Topic 6b Finite Difference Approximations
/8/8 Course Instructor Dr. Rymond C. Rump Oice: A 7 Pone: (95) 747 6958 E Mil: rcrump@utep.edu Topic 6b Finite Dierence Approximtions EE 486/5 Computtionl Metods in EE Outline Wt re inite dierence pproximtions?
Calculating the Values of Multiple Integrals by Replacing the Integrands Interpolation by Interpolation Polynomial
Jour o omputtos & Modeg vo o -5 ISSN: 79-75 prt 79-5 oe Scepress Ltd cutg te Vues o Mutpe Itegrs by Repcg te Itegrds Iterpoto by Iterpoto Poyom S Nzrov d bduzzov bstrct Te or des t te costructo o mutdmeso
Mathematics HL and further mathematics HL formula booklet
Dplom Progrmme Mthemtcs HL d further mthemtcs HL formul boolet For use durg the course d the emtos Frst emtos 04 Publshed Jue 0 Itertol Bcclurete Orgzto 0 5048 Cotets Pror lerg Core Topc : Algebr Topc
Complex Variables. Chapter 19 Series and Residues. March 26, 2013 Lecturer: Shih-Yuan Chen
omplex Vrble hpter 9 Sere d Redue Mrch 6, Lecturer: Shh-Yu he Except where otherwe oted, cotet lceed uder BY-N-SA. TW Lcee. otet Sequece & ere Tylor ere Luret ere Zero & pole Redue & redue theorem Evluto
Algebra: Function Tables - One Step
Alger: Funtion Tles - One Step Funtion Tles Nme: Dte: Rememer tt tere is n input nd output on e funtion tle. If you know te funtion eqution, you need to plug in for tt vrile nd figure out wt te oter vrile
Objective of curve fitting is to represent a set of discrete data by a function (curve). Consider a set of discrete data as given in table.
CURVE FITTING Obectve curve ttg s t represet set dscrete dt b uct curve. Csder set dscrete dt s gve tble. 3 3 = T use the dt eectvel, curve epress s tted t the gve dt set, s = + = + + = e b ler uct plml
Computational Modelling
Computtol Modellg Notes orfeeg Desg d Computg Oct t v.d Computtol Modellg b Pro Smo J. Co sjc@soto.c.uk Wt s Computtol Modellg? Computtol modellg d te use o ssocted umercl metods s bout coosg te rgt lgortm
Centroids & Moments of Inertia of Beam Sections
RCH 614 Note Set 8 S017ab Cetrods & Momets of erta of Beam Sectos Notato: b C d d d Fz h c Jo L O Q Q = ame for area = ame for a (base) wdth = desgato for chael secto = ame for cetrod = calculus smbol