Chapter False-Position Method of Solving a Nonlinear Equation
|
|
|
- Grant Bruce
- 7 years ago
- Views:
Transcription
1 Chpte 006 Flse-Position Method o Solving Nonline Eqution Ate eding this chpte, you should be ble to 1 ollow the lgoithm o the lse-position method o solving nonline eqution, pply the lse-position method to ind oots o nonline eqution Intoduction In Chpte 00, the bisection method ws descibed s one o the simple bcketing methods o solving nonline eqution o the genel om ( 0 (1 ( ( Ect oot O ( Figue 1 Flse-Position Method The bove nonline eqution cn be stted s inding the vlue o such tht Eqution (1 is stisied In the bisection method, we identiy pope vlues o (lowe bound vlue nd (uppe bound vlue o the cuent bcket, such tht ( ( < 0 ( The net pedicted/impoved oot cn be computed s the midpoint between nd s 0061
2 006 Chpte ( The new uppe nd lowe bounds e then estblished, nd the pocedue is epeted until the convegence is chieved (such tht the new lowe nd uppe bounds e suiciently close to ech othe Howeve, in the emple shown in Figue 1, the bisection method my not be eicient becuse it does not tke into considetion tht ( is much close to the zeo o the unction ( s comped to ( In othe wods, the net pedicted oot would be close to (in the emple s shown in Figue 1, thn the mid-point between nd The lse-position method tkes dvntge o this obsevtion mthemticlly by dwing secnt om the unction vlue t to the unction vlue t, nd estimtes the oot s whee it cosses the -is Flse-Position Method Bsed on two simil tingles, shown in Figue 1, one gets 0 ( 0 ( (4 Fom Eqution (4, one obtins ( ( ( ( ( ( { ( ( } The bove eqution cn be solved to obtin the net pedicted oot m s ( ( (5 ( ( The bove eqution, though simple lgebic mnipultions, cn lso be epessed s ( (6 ( ( o ( (7 ( ( Obseve the esemblnce o Equtions (6 nd (7 to the secnt method Flse-Position Algoithm The steps to pply the lse-position method to ind the oot o the eqution ( 0 ollows 1 Choose nd s two guesses o the oot such tht ( ( < 0 ( chnges sign between nd e s, o in othe wods,
3 Flse-Position Method o Solving Nonline Eqution 006 Estimte the oot, o the eqution ( 0 s ( ( ( ( Now check the ollowing I ( ( < 0, then the oot lies between nd ; then nd I ( ( > 0, then the oot lies between nd ; then nd I ( ( 0, then the oot is Stop the lgoithm 4 Find the new estimte o the oot ( ( ( ( Find the bsolute eltive ppoimte eo s new old 0 new whee new estimted oot om pesent itetion old estimted oot om pevious itetion 5 Compe the bsolute eltive ppoimte eo with the pe-speciied eltive eo tolence s I > s, then go to step, else stop the lgoithm Note one should lso check whethe the numbe o itetions is moe thn the mimum numbe o itetions llowed I so, one needs to teminte the lgoithm nd notiy the use bout it Note tht the lse-position nd bisection lgoithms e quite simil The only dieence is the omul used to clculte the new estimte o the oot s shown in steps # nd #4! Emple 1 You e woking o DOWN THE TOIET COMPANY tht mkes lots o ABC commodes The loting bll hs speciic gvity o 06 nd hs dius o 55cm You e sked to ind the depth to which the bll is submeged when loting in wte The eqution tht gives the depth to which the bll is submeged unde wte is given by se the lse-position method o inding oots o equtions to ind the depth to which the bll is submeged unde wte Conduct thee itetions to estimte the oot o the bove eqution Find the bsolute eltive ppoimte eo t the end o ech itetion, nd the numbe o signiicnt digits t lest coect t the end o thid itetion
4 0064 Chpte 006 Solution Figue Floting bll poblem Fom the physics o the poblem, the bll would be submeged between 0 nd R, whee R dius o the bll, tht is 0 R 0 ( et us ssume 0, 011 Check i the unction chnges sign between nd ( ( ( ( ( ( 011 ( ( Hence ( ( ( 0 ( 011 ( 99 ( 66 < 0 Theeoe, thee is t lest one oot between nd, tht is between 0 nd 011 Itetion 1 The estimte o the oot is ( ( ( ( ( ( 0 ( 66 ( 66 ( ( (
5 Flse-Position Method o Solving Nonline Eqution 0065 ( ( ( 0 ( ( + ( < 0 Hence, the oot is bcketed between nd, tht is, between 0 nd So, the lowe nd uppe limits o the new bcket e 0, , espectively Itetion The estimte o the oot is ( ( ( ( 0 ( 1944 ( The bsolute eltive ppoimte eo o this itetion is % ( ( ( ( ( ( ( ( 0 ( ( + ( + > 0 Hence, the lowe nd uppe limits o the new bcket e , , espectively Itetion The estimte o the oot is ( ( ( ( ( 1944 ( The bsolute eltive ppoimte eo o this itetion is % ( 111 ( ( ( ( 0064 ( + ( < 0 Hence, the lowe nd uppe limits o the new bcket e , All itetions esults e summized in Tble 1 To ind how mny signiicnt digits e t lest coect in the lst itetive vlue
6 0066 Chpte m m m 187 The numbe o signiicnt digits t lest coect in the estimted oot o 0064 t the end o d itetion is 1 Tble 1 Root o ( Itetion % ( o lse-position method m Emple Find the oot o ( ( 4 ( + 0, using the initil guesses o 5 nd 10, nd pe-speciied tolence o s 01% Solution The individul itetions e not shown o this emple, but the esults e summized in Tble It tkes ive itetions to meet the pe-speciied tolence Tble Root o ( ( 4 ( + 0 o lse-position method Itetion ( ( % ( N/A To ind how mny signiicnt digits e t lest coect in the lst itetive nswe, m 05 m m 666 Hence, t lest signiicnt digits cn be tusted to be ccute t the end o the ith itetion FASE-POSITION METHOD OF SOVING A NONINEAR EQATION Topic Flse-Position Method o Solving Nonline Eqution Summy Tetbook Chpte o Flse-Position Method Mjo Genel Engineeing Authos Duc Nguyen Dte Septembe 4, 01 m
N V V L. R a L I. Transformer Equation Notes
Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 wite-up. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions
Orbits and Kepler s Laws
Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how
(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a
Comment on The effect of vible viscosity on mied convection het tnsfe long veticl moving sufce by M. Ali [Intentionl Jounl of Theml Sciences, 006, Vol. 45, pp. 60-69] Asteios Pntoktos Associte Pofesso
Intro to Circle Geometry By Raymond Cheong
Into to Cicle Geomety By Rymond Cheong Mny poblems involving cicles cn be solved by constucting ight tingles then using the Pythgoen Theoem. The min chllenge is identifying whee to constuct the ight tingle.
Summary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:
Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos
r (1+cos(θ)) sin(θ) C θ 2 r cos θ 2
icles xmple 66: Rounding one ssume we hve cone of ngle θ, nd we ound it off with cuve of dius, how f wy fom the cone does the ound stt? nd wht is the chod length? (1+cos(θ)) sin(θ) θ 2 cos θ 2 xmple 67:
(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?
Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the
Screentrade Car Insurance Policy Summary
Sceentde C Insunce Policy Summy This is summy of the policy nd does not contin the full tems nd conditions of the cove, which cn be found in the policy booklet nd schedule. It is impotnt tht you ed the
MATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
2.016 Hydrodynamics Prof. A.H. Techet
.016 Hydodynmics Reding #5.016 Hydodynmics Po. A.H. Techet Fluid Foces on Bodies 1. Stedy Flow In ode to design oshoe stuctues, suce vessels nd undewte vehicles, n undestnding o the bsic luid oces cting
Curvature. (Com S 477/577 Notes) Yan-Bin Jia. Oct 8, 2015
Cuvtue Com S 477/577 Notes Yn-Bin Ji Oct 8, 205 We wnt to find mesue of how cuved cuve is. Since this cuvtue should depend only on the shpe of the cuve, it should not be chnged when the cuve is epmetized.
Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
Binary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy
Newton-Raphson Method of Solving a Nonlinear Equation Autar Kaw
Newton-Rphson Method o Solvng Nonlner Equton Autr Kw 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
Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
32. The Tangency Problem of Apollonius.
. The Tngeny olem of Apollonius. Constut ll iles tngent to thee given iles. This eleted polem ws posed y Apollinius of eg (. 60-70 BC), the getest mthemtiin of ntiquity fte Eulid nd Ahimedes. His mjo wok
Factoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
Math 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
Random Variables and Distribution Functions
Topic 7 Rndom Vibles nd Distibution Functions 7.1 Intoduction Fom the univese of possible infomtion, we sk question. To ddess this question, we might collect quntittive dt nd ognize it, fo emple, using
Graphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
Roots of Polynomials. Ch. 7. Roots of Polynomials. Roots of Polynomials. dy dt. a dt. y = General form:
Roots o Polynomils C. 7 Generl orm: Roots o Polynomils ( ) n n order o te polynomil i constnt coeicients n Roots Rel or Comple. For n n t order polynomil n rel or comple roots. I n is odd At lest rel root
Experiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
Operations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
Exam in physics, El-grunder (Electromagnetism), 2014-03-26, kl 9.00-15.00
Umeå Univesitet, Fysik 1 Vitly Bychkov Em in physics, El-gunde (Electomgnetism, 14--6, kl 9.-15. Hjälpmedel: Students my use ny book(s. Mino notes in the books e lso llowed. Students my not use thei lectue
Review guide for the final exam in Math 233
Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered
Is Competition Among Charities Bad?
Is Competition Among Chrities Bd? Inkyung Ch nd Willim Neilson Tes A&M University, College Sttion, TX 7783 December Abstrct This pper studies tht the eect o incresed competition mong chrities or dontions,
Chapter 23 Electrical Potential
hpte Electicl Potentil onceptul Polems [SSM] A poton is moved to the left in unifom electic field tht points to the ight. Is the poton moving in the diection of incesing o decesing electic potentil? Is
Or more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
Module Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials
MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic
Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
16. Mean Square Estimation
6 Me Sque stmto Gve some fomto tht s elted to uow qutty of teest the poblem s to obt good estmte fo the uow tems of the obseved dt Suppose epeset sequece of dom vbles bout whom oe set of obsevtos e vlble
PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
Chapter 22 The Electric Field II: Continuous Charge Distributions
Chpte The lectic Field II: Continuous Chge Distibutions Conceptul Poblems [SSM] Figue -7 shows n L-shped object tht hs sides which e equl in length. Positive chge is distibuted unifomly long the length
and thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
AREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
SPECIAL PRODUCTS AND FACTORIZATION
MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come
MA 15800 Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!
MA 5800 Lesson 6 otes Summer 06 Rememer: A logrithm is n eponent! It ehves like n eponent! In the lst lesson, we discussed four properties of logrithms. ) log 0 ) log ) log log 4) This lesson covers more
Section 7-4 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
10.6 Applications of Quadratic Equations
10.6 Applictions of Qudrtic Equtions In this section we wnt to look t the pplictions tht qudrtic equtions nd functions hve in the rel world. There re severl stndrd types: problems where the formul is given,
LAPLACE S EQUATION IN SPHERICAL COORDINATES. With Applications to Electrodynamics
LALACE S EQUATION IN SHERICAL COORDINATES With Appitions to Eetodynmis We hve seen tht Lpe s eqution is one of the most signifint equtions in physis. It is the soution to pobems in wide viety of fieds
Adaptive Control of a Production and Maintenance System with Unknown Deterioration and Obsolescence Rates
Int J of Mthemtic Sciences nd Appictions, Vo, No 3, Septembe Copyight Mind Rede Pubictions wwwjounshubcom Adptive Conto of Poduction nd Mintennce System with Unknown Deteiotion nd Obsoescence Rtes Fwzy
Numerical Methods of Approximating Definite Integrals
6 C H A P T E R Numericl Methods o Approimting Deinite Integrls 6. APPROXIMATING SUMS: L n, R n, T n, AND M n Introduction Not only cn we dierentite ll the bsic unctions we ve encountered, polynomils,
4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
19. The Fermat-Euler Prime Number Theorem
19. The Fermt-Euler Prime Number Theorem Every prime number of the form 4n 1 cn be written s sum of two squres in only one wy (side from the order of the summnds). This fmous theorem ws discovered bout
Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
Econ 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
Network Configuration Independence Mechanism
3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
2005-06 Second Term MAT2060B 1. Supplementary Notes 3 Interchange of Differentiation and Integration
Source: http://www.mth.cuhk.edu.hk/~mt26/mt26b/notes/notes3.pdf 25-6 Second Term MAT26B 1 Supplementry Notes 3 Interchnge of Differentition nd Integrtion The theme of this course is bout vrious limiting
PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,
Rate and Activation Energy of the Iodination of Acetone
nd Activtion Energ of the Iodintion of Acetone rl N. eer Dte of Eperiment: //00 Florence F. Ls (prtner) Abstrct: The rte, rte lw nd ctivtion energ of the iodintion of cetone re detered b observing the
Design Example 1 Special Moment Frame
Design Exmple 1 pecil Moment Frme OVERVIEW tructurl steel specil moment frmes (MF) re typiclly comprised of wide-flnge bems, columns, nd bem-column connections. Connections re proportioned nd detiled to
Lecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity
Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University
Reasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
Basic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
Derivatives and Rates of Change
Section 2.1 Derivtives nd Rtes of Cnge 2010 Kiryl Tsiscnk Derivtives nd Rtes of Cnge Te Tngent Problem EXAMPLE: Grp te prbol y = x 2 nd te tngent line t te point P(1,1). Solution: We ve: DEFINITION: Te
g(y(a), y(b)) = o, B a y(a)+b b y(b)=c, Boundary Value Problems Lecture Notes to Accompany
Lecture Notes to Accompny Scientific Computing An Introductory Survey Second Edition by Michel T Heth Boundry Vlue Problems Side conditions prescribing solution or derivtive vlues t specified points required
Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:
Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you
The Velocity Factor of an Insulated Two-Wire Transmission Line
The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
www.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values)
www.mthsbo.org.uk CORE SUMMARY NOTES Functions A function is rule which genertes ectl ONE OUTPUT for EVERY INPUT. To be defined full the function hs RULE tells ou how to clculte the output from the input
Integration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
GRAVITATION 1. BASIC FORCES IN NATURE
GRAVITATION. BASIC ORCES IN NATURE POINTS TO REMEMBER. Bsing on the ntue nd eltive stength the bsic foces in ntue e clssified into fou ctegoies. They e ) Gvittionl foce ) Electomgnetic foce 3) Stong Nucle
1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
Exponential and Logarithmic Functions
Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define
AMPERE S LAW. by Kirby Morgan MISN-0-138
MISN-0-138 AMPERE S LAW by Kiby Mogn 1. Usefullness................................................ 1 AMPERE S LAW 2. The Lw................................................... 1. The Integl Reltionship...............................
Valuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
Helicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
Unit 6: Exponents and Radicals
Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -
The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O
The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem Publiction
Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only
Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn
33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of
ORBITAL MANEUVERS USING LOW-THRUST
Proceedings of the 8th WSEAS Interntionl Conference on SIGNAL PROCESSING, ROBOICS nd AUOMAION ORBIAL MANEUVERS USING LOW-HRUS VIVIAN MARINS GOMES, ANONIO F. B. A. PRADO, HÉLIO KOII KUGA Ntionl Institute
Marketing Logistics: Opportunities and Limitations
Mketig Logistics: Oppotuities d Limittios Pethip Vdhsidhu 1, Ugul Lpted 2 1 Gdute School, MBA i Itetiol Busiess, The Uivesity of the Thi Chmbe of Commece Vibhvdee-Rgsit Rod, Dideg, Bgkok, 10400, Thild
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS Known for over 500 yers is the fct tht the sum of the squres of the legs of right tringle equls the squre of the hypotenuse. Tht is +b c. A simple proof is
PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.
body.allow-sidebar OR.no-sidebar.home-page (if this is the home page).has-custom-banner OR.nocustom-banner .IR OR.no-IR
body.llow-sidebr OR.no-sidebr.home-pge (if this is the home pge).hs-custom-bnner OR.nocustom-bnner.IR OR.no-IR #IDENTIFIER_FOR_THIS_SITE div#pge-continer.depends_on_page_ty PE llow-sidebr mens tht there
Algebra Review. How well do you remember your algebra?
Algebr Review How well do you remember your lgebr? 1 The Order of Opertions Wht do we men when we write + 4? If we multiply we get 6 nd dding 4 gives 10. But, if we dd + 4 = 7 first, then multiply by then
Review Problems for the Final of Math 121, Fall 2014
Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since
G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS
G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS Regul polygon e of inteet to u becue we begin looking t the volume of hexgonl pim o Tethedl nd to do thee type of clcultion we need to be ble to olve fit
Chapter 4 Newton s Laws
Chpte 4 Newton s Lws Conceptul Pobles While on ve sooth level tnscontinentl plne fliht, ou coffee cup sits otionless on ou t. Ae thee foces ctin on the cup? If so, how do the diffe fo the foces tht would
Tutorial on How to Create Electric Machine Models
PSIM Sotwre Tutoril on How to Crete Electric Mchine Models Powersi Inc. Septber 2009 www.powersitech.co Tutoril on Creting Electric Mchine Models Users cn crete electric chine odels using the bsic unction
Vectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
CHAPTER 11 Numerical Differentiation and Integration
CHAPTER 11 Numericl Differentition nd Integrtion Differentition nd integrtion re bsic mthemticl opertions with wide rnge of pplictions in mny res of science. It is therefore importnt to hve good methods
Physics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x
tools for Web data extraction
HTML-we tools fo Web dt extction Thesis pesenttion 1 Student: Xvie Azg Supeviso: Andes Tho Tble of contents Intoduction Dt Extction Pocess Dt Extction Tools Relized tests Futue Wok 2 Intoduction We e going
Skills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
Multiple choice questions [60 points]
![Multiple choice questions [60 points]](/thumbs/40/20623569.jpg "Multiple choice questions [60 points]")
1 Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect bubble on you scanton sheet. Each question has exactly one coect answe. All questions
SOEPpapers on Multidisciplinary Panel Data Research
Deutsches Institut fü Witschftsfoschung www.diw.de SOEPppes on Multidiscipliny Pnel Dt Resech 136 Thoms Conelissen John S. Heywood Uwe Jijhn S, Pefomnce Py, Risk Attitudes nd Job Stisfction Belin, Octobe
1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
Radius of the Earth - Radii Used in Geodesy James R. Clynch February 2006
dius of the Erth - dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.
Rotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
by K.-H. Rutsch*, P.J. Viljoen*, and H. Steyn* The need for systematic project portfolio selection
An investigtion into the cuent pctice of poject potfolio selection in esech nd development division of the South Aficn minels nd enegy industy by K.-H. Rutsch*, P.J. Viljoen*, nd H. Steyn* J o u n l Synopsis
ON THE CHINESE CHECKER SPHERE. Mine TURAN, Nihal DONDURMACI ÇİN DAMA KÜRESİ ÜZERİNE
DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı ON THE CHINESE CHECKER SHERE Mine TURAN Nihl DONDURMACI Deptment of Mthemtis Fult of Ats n Sienes Dumlupin Univesit
Cypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:
Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A
STATUS OF LAND-BASED WIND ENERGY DEVELOPMENT IN GERMANY
Yer STATUS OF LAND-BASED WIND ENERGY Deutsche WindGurd GmbH - Oldenburger Strße 65-26316 Vrel - Germny +49 (4451)/9515 - info@windgurd.de - www.windgurd.com Annul Added Cpcity [MW] Cumultive Cpcity [MW]
FUNCTIONS DEFINED BY IMPROPER INTEGRALS
FUNCTIONS DEFINED BY IMPROPER INTEGRALS Willim F. Tench Andew G. Cowles Distinguished Pofesso Emeitus Deptment of Mthemtics Tinity Univesity Sn Antonio, Tes, USA wtench@tinity.edu This is supplement to