we define ={U V Ue3, C, 4 ) i - ( x y ) that the such top Ux Y ' ( v ) = Xx V UEJ } U { Th, top spaces Ong Xi Is the coarsest projection, IJTU
|
|
|
- Alannah Short
- 5 years ago
- Views:
Transcription
1 such T Etr ics I Topology * Product ology Recll tht for spces Y we defie product ology Y Ty o B {UV Ue3 ve Ty 2 y y C 4 i ( y Ty Y y Ty corsest tht projectis Tl Tly re ctiuous Note Ue J ( U U Y VE Jy Thi ( v V 5 { Ttjllu UEJ U { Th ( v VET is bsis Now how bout product YZ? Ty Suppose ; re spces wh s J respectively Wht product ology defie Csider i th Og product projecti It such tht Tht mes tht t Uje Jj IJTU IT j ( li corsest ology projecti d such elemets geerted product tht S µ { Ttw ; UJET ; j lejs is ctiuous for y j j It Ujj Jii bsis product
2 R( i lr ll Rmk If V ; ti U U Ti ( Ui I product ii E lrc lrt typicl set ( b C c d I e f HEIL! this is bo such boes become bsis to geerte product which sme s obtied by blls I geerl 2 lr IRC 23 IRL I ology Two suppose z s is Ifie fmily ologicl 7m we c defie II { ( ili ie ti Wht is product? Eve more geerlly let be empty ologicl spce for y iet T is Ide set TYTI { ( li ie tie T Wht is product Tel? Ide tjel IT i like j j product ITI corsest ology such tht j th projecti ctiuous tj ET Rmk this mes t Uje F d ll such elemets geerte i e S ( Uj ITI ietllj product { TJYU ; Uje Jj bsis Ti iet Uj Tl
3 Let i let El Rmk If T is Ifie set Vie Ji tie ttv ; tiiwi NOT I product ology ctully sets IT re forms IT Ui IT ie TI where C T y fie set d U ; tie be spce tiet i C ti IT T TIT Pro let Ihm il e IT T iet Ee IF lie t i e ielti tie T We bhd U U t bhd U ± U is form U TV where C T is fie sice ie T ti Uii to tie Tke YIEUII I ( z Yie i ie H suppose ± ( so UNIT ; t $ iletl# we pre IE prove tht O Yile UII ETTI IT ; IEH tht ±lil Iti lijej t bhd U bhd i y Ti ( U ti if i i so ± I;Yu ; U ; I c TH ti Vj J to je T tj
4 { { 2{ Thm if f ; ; ctiuous tie T f( file IT ctiuous ( give iet lfii i Product im?k Pro elemet I form bsis TII ( Uj for some JET Uj E Tj IT f ( Uj UjT ( Ij ( Ujl HJ ( Ttj ( Vj f IT fj i tj fj ( U ; C is j sice fj ctiuous tj f is ctiuous Eh Emple i 23 { 2 B{ { i 4 S{ 3{4443 sets re? { i { 2 { 2 {242 {242 { 2{442 W I Z{ 23 CZ fie il typicl set is IT { 2 TI IE iczl Rmk 0420 E lrc Prop let ie T be fmily spce product tyi i Yi C where spres Teti Y i C sme s Y C ; csidered s spce
5 ( bsis ie bsis J y * metric ology If ( d metric spce B{ Bl e E > o is which geerte J This metric is spce wh is clled metrizble if eists metric d such tht 3 is sme s from d I this cse is Clled metric spce wh metric ( d ology E lr B{ ( b c b lr metric spce wh d( y Thm If Y is metric spce wh metric dy f Y homeomorphism is metrizble ( this mes tht metrizble ologicl property Pro d Y ( e i z d( dy ( fc flz Esy to check tht d is metric which iduces sme Thm d metric spce t IR I ( y mi { dc y El d lso metric which Iduce sme s d Pro Ic y zo o y I ( 4 I ( y d ( y s d ( z t ( z y t y ZE ( if I ( z 2 or d ( z g 2 true ; If I ( z < I d ( z y c d ( y s d ( g d( Y Z d ( y e t ( g d ( y z l 2 Whey y iduce sme ology? B{ Bdc e oyy for ( d
6 D D Ei bl Yill ( IR lrdp dp ( Eli i i pe d ( m{ li Yil ieie d IR ologies lr dp ph ll pb re sme IR dz Euclide metric TIR Rw hm IR be IR defie I ( b mi { I For ± IE defie D( ± g This bouded metric sup { dkili izi D metric tht iduces product Pro is metric ( 20 o D ( 7 trigle Iequly I t s DC z Dlz dyig izl izl dig dye DC I e D ( 2 D( I I 2 3 product Jz is metric ( i # IR j H U E Tz t±( ; e U let IE By ( E CU choose N lrge eough such tht µt < E clim E V IT li e IF Pro Ie V Dc < E e Idiiyi < e { ye Bgcz!R C B < E iz ee IEN El C E t VET csider bsis elemet U TIUI for ology where Ui CIR for i i N Zt product d Ui lr for tiztl e U 7 o< E < leis N such tht ie ( ii Ei C Ui ie E mi { Eili IEIEN
7 I Ei Clim Bp ( c C U Pro t I ( iilil ye Bp i e tdus < E ti lei EN ( i Yi < IE < Ei < I Hi il < Ei Y ; e ( i t Ei C Ui lei < N is N iinil y e ITUI ITIR Or defie metric by f ( ± sup { dciiyi izi metric f clled uiform metric LRW 2 bo is geerted by bcis * Ui where Ui CIR is ti Thm uiform is fier th product ology
Taylor Polynomials. The Tangent Line. (a, f (a)) and has the same slope as the curve y = f (x) at that point. It is the best
Tylor Polyomils Let f () = e d let p() = 1 + + 1 + 1 6 3 Without usig clcultor, evlute f (1) d p(1) Ok, I m still witig With little effort it is possible to evlute p(1) = 1 + 1 + 1 (144) + 6 1 (178) =
Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.
![Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.](/thumbs/92/109036622.jpg "Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.")
te SelfGi ZltAn Dbnyei Intdtin ; ) Q) 4 t? ) t _ 4 73 y S _ E _ p p 4 t t 4) 1_ ::_ J 1 `i () L VI O I4 " " 1 D 4 L e Q) 1 k) QJ 7 j ZS _Le t 1 ej!2 i1 L 77 7 G (4) 4 6 t (1 ;7 bb F) t f; n (i M Q) 7S
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
Review of the Riemann Integral
Chpter 1 Review of the Riem Itegrl This chpter provides quick review of the bsic properties of the Riem itegrl. 1.0 Itegrls d Riem Sums Defiitio 1.0.1. Let [, b] be fiite, closed itervl. A prtitio P of
SOLUTION OF SYSTEM OF LINEAR EQUATIONS. Lecture 4: (a) Jacobi's method. method (general). (b) Gauss Seidel method.
SOLUTION OF SYSTEM OF LINEAR EQUATIONS Lecture 4: () Jcobi's method. method (geerl). (b) Guss Seidel method. Jcobi s Method: Crl Gustv Jcob Jcobi (804-85) gve idirect method for fidig the solutio of system
~,. :'lr. H ~ j. l' ", ...,~l. 0 '" ~ bl '!; 1'1. :<! f'~.., I,," r: t,... r':l G. t r,. 1'1 [<, ."" f'" 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'..
,, 'l t (.) :;,/.I I n ri' ' r l ' rt ( n :' (I : d! n t, :?rj I),.. fl.),. f!..,,., til, ID f-i... j I. 't' r' t II!:t () (l r El,, (fl lj J4 ([) f., () :. -,,.,.I :i l:'!, :I J.A.. t,.. p, - ' I I I
Dear Friends. St. John the Baptist Greek Orthodox Church Sterling Heights, Michigan. Volume 25 Issue 6 June, July & August 2018
D Fi J Bi k x li i ii Vl 25 6 j J Jl & 2018 JR ER FE DY (B i k) JE 3 RD - LL : iil i l i ii il i i li k l k vi i vi i li i l iii lvi B l ii k l vi vil lik i iii li i i i l l l i W i i i v ji i k lik l
J={ Infinite. if txty EX. yet U. properties X={ Example. infinite. Def. t ±Y X. top. Example : X = Rmk : X is To but not T, yet. FZCX finite set.
( TO Tr 71 Husdorft Seprtion xiom l is To if txty E 7 set U such tht xeu y U or ye U xcf U c y is T if t ±Y 7 set U such tht xe U yet U h is Tz ( Husdorff V such tht xe U if ttxt Y E 9 V 7 sets U nd UV
FOURIER SERIES PART I: DEFINITIONS AND EXAMPLES. To a 2π-periodic function f(x) we will associate a trigonometric series. a n cos(nx) + b n sin(nx),
FOURIER SERIES PART I: DEFINITIONS AND EXAMPLES To -periodic fuctio f() we will ssocite trigoometric series + cos() + b si(), or i terms of the epoetil e i, series of the form c e i. Z For most of the
10.5 Power Series. In this section, we are going to start talking about power series. A power series is a series of the form
0.5 Power Series I the lst three sectios, we ve spet most of tht time tlkig bout how to determie if series is coverget or ot. Now it is time to strt lookig t some specific kids of series d we will evetully
::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2...
Math 3298 Exam 1 NAME: SCORE: l. Given three points A(I, l, 1), B(l,;2, 3), C(2, - l, 2). (a) Find vectors AD, AC, nc. (b) Find AB+ DC, AB - AC, and 2AD. -->,,. /:rf!:,-t- f1c =-
Chapter 5. The Riemann Integral. 5.1 The Riemann integral Partitions and lower and upper integrals. Note: 1.5 lectures
Chpter 5 The Riem Itegrl 5.1 The Riem itegrl Note: 1.5 lectures We ow get to the fudmetl cocept of itegrtio. There is ofte cofusio mog studets of clculus betwee itegrl d tiderivtive. The itegrl is (iformlly)
Math 61CM - Solutions to homework 9
Mth 61CM - Solutions to homework 9 Cédric De Groote November 30 th, 2018 Problem 1: Recll tht the left limit of function f t point c is defined s follows: lim f(x) = l x c if for ny > 0 there exists δ
Prior distributions. July 29, 2002
Prior distributios Aledre Tchourbov PKI 357, UNOmh, South 67th St. Omh, NE 688-694, USA Phoe: 4554-64 E-mil: tchourb@cse.ul.edu July 9, Abstrct This documet itroduces prior distributios for the purposes
I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. l"l. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S l"l. \ (?
>. 1! = * l >'r : ^, : - fr). ;1,!/!i ;(?= f: r*. fl J :!= J; J- >. Vf i - ) CJ ) ṯ,- ( r k : ( l i ( l 9 ) ( ;l fr i) rf,? l i =r, [l CB i.l.!.) -i l.l l.!. * (.1 (..i -.1.! r ).!,l l.r l ( i b i i '9,
Content: Essential Calculus, Early Transcendentals, James Stewart, 2007 Chapter 1: Functions and Limits., in a set B.
Review Sheet: Chpter Cotet: Essetil Clculus, Erly Trscedetls, Jmes Stewrt, 007 Chpter : Fuctios d Limits Cocepts, Defiitios, Lws, Theorems: A fuctio, f, is rule tht ssigs to ech elemet i set A ectly oe
Problem Set 4: Solutions Math 201A: Fall 2016
Problem Set 4: s Mth 20A: Fll 206 Problem. Let f : X Y be one-to-one, onto mp between metric spces X, Y. () If f is continuous nd X is compct, prove tht f is homeomorphism. Does this result remin true
The Exponential Function
The Epoetil Fuctio Defiitio: A epoetil fuctio with bse is defied s P for some costt P where 0 d. The most frequetly used bse for epoetil fuctio is the fmous umber e.788... E.: It hs bee foud tht oyge cosumptio
176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
Qtr. Bryysofx. Bsyly. &B b ,!DD)< If,( r=mff!rs ; g igk yq. p± : }y s. Any compact. disjoint. Det. space. of s. Bsgcy ;) Bry!Yj ),
metric SCE spce Any compct subset S of is closed p± We show tht Sc is S we every yes find disjoint Bryysofx is y s Bsyly n Tke K 5 nbhds For cover of s WTS Brix 5 Qtr of Y &B b compctness of S there exist
fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.
OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te
Why study large deviations? The problem of estimating buer overow frequency The performance of many systems is limited by events which have a small pr
Why study lrge devitios? The problem of estimtig buer overow frequecy The performce of my systems is ited by evets which hve smll probbility of occurrig, but which hve severe cosequeces whe they occur.
We enclose herewith a copy of your notice of October 20, 1990 for your reference purposes.
W-E AND ISuC ATTORNEYS AT lhw 10 QUEEN STIlEET P. 0. BOX NO. 201 NEWTOWN. CONNEWICUT 06470 OEOROE N. WNCELEE HENRY J. ISAAC BUWrpOff 203 9992218 FAX NO. 903-4P6-3011 October 30, 1990.. The Master Collectors
b a 2 ((g(x))2 (f(x)) 2 dx
Clc II Fll 005 MATH Nme: T3 Istructios: Write swers to problems o seprte pper. You my NOT use clcultors or y electroic devices or otes of y kid. Ech st rred problem is extr credit d ech is worth 5 poits.
Chapter 2 Infinite Series Page 1 of 9
Chpter Ifiite eries Pge of 9 Chpter : Ifiite eries ectio A Itroductio to Ifiite eries By the ed of this sectio you will be ble to uderstd wht is met by covergece d divergece of ifiite series recogise geometric
STEEL PIPE NIPPLE BLACK AND GALVANIZED
Price Sheet Effective August 09, 2018 Supersedes CWN-218 A Member of The Phoenix Forge Group CapProducts LTD. Phone: 519-482-5000 Fax: 519-482-7728 Toll Free: 800-265-5586 www.capproducts.com www.capitolcamco.com
Inner Product Spaces (Chapter 5)
Ier Product Spces Chpter 5 I this chpter e ler out :.Orthogol ectors orthogol suspces orthogol mtrices orthogol ses. Proectios o ectors d o suspces Orthogol Suspces We ko he ectors re orthogol ut ht out
9.9 L1N1F_JL 19bo. G)&) art9lej11 b&bo 51JY1511JEJ11141N0fM1NW15tIr1
thunyitmn tn1 zni f1117n.nllfmztri Lrs v wu 4 t t701 f 171/ ti 141 o&oiv,3 if 042 9.9 L1N1F_JL 19bo vitioluutul fly11.1.g)onoo b5 et Nn`15fiwnwiymri1 nrikl5fini1nvi Ltol : Aeniln,flvnu 6m,wiutrmntn15Y
Citation for published version (APA): Harinck, S. (2001). Conflict issues matter : how conflict issues influence negotiation
UvA-DARE (Digital Academic Repository) Conflict issues matter : how conflict issues influence negotiation Harinck, S. Link to publication Citation for published version (APA): Harinck, S. (2001). Conflict
Approximate Integration
Study Sheet (7.7) Approimte Itegrtio I this sectio, we will ler: How to fid pproimte vlues of defiite itegrls. There re two situtios i which it is impossile to fid the ect vlue of defiite itegrl. Situtio:
The Weierstrass Approximation Theorem
The Weierstrss Approximtio Theorem Jmes K. Peterso Deprtmet of Biologicl Scieces d Deprtmet of Mthemticl Scieces Clemso Uiversity Februry 26, 2018 Outlie The Wierstrss Approximtio Theorem MtLb Implemettio
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
SOME SHARP OSTROWSKI-GRÜSS TYPE INEQUALITIES
Uiv. Beogrd. Publ. Elektroteh. Fk. Ser. Mt. 8 006 4. Avilble electroiclly t http: //pefmth.etf.bg.c.yu SOME SHARP OSTROWSKI-GRÜSS TYPE INEQUALITIES Zheg Liu Usig vrit of Grüss iequlity to give ew proof
Notes 17 Sturm-Liouville Theory
ECE 638 Fll 017 Dvid R. Jckso Notes 17 Sturm-Liouville Theory Notes re from D. R. Wilto, Dept. of ECE 1 Secod-Order Lier Differetil Equtios (SOLDE) A SOLDE hs the form d y dy 0 1 p ( x) + p ( x) + p (
Theoretical foundations of Gaussian quadrature
Theoreticl foundtions of Gussin qudrture 1 Inner product vector spce Definition 1. A vector spce (or liner spce) is set V = {u, v, w,...} in which the following two opertions re defined: (A) Addition of
Časopis pro pěstování matematiky
Časopis pro pěstování matematiky Jan Ligȩza On distributional solutions of some systems of linear differential equations Časopis pro pěstování matematiky, Vol. 102 (1977), No. 1, 37--41 Persistent URL:
Mv3" L7-- Art L 31. am rt. ao - M rr. a cn. art O' N. t00. to o( C7 c O. Ort. n ' C ( a ( W 0. z D0) Ln rni 90 O H N rt 0. to0) O mx rt N. W n.
S = TG _. -. t s e- ' F F J l T L L " m - F+ m G T. G m ( ( F+ v ( _ = ). i i vi vi t g d d --( ( ( t t ( - : m ET 7 ' m : ( 7 c t+ ) c - 7 7de 7( ( d;:', ` m G - L Lm ) 7 ` 7 [ t d `< ( ) ( m ( ) c. (
necessita d'interrogare il cielo
gigi nei necessia d'inegae i cie cic pe sax span s inuie a dispiegaa fma dea uce < affeandi ves i cen dea uce isnane " sienzi dei padi sie veic dei' anima 5 J i f H 5 f AL J) i ) L '3 J J "' U J J ö'
We will begin by supplying the proof to (a).
(The solutios of problem re mostly from Jeffrey Mudrock s HWs) Problem 1. There re three sttemet from Exmple 5.4 i the textbook for which we will supply proofs. The sttemets re the followig: () The spce
POWER SERIES R. E. SHOWALTER
POWER SERIES R. E. SHOWALTER. sequeces We deote by lim = tht the limit of the sequece { } is the umber. By this we me tht for y ε > 0 there is iteger N such tht < ε for ll itegers N. This mkes precise
Riemann Integral and Bounded function. Ng Tze Beng
Riem Itegrl d Bouded fuctio. Ng Tze Beg I geerlistio of re uder grph of fuctio, it is ormlly ssumed tht the fuctio uder cosidertio e ouded. For ouded fuctio, the rge of the fuctio is ouded d hece y suset
Fast Fourier Transform 1) Legendre s Interpolation 2) Vandermonde Matrix 3) Roots of Unity 4) Polynomial Evaluation
Algorithm Desig d Alsis Victor Admchi CS 5-45 Sprig 4 Lecture 3 J 7, 4 Cregie Mello Uiversit Outlie Fst Fourier Trsform ) Legedre s Iterpoltio ) Vdermode Mtri 3) Roots of Uit 4) Polomil Evlutio Guss (777
Advanced Calculus Test File Spring Test 1
Advced Clculus Test File Sprig 009 Test Defiitios - Defie the followig terms.) Crtesi product of A d B.) The set, A, is coutble.) The set, A, is ucoutble 4.) The set, A, is ifiite 5.) The sets A d B re
MATRIX ALGEBRA, Systems Linear Equations
MATRIX ALGEBRA, Systes Lier Equtios Now we chge to the LINEAR ALGEBRA perspective o vectors d trices to reforulte systes of lier equtios. If you fid the discussio i ters of geerl d gets lost i geerlity,
Vectors. Vectors in Plane ( 2
Vectors Vectors i Ple ( ) The ide bout vector is to represet directiol force Tht mes tht every vector should hve two compoets directio (directiol slope) d mgitude (the legth) I the ple we preset vector
The Algebra (al-jabr) of Matrices
Section : Mtri lgebr nd Clculus Wshkewicz College of Engineering he lgebr (l-jbr) of Mtrices lgebr s brnch of mthemtics is much broder thn elementry lgebr ll of us studied in our high school dys. In sense
The Regulated and Riemann Integrals
Chpter 1 The Regulted nd Riemnn Integrls 1.1 Introduction We will consider severl different pproches to defining the definite integrl f(x) dx of function f(x). These definitions will ll ssign the sme vlue
fnm 'et Annual Meeting
UUVtK Ht.t, A 0 8 4 S.. Rittin Nub t, n L Y t U N i, n ' A N n, t\ V n b n k pny' ull N) 0 R Z A L A V N U X N S N R N R H A V N U R A P A R K A L A N Y Buin Add. N. Stt ity wn / Pvin) Ali l) lil tal?l
MATH 104 FINAL SOLUTIONS. 1. (2 points each) Mark each of the following as True or False. No justification is required. y n = x 1 + x x n n
MATH 04 FINAL SOLUTIONS. ( poits ech) Mrk ech of the followig s True or Flse. No justifictio is required. ) A ubouded sequece c hve o Cuchy subsequece. Flse b) A ifiite uio of Dedekid cuts is Dedekid cut.
A Hallelujah for My Father
Univeity o New Mexico UNM Digital Repoitoy New Mexico Compoe' chive Reeach Collection and Data 1312011 Hallelujah o My Fathe lan Stinge Robet Fanci Follow thi and additional wok at: http://digitalepoitoyunmedu/nm_compoe_achive
MA261-A Calculus III 2006 Fall Homework 7 Solutions Due 10/20/2006 8:00AM
MA26-A Calculus III 2006 Fall Homework 7 Solutions Due 0/20/2006 8:00AM 3 #4 Find the rst partial derivatives of the function f (; ) 5 + 3 3 2 + 3 4 f (; ) 5 4 + 9 2 2 + 3 4 f (; ) 6 3 + 2 3 3 #6 Find
SPACES DOMINATED BY METRIC SUBSETS
Volume 9, 1984 Pges 149 163 http://topology.uburn.edu/tp/ SPACES DOMINATED BY METRIC SUBSETS by Yoshio Tnk nd Zhou Ho-xun Topology Proceedings Web: http://topology.uburn.edu/tp/ Mil: Topology Proceedings
Riemann is the Mann! (But Lebesgue may besgue to differ.)
Riemnn is the Mnn! (But Lebesgue my besgue to differ.) Leo Livshits My 2, 2008 1 For finite intervls in R We hve seen in clss tht every continuous function f : [, b] R hs the property tht for every ɛ >
Solutions to RSPL/1. log 3. When x = 1, t = 0 and when x = 3, t = log 3 = sin(log 3) 4. Given planes are 2x + y + 2z 8 = 0, i.e.
olutios to RPL/. < F < F< Applig C C + C, we get F < 5 F < F< F, $. f() *, < f( h) f( ) h Lf () lim lim lim h h " h h " h h " f( + h) f( ) h Rf () lim lim lim h h " h h " h h " Lf () Rf (). Hee, differetile
20... Figure 9.6 Thermal efficiency of the cold air standard Diesel cycle, k = 1.4.
408 Chapter 9 Gas Power Systems ~ I=",:; u '" 'u!.:::... 0; " E ~ ~ 70 60 50 40 30 20 10 0 5 10 15 Compression ralio, r 20... Figure 9.6 Thermal efficiency of the cold air standard Diesel cycle, k = 1.4.
Definition. special name. 72 spans 5. Last time we proved that if Ju's is. t.vtts.tt turn. This subspace is se important that we give it
1.7 Spanningsetsilinearndependencey 1.2 in text Last time we proved that if 72 148 Ju's is a set of vectors in R then is a subspace of R t.vtts.tt turn t tz the R This subspace is se important that we
Limit of a function:
- Limit of fuctio: We sy tht f ( ) eists d is equl with (rel) umer L if f( ) gets s close s we wt to L if is close eough to (This defiitio c e geerlized for L y syig tht f( ) ecomes s lrge (or s lrge egtive
Math 104: Final exam solutions
Mth 14: Fil exm solutios 1. Suppose tht (s ) is icresig sequece with coverget subsequece. Prove tht (s ) is coverget sequece. Aswer: Let the coverget subsequece be (s k ) tht coverges to limit s. The there
LNT. R Mod. Rtdd. Stlod. next. the. two. Rtlod. fenctov of the MQR LNTH. Lectured MORP. Mar, Torre 1. exact. for. any. natural. point. claim.
We hve defied dditive fu dor Tor exmple of fix D# T Give left LT fuctio left derived ext od derived fuctio Tory T set d exmie y Throughout put # R lectures two fectov of ot ecessrily commuttive R S Rtlod
TOPOLOGY HW 2. x x ± y
TOPOLOGY HW 2 CLAY SHONKWILER 20.9 Show that the euclidean metric d on R n is a metric, as follows: If x, y R n and c R, define x + y = (x 1 + y 1,..., x n + y n ), cx = (cx 1,..., cx n ), x y = x 1 y
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
$%! & (, -3 / 0 4, 5 6/ 6 +7, 6 8 9/ 5 :/ 5 A BDC EF G H I EJ KL N G H I. ] ^ _ ` _ ^ a b=c o e f p a q i h f i a j k e i l _ ^ m=c n ^
![$%! & (, -3 / 0 4, 5 6/ 6 +7, 6 8 9/ 5 :/ 5 A BDC EF G H I EJ KL N G H I. ] ^ _ ` _ ^ a b=c o e f p a q i h f i a j k e i l _ ^ m=c n ^](/thumbs/92/108125918.jpg "$%! & (, -3 / 0 4, 5 6/ 6 +7, 6 8 9/ 5 :/ 5 A BDC EF G H I EJ KL N G H I. ] ^ _ ` _ ^ a b=c o e f p a q i h f i a j k e i l _ ^ m=c n ^")
! #" $%! & ' ( ) ) (, -. / ( 0 1#2 ' ( ) ) (, -3 / 0 4, 5 6/ 6 7, 6 8 9/ 5 :/ 5 ;=? @ A BDC EF G H I EJ KL M @C N G H I OPQ ;=R F L EI E G H A S T U S V@C N G H IDW G Q G XYU Z A [ H R C \ G ] ^ _ `
Affidavit and Revenue Certification Chimp Haven, Inc. Caddo Parish Keithville, LA
/ / / / Affivit Revee Certifiti Chi Hve, I. C Prih Keithville, LA ANNAL WRN FINANCL TATNT AND CRTIFICATIN F RN $0,0 R L (if lible) The l wr fiil tteet re reqire by Lii Revie ttte 24:14 t be file with the
Lecture 3. Limits of Functions and Continuity
Lecture 3 Limits of Functions nd Continuity Audrey Terrs April 26, 21 1 Limits of Functions Notes I m skipping the lst section of Chpter 6 of Lng; the section bout open nd closed sets We cn probbly live
Math Solutions to homework 1
Mth 75 - Solutions to homework Cédric De Groote October 5, 07 Problem, prt : This problem explores the reltionship between norms nd inner products Let X be rel vector spce ) Suppose tht is norm on X tht
DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS
3 DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS This chpter summrizes few properties of Cli ord Algebr nd describe its usefulness in e ecting vector rottions. 3.1 De nition of Associtive
Canonical Form and Separability of PPT States on Multiple Quantum Spaces
Coicl Form d Seprbility of PPT Sttes o Multiple Qutum Spces Xio-Hog Wg d Sho-Mig Fei, 2 rxiv:qut-ph/050445v 20 Apr 2005 Deprtmet of Mthemtics, Cpitl Norml Uiversity, Beijig, Chi 2 Istitute of Applied Mthemtics,
1.3 Continuous Functions and Riemann Sums
mth riem sums, prt 0 Cotiuous Fuctios d Riem Sums I Exmple we sw tht lim Lower() = lim Upper() for the fuctio!! f (x) = + x o [0, ] This is o ccidet It is exmple of the followig theorem THEOREM Let f be
o C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco
> p >>>> ft^. 2 Tble f Generl rdnes. t^-t - +«0 -P k*ph? -- i t t i S i-h l -H i-h -d. *- e Stf H2 t s - ^ d - 'Ct? "fi p= + V t r & ^ C d Si d n. M. s - W ^ m» H ft ^.2. S'Sll-pl e Cl h /~v S s, -P s'l
Basic Maths. Fiorella Sgallari University of Bologna, Italy Faculty of Engineering Department of Mathematics - CIRAM
Bsic Mths Fiorell Sgllri Uiversity of Bolog, Itly Fculty of Egieerig Deprtmet of Mthemtics - CIRM Mtrices Specil mtrices Lier mps Trce Determits Rk Rge Null spce Sclr products Norms Mtri orms Positive
Frequency-domain Characteristics of Discrete-time LTI Systems
requecy-domi Chrcteristics of Discrete-time LTI Systems Prof. Siripog Potisuk LTI System descriptio Previous bsis fuctio: uit smple or DT impulse The iput sequece is represeted s lier combitio of shifted
5 Probability densities
5 Probbility densities 5. Continuous rndom vribles 5. The norml distribution 5.3 The norml pproimtion to the binomil distribution 5.5 The uniorm distribution 5. Joint distribution discrete nd continuous
Equations, expressions and formulae
Get strted 2 Equtions, epressions nd formule This unit will help you to work with equtions, epressions nd formule. AO1 Fluency check 1 Work out 2 b 2 c 7 2 d 7 2 2 Simplify by collecting like terms. b
Chapter 9. Arc Length and Surface Area
Chpter 9. Arc Length nd Surfce Are In which We ppl integrtion to stud the lengths of curves nd the re of surfces. 9. Arc Length (Tet 547 553) P n P 2 P P 2 n b P i ( i, f( i )) P i ( i, f( i )) distnce
Hoeffding, Azuma, McDiarmid
Hoeffding, Azum, McDirmid Krl Strtos 1 Hoeffding (sum of independent RVs) Hoeffding s lemm. If X [, ] nd E[X] 0, then for ll t > 0: E[e tx ] e t2 ( ) 2 / Proof. Since e t is conve, for ll [, ]: This mens:
DIFFERENTIAL MANIFOLDS HW Exercise Employing the summation convention, we have: [u, v] i = ui x j vj vi. x j u j
![DIFFERENTIAL MANIFOLDS HW Exercise Employing the summation convention, we have: [u, v] i = ui x j vj vi. x j u j](/thumbs/93/111950451.jpg "DIFFERENTIAL MANIFOLDS HW Exercise Employing the summation convention, we have: [u, v] i = ui x j vj vi. x j u j")
DIFFERENTIAL MANIFOLDS HW 3 KELLER VANDEBOGERT. Exercise.4 Employing the summation convention, we have: So that: [u, v] i = ui x j vj vi x j uj [w, [u, v]] i = wi x [u, k v]k x j x k wk v j ui v j x j
really ultimately take the view that this geometric Liveartrausfomatiousthesaelofliuearalgebrwe doing function that of what A is will
vecr However 14 Feb 2017 18 wht is mtrix wnt more geometric picture doing product I I in Livertrusfomtiousselliuerlgebrwe we will ultimtely tke view tht this geometric ction Is wht mtrices re bout relly
Grain Reserves, Volatility and the WTO
Grain Reserves, Volatility and the WTO Sophia Murphy Institute for Agriculture and Trade Policy www.iatp.org Is v o la tility a b a d th in g? De pe n d s o n w h e re yo u s it (pro d uc e r, tra d e
440-2 Geometry/Topology: Differentiable Manifolds Northwestern University Solutions of Practice Problems for Final Exam
440-2 Geometry/Topology: Differentible Mnifolds Northwestern University Solutions of Prctice Problems for Finl Exm 1) Using the cnonicl covering of RP n by {U α } 0 α n, where U α = {[x 0 : : x n ] RP
2. Infinite Series 3. Power Series 4. Taylor Series 5. Review Questions and Exercises 6. Sequences and Series with Maple
Chpter II CALCULUS II.4 Sequeces d Series II.4 SEQUENCES AND SERIES Objectives: After the completio of this sectio the studet - should recll the defiitios of the covergece of sequece, d some limits; -
Accumulated provision for depreciation and amortization. cs fl
Accumulated pvision for depreciation and amortization. M 530 ch cs fl u s Schedule C-1: Accumulated pvision for depreciation and amortization by functional classification and detailed plant account. Schedule
RESEARCH STUDY ON ADOPTION OF SOCIAL MEDIA MARKETING IN THE ENTERPRISE (MALAYSIA CONTEXT) KEE YONG HONG LEOW XIN YI TANG XIN YI WONG SIONG MUNG
RESEARCH STUDY ON ADOPTION OF SOCIAL MEDIA MARKETING IN THE ENTERPRISE (MALAYSIA CONTEXT) KEE YONG HONG LEOW XIN YI TANG XIN YI WONG SIONG MUNG BACHELOR OF MARKETING (HONS) UNIVERSITI TUNKU ABDUL RAHMAN
0 otherwise. sin( nx)sin( kx) 0 otherwise. cos( nx) sin( kx) dx 0 for all integers n, k.
. Computtio of Fourier Series I this sectio, we compute the Fourier coefficiets, f ( x) cos( x) b si( x) d b, i the Fourier series To do this, we eed the followig result o the orthogolity of the trigoometric
Visit to meet more individuals who benefit from your time
NOURISHINGN G. Vlz S 2009 BR i y ii li i Cl. N i. J l l. Rl. A y l l i i ky. Vii.li.l. iiil i y i &. 71 y l Cl y, i iil k. 28 y, k My W i ily l i. Uil y, y k i i. T j il y. Ty il iy ly y - li G, y Cl.
.Sua. 8f fc"g. II f 8. *1 w. a -a M +» * <N H Q. o * H CO. * o M < a «* n 55 ti 55 «55 «55 Pi. u < < M C C * Ztf fc tf fctf tf tf ISO.
04 ti tf ti -0 T T5 T) " rt..9..9 *>!. +» 1 +* cc +> 0" +» c >. 0> v > U rt +» P p. e rt i < I' T rt >
Tranformations. Some slides adapted from Octavia Camps
Trformtio Some lide dpted from Octvi Cmp A m 3 3 m m 3m m Mtrice 5K C c m ij A ij m b ij B A d B mut hve the me dimeio m 3 Mtrice p m m p B A C H @K?J H @K?J m k kj ik ij b c A d B mut hve A d B mut hve
Discrete Mathematics and Probability Theory Spring 2016 Rao and Walrand Lecture 17
CS 70 Discrete Mthemtics d Proility Theory Sprig 206 Ro d Wlrd Lecture 7 Vrice We hve see i the previous ote tht if we toss coi times with is p, the the expected umer of heds is p. Wht this mes is tht
5.2 Exponent Properties Involving Quotients
5. Eponent Properties Involving Quotients Lerning Objectives Use the quotient of powers property. Use the power of quotient property. Simplify epressions involving quotient properties of eponents. Use
1. (25 points) Use the limit definition of the definite integral and the sum formulas to compute. [1 x + x2
Mth 3, Clculus II Fil Exm Solutios. (5 poits) Use the limit defiitio of the defiite itegrl d the sum formuls to compute 3 x + x. Check your swer by usig the Fudmetl Theorem of Clculus. Solutio: The limit
R e p u b lic o f th e P h ilip p in e s. R e g io n V II, C e n tra l V isa y a s. C ity o f T a g b ila ran
R e p u b l f th e P h lp p e D e p rt e t f E d u t R e V, e tr l V y D V N F B H L ty f T b l r Ju ly, D V N M E M R A N D U M N. 0,. L T F E N R H G H H L F F E R N G F R 6 M P L E M E N T A T N T :,
Chapter 14. Matrix Representations of Linear Transformations
Chpter 4 Mtrix Representtions of Liner Trnsformtions When considering the Het Stte Evolution, we found tht we could describe this process using multipliction by mtrix. This ws nice becuse computers cn
Eigenfunction Expansion. For a given function on the internal a x b the eigenfunction expansion of f(x):
Eigefuctio Epsio: For give fuctio o the iterl the eigefuctio epsio of f(): f ( ) cmm( ) m 1 Eigefuctio Epsio (Geerlized Fourier Series) To determie c s we multiply oth sides y Φ ()r() d itegrte: f ( )
Week 13 Notes: 1) Riemann Sum. Aim: Compute Area Under a Graph. Suppose we want to find out the area of a graph, like the one on the right:
Week 1 Notes: 1) Riem Sum Aim: Compute Are Uder Grph Suppose we wt to fid out the re of grph, like the oe o the right: We wt to kow the re of the red re. Here re some wys to pproximte the re: We cut the
THIS PAGE DECLASSIFIED IAW E
THS PAGE DECLASSFED AW E0 2958 BL K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW E0 2958 B L K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW EO 2958 THS PAGE DECLASSFED AW EO 2958 THS
Convergence rates of approximate sums of Riemann integrals
Jourl of Approximtio Theory 6 (9 477 49 www.elsevier.com/locte/jt Covergece rtes of pproximte sums of Riem itegrls Hiroyuki Tski Grdute School of Pure d Applied Sciece, Uiversity of Tsukub, Tsukub Ibrki
Best Approximation. Chapter The General Case
Chpter 4 Best Approximtion 4.1 The Generl Cse In the previous chpter, we hve seen how n interpolting polynomil cn be used s n pproximtion to given function. We now wnt to find the best pproximtion to given
Review of Sections
Review of Sectios.-.6 Mrch 24, 204 Abstrct This is the set of otes tht reviews the mi ides from Chpter coverig sequeces d series. The specific sectios tht we covered re s follows:.: Sequces..2: Series,
Probability for mathematicians INDEPENDENCE TAU
Probbility for mthemticis INDEPENDENCE TAU 2013 21 Cotets 2 Cetrl limit theorem 21 2 Itroductio............................ 21 2b Covolutio............................ 22 2c The iitil distributio does
Math 6455 Oct 10, Differential Geometry I Fall 2006, Georgia Tech
Mth 6455 Oct 10, 2006 1 Differentil Geometry I Fll 2006, Georgi Tech Lecture Notes 12 Riemnnin Metrics 0.1 Definition If M is smooth mnifold then by Riemnnin metric g on M we men smooth ssignment of n