167 Pages

4013-l15

Course: MATH 4013, Fall 2008
School: Oklahoma State
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Word Count: 809

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f2 F 1 f2 2 - )F g - g2 g + )g f (2 + F f + ) F ( f = ) F f( 0 = )F ( )G ( F - )F ( G = )G F( F f + ) F ( f = ) F f( G + F = )G + F( G + F = )G + F( ( = )F ( f = ) f g g f( 0 = )g f ( f = ) g f( 2 0 = )f ( g2 - 2 g / ) g f - f g( = ) g / f ( ) g ( f + ) f ( g = ) g f( c tnatsnoc yna rof ) f (c = ) fc( g + f = ) g + f( .51 .41 .31 .21 .11 .01 .9 .8 .7 .6 .5 .4 .3 .2 .1 3...

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f2 F 1 f2 2 - )F g - g2 g + )g f (2 + F f + ) F ( f = ) F f( 0 = )F ( )G ( F - )F ( G = )G F( F f + ) F ( f = ) F f( G + F = )G + F( G + F = )G + F( ( = )F ( f = ) f g g f( 0 = )g f ( f = ) g f( 2 0 = )f ( g2 - 2 g / ) g f - f g( = ) g / f ( ) g ( f + ) f ( g = ) g f( c tnatsnoc yna rof ) f (c = ) fc( g + f = ) g + f( .51 .41 .31 .21 .11 .01 .9 .8 .7 .6 .5 .4 .3 .2 .1 3 nehT . 3R no sdlefi rotcev eb G dna F tel dna R no snoitcnuf deulav-laer eb g dna f teL .)sisylanA rotceV fo seititnedI latnemadnuF( .1.51 meroehT y 2x 2z + 2 + f2 f 2 f 2 = z y x , , f f f z y x , , = )f ( = f) ( f2 denfied si taht n aica lpaL yb eht ,rotarepo laitnereffid redro dnoces a ecudortni won ew senil emas eseht gnolA zF z + y - yx , xzF - xzF , yzF - zy = xF F F z y x = F ) zF , yF , x F ( , , y x z y x = F = ) zF , yF , x F ( + , , yF xF z y x z y x =f , , =f , , f f f :lruc dna ecnegrevid ,tneidarg eht rof desu noitaton eht dnatsrednu retteb nac ew ,ytidrusba lanoitaton siht sevlesruo timrep ew fi tuB .noitcnuf a fo tca yeht litnu esnes yna ekam t'nod yllaer fo stnenopmoc eht ,esruoc fO .rotcev lanoisnemid-3 a sa fo thguoht z y x , , lobmys lamrof eht etoned teL noitatoN rotarepO laitnereffiD .1 sisylanA rotceV fo seititnedI 51 ERUTCEL si eulav sti dna muucav eht fo ytilibaemrep citengam eht dellac si tI .tnatsnoc denimreted yllatnemirepxe rehtona si o dna ,x tniop eht ta tnerruc lacirtcele fo ytisned eht si )x(j 3 )retem()gk( 2-)bmoluoc( 6-01 62.1 = o -)retem( 1-)gk( 2)ces( 2)bmoloc( 21-01 58.8 = o r3 r o 4 2q 1q ot lauqe si dna =F cirtcele eht dellac tnatsnoc a si o .x tniop eht ta ytisned egrahc eht si )x( ,t emit ta x tniop eht ta htgnerts dlefi citengam eht si )t ,x(B = B ,t emit ta x tniop eht ta htgnerts dlefi cirtcele eht si )t ,x(E = E ereH t )waL s'erepmA( )x(j o + E o o = B t )waL s'yadaraF( B - = E )dleiF citengaM rof waL 'ssuaG( 0=B )waL 'ssuaG( )x( o14 = E neewteb noitcartta fo ecrof eht gnirusaem yb yllatnemirepxe denimreted si ti ,muucav eht fo ytivitimrep segrahc cirtcele :noitauqe s'llewxaM era esehT .sdlefi dna citengam cirtcele fo roivaheb eht gninrevog snoitauqe eht redisnoc su tel ,noitces gnidecerp eht ni detsil seititnedi eht fo ytilitu eht fo elpmaxe na sA snoit auqE s 'llewx aM :noitaci lppA .2 x xF y - yx , zx - xzF , yz - zy F F F F 2z zF x - .51 ytitnedI fo tnenopmoc-x eht demrfinoc won evew oS x ) S H R( = y 2z - x2F - zzx + yFx = xF y F 2 2 2 xz z y + x2F - x2F - xFy = xF y 2 2 2 2 z z - xyF - yx y = xF F z y x = , , x) ) F ( ( = x ) S H L ( si edis dnah tfel eht fo tnenopmoc-x ehT 2 xF 2 y - x2F - zzx + yFx = y F 2 xF 2z 2 y x x 2z - x2F - x2F - zzx + yFx + x2F = xF y F 2 2 2 2 2 + 2y + 2x - zz + yy + xx x = F F F 2 2 x F tnenopmoc x eht ta ylno kool llahs ew ;)dne eht ni( sdlefi rotcev era noitauqe siht fo sedis htoB .eurt eb dluohs ti yhw ot sa noitacidni feirb a evig em tel ,woleb 51 ytitnedI esu llahs ew ecniS 2 -) ( F xF - )F ( x = 2 x F - ) F ( = x ) S HR( 2 si edis dnah thgir eht fo tneno pmoc-x eht woN = x))F ( ( 2 SNOITAUQE S'LLEWXAM :NOITACILPPA .2 . ))retem()gk( 2-)bmoluoc( 6-01 s/m 801 99 2 = 62 1( ) 3-)retem( 1-)gk( 2)ces( 2)bmoloc( 21-01 58 8( . . =c 1 yticolev htiw noitauqe evaw a sefisitas dlefi cirtcele eht fo tneno pmoc hcae ,suhT .c yticolev htiw ecaps lanoisnemid-3 a ...

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Oklahoma State - MATH - 4013
1d y c , )y( 2 x )y( 1 | 2R )y ,x( yfo seulav tnatsnoc owt fo stsisnoc yradnuob sti fi= I ISII epyT dellac si 2R S noiger A .2.71 noitinifeD:y fo snoitcnuf owt fo shparg eht dna)x( 2 y )x( 1 , b x a | 2R )y ,x( = ISxfo seul
Oklahoma State - MATH - 4013
1.edis dn ah t hgir eht no noitargetni f o redro eht f o tnednep edni si eula v sti,revoeroMxd yd zd) z ,y ,x( fe f dc b Ra=Vd) z ,y ,x( fRdna stsixeVd) z , y ,x( fneht . jkiRno su ounitnoc sip stniop fo eciohc eht fo tned
Oklahoma State - MATH - 4013
1)t,0(,)tt t + )t ,s( = )t ,0( , ) - t ( , v u t t )t ,0( , + ) - t ( v + )t ,s(v , ) - t ( u + )t ,s(u = )t ,0( , ) - t + t ,s( v ,) - t + t ,s(u( = ) ( 4 t t s s + )t ,s( = )s ,0( , t , + ) - s ( , v u v u t t s
Oklahoma State - MATH - 4013
1t + 0 0 t 0 t 0t 1 = 1 mil = 2 2 mil = )t ,0( f mil 2t sdleiy sixa-y eht gnola nigiro eht gnihcaorppa elihw 0 + 2t 0 t 0 t 0t 0 = 0 mil = 2 mil = )0 ,t( f mil 20 sdleiy sixa-x eht gnola nigiro eht gnihcaorppa tuB .)0,0( tniop timil eht hcaorppa e
Oklahoma State - MATH - 4013
10 t5 1 2td )3 ,2 ,1(= tdt010 1 1 0= td )t3 + t4 + t3( = tdtd d0 1 1 05 = = =sd )t ,t2 ,t3( ) )t( ( FFC)t3 ,t2 ,t( = )t(:C3oS R ] 1 ,0 [ : sa deziretemarap eb nac C evruc ehT sdFetaluclaC . 3R ni )3 ,2 ,1( ot )
Oklahoma State - MATH - 4013
1yx- ) y , x(,R2R: f)b(C-2+x= y C = 2+y-xsenil eht tsuj era sevruc level ehT2+y- x ) y , x(,R2R: f)a(:snoitcnuf gniwollof eht fo shparg dna sevruc level eht hctekS 1.1.2 1.2 noitceS2 retpahC morf smelborP
Oklahoma State - MATH - 4013
10 =y y-e- =-ex- = f 0 =yy z f y x f y x z f x y x-e- = f xy2 -e + 1 - = f .0 = x ,y-ex + )x/1( + ze = )z ,y ,x( f )b(.y x f =x y f taht etoNy x f 2 y 2x 2y) y + 2x( 4 2 63 + 4y6 - 4x6- =2y) y2( 22y
Oklahoma State - MATH - 4013
11- 2/321 2 2/ 33= =u1=t+1 = u,udu 2 10=tdt + 13it= ] [Lt d )t( ft,suhTt+1)t + 1 ( 93= = = )t(t9 + )t3 ( nis 9 + )t3 ( 2soc 92,os2/ 1t3 ,)t3(nis 3- ,)t3(soc 3]1 ,0[= )t(,lleWt,
Oklahoma State - MATH - 4013
11 3341 25 = = t41 2 1 1t d 2t 4 1 6 3 t d 4 1 ) t2 ( ) t 3 ( 3= =evah eW 41 = 4 + 9 + 1 = td dos dna woN)2 ,3 ,1( =td d.]3 ,1[ t ,)t2 ,t3 ,t( t : yb deziretemarap evruc eht si C dna zy = ) z ,y ,x( f erehwsd fClarge
Oklahoma State - MATH - 4013
11 = z 1 = y t1 = xv P xro1)0 ,0 ,t( + )1 ,1 ,1( = t + 1 = yb nevig suht si enil eht fo noitaziretemarap A .enil eht no tniop a si )0 ,0 ,1( = )1 ,1 ,1( )1 ,1 ,0( = 1 2 =P P vP dnasi enil eht fo noitcerid ehT=2P dna )1 ,1 ,1(
Oklahoma State - MATH - 4013
MATH 4013 Extra Credit 21. (2 points) Find the rst and the second order partial derivatives for the z function u = xy , where x, y and z are independent variables. 2. (4 points) How many dierent partial derivatives of order n may a function f (x, y
Oklahoma State - MATH - 4013
TEST 1MATH 4013Name: Please give complete and clearly written solutions. 1. (20 points) Find an equation of the plane containing two parallel lines v1 = (1, 2, 2) + t(-1, 1, 3) and v2 = (-2, 0, 1) + t(-3, 3, 9). The general equation of a plane is A
Oklahoma State - MATH - 4013
TEST 2MATH 4013Name: Please give complete and clearly written solutions. 1. (20 points) Determine the second-order Taylor formula for f (x, y) = sin(xy) + cos(xy) near (0, 0). Recall that the second-order Taylor formula is given by f f (x0 , y0 )(x
Oklahoma State - MATH - 4013
Oklahoma State - MATH - 4013
TEST 1MATH 4013Name: Please give complete and clearly written solutions. 1. (20 points) Find an equation of the plane containing two parallel lines v1 = (1, 2, 2) + t(-1, 1, 3) and v2 = (-2, 0, 1) + t(-3, 3, 9). SSN:12. (20 points) Can we make
Oklahoma State - MATH - 4013
TEST 2MATH 4013Name: Please give complete and clearly written solutions. 1. (20 points) Determine the second-order Taylor formula for f (x, y) = sin(xy) + cos(xy) near (0, 0). SSN:12. (20 points) Find all critical points of f (x, y) = 3x2 + 2xy
UNI - CS - 062
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UNI - CS - 062
vti_encoding:SR|utf8-nlvti_author:SR|BEN-SCHAFER\schafervti_modifiedby:SR|BEN-SCHAFER\schafervti_timelastmodified:TR|04 Nov 2008 19:19:46 -0000vti_timecreated:TR|25 Apr 2003 21:03:12 -0000vti_extenderversion:SR|5.0.2.6790vti_syncwith_localhost\
UNI - CS - 062
vti_encoding:SR|utf8-nlvti_author:SR|BEN-SCHAFER\schafervti_modifiedby:SR|BEN-SCHAFER\schafervti_timelastmodified:TR|04 Nov 2008 19:19:47 -0000vti_timecreated:TR|25 Apr 2003 21:03:11 -0000vti_extenderversion:SR|5.0.2.6790vti_syncwith_localhost\
Wake Forest - PHY - 11401
Chapter 37 Solutions37.5 For the tenth minimum, m = 9. Using Equation 37.3, 1 sin = d 9 + 2 y For small , sin tan . Thus, Also, tan = L . 9.5 9.5 L 9.5(589 109 m)(2.00 m) d= = y = sin 7.26 103 m = 1.54 mm2 yd I = I max cos L = 1.5
Buffalo State - TECH - 465
Cordero King Design Project Abstract Using a Tesla Coil for Wireless Energy Transfer In the field of electronics, Nikola Tesla was one of its unsung heroes. His inventions and ideas paved the way for how electricity is transmitted and even collaborat
Buffalo State - TECH - 465
BUFF STATE PROJECT 1-27-2008 WAYNE R. CAMERON BACKGROUND: I HAVE BEEN USING ROPE LIGHTS IN THE FLOWER BEDS IN FRONT OF THE HOUSE FOR MANY YEARS. UNTIL NOVEMBER OF 2007, THEY WERE CONTROLLED BY A RADIO SHACK PLUG N' POWER RECEPTACLE, (SIMILAR TO X10 D
Buffalo State - TECH - 465
Student Research and Creativity Celebration abstracts Related to ENT 465 Sixth 2006 Student Research and Creativity Celebration Using a Microcontroller in an End ofLine TesterNavindra Bhajan, Brandon Davis, Ed Petre, andWosen Wolde, ENT465, El
Buffalo State - TECH - 465
10th 2008 Student Research and Creativity CelebrationInfrared Safe OpenerJoe Siegmann, Lawrence Guilford III, and Paul Whissel,ENT465, Electrical Circuit DesignFaculty Mentor: Professor Stephanie Goldberg, TechnologyAs part of the Engineering Te
Buffalo State - TECH - 465
Ninth 2007 Student Research and Creativity CelebrationAutomated Temperature-ControlledChamberThomas Chiantia, Kazi Karim, and Drew Gugliuzza,ENT 465, Electronic DesignFaculty Mentor: Professor Stephanie Goldberg, TechnologyThe main objective of
Buffalo State - TECH - 465
Cordero King Hugo Pineda Christopher FowlerPreliminary Design ReviewConstruct Tesla coil for wireless energy transfer Items discussed Procedure Basic schematic Items required Safety GoalsSchematicFinished secondary coil Finished generatin
Buffalo State - TECH - 465
"Leak Test Apparatus" Capstone Project Middle Design ReviewENT465 Buffalo State College Spring 2009Operational Project Definition ENT465 Electrical Design Capstone project team consisting of David Siembida, Jeffrey Przepasniak and Danny Kolanda
Buffalo State - TECH - 465
Buffalo State - TECH - 465
Sheet18 9 8 7 0 9 7 8 8 9 8 9 7.5 Tesla Coil Average in last column and last row Comments: Item 3: User manual should have been printed out Item 3: Oscilloscope have no values and are chopped Item 5: Fuse should be before the switch Item 6: Hard to
UMass Lowell - ENG - 16572
File: H:\16472F2001\Program1\printme.c10/11/2001, 3:51:21PM#ifndef NUMBER_H #define NUMBER_H /*- N u m b e r . h -*/ /* by: George Chene Cheney Embedded Real Time System Systems Electrical and Computer Engineering Dept Dept. UMASS Lowel Lowell*
SUNY Stony Brook - AMS - 501
Homework 2, due March 3 1. Solve problem 1.20 from Bender, Orszag, Advanced mathematical methods for scientists and engineers, page 32.2. Find eigenvalues and eigenfunctions (if any) to the following boundary value problems a) y + 2y + 2 y = 0, b
SUNY Stony Brook - AMS - 501
~Aer~,{P~p&J1Ad c~ce .CFc'Y1-('I.e?-t1-./-erv J.L J -=:1 / y 13 (1 (CC-) ~ J1(c?, 6 Jf3Z(:J (p)-z-IS'p41 lieSek ,0oA ja.v4tJ/ n. ci:IL~~ -t Zr/7,)~Lu-z/,8" /t{rq)}-=- (/r( ( j '/7T-z-O131(~(~)-z- cI-'~ 2-
SUNY Stony Brook - AMS - 501
HW 4, due April 30.Problem 1 Classify all singular points of the dierential equation x(1 x)y 3xy y = 0, and nd two independent solutions using the method of Frobenius about x = 0.Problem 2 Obtain the leading behavior of the following equation
SUNY Stony Brook - AMS - 341
AMS 341 (Spring, 2009) Exam 1 - Solution notes Mean 77.6, median 81, high 99 (2 of them!), low 34. 1. (20 points) Consider the following LP: max z = 2x1 - x2 + x3 s.t. x1 + 2x2 - x3 3x1 - 2x2 + x3 x1 , x2 x3 (a). Rewrite the LP in standard form. max
SUNY Stony Brook - AMS - 540
AMS 540 / MBA 540 (Fall, 2008)Estie ArkinHomework Set # 7: Solution notes 1). (a). Dual solution is w1 = 4, w2 = 0, w3 = 10, objective = 440. Therefore, I would choose to increase the amount of resource 3, it has the highest shadow price. (b).
SUNY Stony Brook - AMS - 540
AMS 540 / MBA 540 (Fall, 2008)Estie ArkinLinear Programming - FinalDo all problems. Write your answers on the exam. You are permitted to use the text, your notes and any material handed out in class. The exam time is 2 hours and 30 minutes. GOOD
SUNY Stony Brook - AMS - 315
AMS 315 Data Analysis. Homework Set 1.Due to February 5th. (Thursday) Please, do the following problems from the book: 3.58, 4.59, 4.61, 4.65, 4.78, 4.90, 4.91, 4.97.1
SUNY Stony Brook - AMS - 315
AMS 315 Data Analysis. Homework Set 2.Due to February 12th. Please, do the following problems from the book: 4.104, 4.110, 4.114, 5.10, 5.14, 5.22, 5.23, 10.531
SUNY Stony Brook - AMS - 315
AMS 315 Data Analysis. Homework Set 3.Due to February 19th. Please, do the following problems from the book: 5.25, 5.26, 5.32, 5.37, 5.76, 5.77, 5.961
SUNY Stony Brook - AMS - 315
AMS 315 Data Analysis. Homework Set 6.Due to March 31st. Please, do the following problems from the book: 10.05(a,b,c), 10.06, 10.16, 10.18, 10.19(a,b), 10.22.1
SUNY Stony Brook - AMS - 315
AMS 315 Data Analysis. Homework Set 8.Due to April 30th. Please, do the following problems from the book: 11.07, 11.08, 11.09, 11.27, 11.291
SUNY Stony Brook - AMS - 311
AMS 311 (Fall, 2008)Joe MitchellPROBABILITY THEORYFinal Tuesday, December 23, 2008 READ THESE INSTRUCTIONS CAREFULLY. Do not start the exam until told to do so. Make certain that you have all 10 pages (including this cover sheet, and a page at t
SUNY Stony Brook - AMS - 527
AMS 527, Spring 2009, Homework 370 points. Due: Monday 02/23Electronic submission of homework assignments is strongly encouraged for the computer problems. For A the written part, you are encouraged (but not required) to typeset using L TEX or LYX
SUNY Stony Brook - AMS - 527
AMS 527, Spring 2009, Homework 6100 points. Due: Monday 04/20Electronic submission of homework assignments is strongly encouraged for the computer problems. For A the written part, you are encouraged (but not required) to typeset using L TEX or LYX
SUNY Stony Brook - AMS - 527
AMS 527, Spring 2009, Homework 7100 points. Due: Monday 05/04Electronic submission of homework assignments is strongly encouraged for the computer problems. For A the written part, you are encouraged (but not required) to typeset using L TEX or LYX
SUNY Stony Brook - AMS - 527
AMS527: Numerical Analysis IILecture 1: Course Overview & Overview of Scientific ComputingXiangmin JiaoSUNY Stony BrookJanuary 26, 2009Xiangmin JiaoAMS527: Numerical Analysis IICourse DescriptionFundamentals of numerical computation Top
SUNY Stony Brook - AMS - 527
Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear EquationsScientific Computing: An Introductory SurveyChapter 5 Nonlinear EquationsProf. Michael T. HeathDepartment of Computer Science University of Illino
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Interpolation Polynomial Interpolation Piecewise Polynomial InterpolationScientic Computing: An Introductory SurveyChapter 7 InterpolationProf. Michael T. HeathDepartment of Computer Science University of Illinois at Urbana-ChampaignCopyrigh
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Numerical Integration Numerical Differentiation Richardson ExtrapolationScientific Computing: An Introductory SurveyChapter 8 Numerical Integration and DifferentiationProf. Michael T. HeathDepartment of Computer Science University of Illinois
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AMS526: Numerical Analysis I (Numerical Linear Algebra)Lecture 17: Eigenvalue Problems ContdXiangmin JiaoSUNY Stony BrookNovember 6, 2008Xiangmin Jiao (SUNY Stony Brook) AMS526: Numerical Analysis I (Numerical Linear Algebra) 6, 2008 November
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AMS526: Numerical Analysis I (Numerical Linear Algebra)Review Session Xiangmin JiaoSUNY Stony BrookDecember 15, 2008Xiangmin Jiao (SUNY Stony Brook) AMS526: Numerical Analysis I (Numerical Linear Algebra) 15, 2008 December1/9Announcement: F
SUNY Stony Brook - AMS - 31209
February 2nd Binomial Experiment A binomial Experiment1. Consists of n trials 2. Each trial has 2 possible outcomes, say `S' or `F'. 3. The probability of getting an outcome of `S' remarks the same from trial to trial. P (' S ') = p 4. These trial
SUNY Stony Brook - AMS - 31209
February 2nd Binomial Experiment A binomial Experiment1. Consists of n t r ials 2. Each t r ial has 2 possible outcomes, say `S' or `F'. 3. The probability of getting an outcome of `S' remarks the same from t r ial to t r ial. P'S'=p 4. These t r
SUNY Stony Brook - AMS - 31209
February 6th Sampling from the normal populationTheorem. Let X 1 , X 2 ,L , X n be a random sample from a normal population N ( , 2 ) . Then, we have the following: 1.X ~ N ( ,2 ~ n -12 ) n2.( n - 1) S 223.X and S 2 are independent
SUNY Stony Brook - AMS - 31209
February 9th Point EstimatorsExample. Let X 1 , X 2 ,L , X n be a random sample from N ( , 2 ) . Please find a good point estimator for 1.2. 2^ Solutions. 1. = X^ 2. 2 = S 2There are the typical estimators for and S 2 . Both are unbiased e