Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.
10 Pages
apm236_mid2a_2002
Course: APM 236, Fall 2009School: University of Toronto
Rating:
Word Count: 852
Document Preview
RFC XI X V C W`YFy6 9 X V C rW`YFy6 X V C rW`YFy6 X V C W`YFy6 X V C rW`YFy6 X V C $W`YFy6 `` G EQ `Q X TU'TWUyW` X X ` V G I G` IQ C I E )WUW`yDm1P'UU'TFSPHGU6 X X ` G C I E )WUW`Y'TFSPHGU6 g hx s f 4ky'pt et pYq owpt Yt Y~}Y|u{4Yfy4u 8Sh 8Y6f p p f v f q q f q b s s p b q dx b s d b p db e b n f q d t s f tx g p q f q s t bv t n t t b q s t q t q p t...
Unformatted Document Excerpt
Coursehero >> Canada >> University of Toronto >> APM 236Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
RFC XI X V C W`YFy6 9 X V C rW`YFy6 X V C rW`YFy6 X V C W`YFy6 X V C rW`YFy6 X V C $W`YFy6 `` G EQ `Q X TU'TWUyW` X X ` V G I G` IQ C I E )WUW`yDm1P'UU'TFSPHGU6 X X ` G C I E )WUW`Y'TFSPHGU6 g hx s f 4ky'pt et pYq owpt Yt Y~}Y|u{4Yfy4u 8Sh 8Y6f p p f v f q q f q b s s p b q dx b s d b p db e b n f q d t s f tx g p q f q s t bv t n t t b q s t q t q p t pmzgyh1pxfyY'6P"Ywpmup8sTrYY8ht Yq f t t s f tx g tx n s s b s q t v x f q f g e f e t q p pYqupc4ou'4mcylk YwjY'ihft Yd yd s b s p b xx t v s b q fx d vx f v t s d q cr4)t 4cyw)yw$ur6b p ige 4ca hf db W`YWVUUTDSRPHGFDB9 X EQQ C A QI EC A @ 57753753 6686642 0 ( & # ! 1)'%$"
A `X V C A X ` I QE I BWYFywY'RSHyY @ @ 8 ! 4 4& `` %q95765'y'y
2
1
2 0 0 0
0
! ")
!" 2 & ' ! "3 2 & ' & )('
CI `$ V yI %%u # ! " H' ` E E
X V C C A ` E X ` ` EQ G C QI E C A iW`YFyA 'HGE FUS'HGHEX 'HGyWCHXFC uRI 'HUTUPHGTDm9
4%1 )' & % " 5320(#$#!
`X V I C I I Q ` ' W 8 yR'uRI ` E G EI XCQ X EI A G G C C I` F'TWCR'HFUD HUFC YUI u'U W`HU'Ry yST TC X A EQ ` I `Q CI I G 2 @ %q8 8 8
! 4 4& `` 54 " 765'U' )3 3 2 ' ! & ) " 2 ! & ' 2
~
CI `$ V yI %%u # ! 2 E `
H' E
X VC E C A ` E X ` ` EQ G C QI E C @ iW`YUA 'HG FUS'HGHEX uHGyWCHXTC 'UI 'HUT4 RPHGTA y
4%1 )' & % " 5320(#$#!
` E I I I `X V I ` I ` & HUI YU WY o'UoFE $' G ! ` Q X E EQ V ` I C I` X A EQ ` I E I E C A ` G C 4 UW`YV R UYyuRFu'RB W`YHUy'RuHGR'THGTD'T6I %q8 @ 'yuy 4& ``
0 0
6) 6)
& & ' 2
6 2 ' &
CI `$ V yI %%u # ` E E H'
X VC E C A ` E X ` ` EQ G C QI E C @ iW`YUA 'HG FUS'HGHEX uHGyWCHXTC 'UI 'HUT4 RPHGTA y
G CE I X C Q X E I A C ` IE G C G I V Q G CE I X C Q `X VE Q Q X 'TWR'HFU) HR'FoyWY'y'STWRuHTyoWYWU` YY `Q C X V C yT' W`FUA uHGE RFFU''HGHEX 8 C W`Y RPHGTA y" C A ` X A ` G ` E QI E C @
% ! $
! !
! !
! #"
! !
!
X V I E X ` I `I X A C QI E C A wW`Y B'HGWCHXTC 'RyW`YTUPHGTDm9 9
E R
77HoWYV R uHTFUuToWYWUUTDA WFuR4& FC C # 7 yDV $ QE `X E GE C I C `X VE Q Q C X G C ` I `Q ` E C I C ` V " G C `Q ` V E C I C ` V CI E C I C G ` 'HGFFU'FfDI #F8 G y U' 'HGTFy'TfDjy'HGTF'fy 6 )YUI '1! ') 66 " i1WX UmY uRI G ! I C G G ! I C C CI ` G` 'HGE TC YHGHQ& " FHEf'HGU` TyHG W`YWVURFD4U}YUQ W`Y E E ` X E I CQ E X EQQC A ` I I XV E CI C ` I ` E X V E E X EQQ C A ` C I A 'HGTU'TfuRyFFF W`Y U'HGE TC YHGfW`YWVUUTD FF'o
V
I
@ 7WY U Q `X V E 1
'HGTC YHGD ` TuwW`YWVUUTDuTC yU' '8y E E C Q E C X EQQ C A ` `` I A
@ @ @
A ` I ` %uRoy
%
@
@
1
k
@ @ @
@
@ @
@ @ @ @ @
@
@
k % @
k
@ %
!
& '
% @ %
6 !
X V I E X ` ` EQ GC wW`Y B'HGWCHXTC 'RI 'HUF49
IE ` Q C C " C 7WyT1' i #T Py G `Q C C X C C E E QQ E C ` I E Q X E yT1uw HT4 TWA U RHQ) y 'RI UHQ W`YV R ECI C G E C Q E A C G E X ` C I A 'HGFFU'FBouHGE TC YHGD}UWY TWCRI W`HXTC F 'G FC y
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
Below is a small sample set of documents:
Below is a small sample set of documents:
University of Toronto - APM - 236
XI RFC X V C W`YFy6 9 X V C rW`YFy6 X V C rW`YFy6 X V C W`YFy6 X V C rW`YFy6 X V C $W`YFy6 ` G EQ `Q X TU'TWUyW` X X ` V G I G` IQ C I E )WUW`yDm1P'UU'TFSPHGU6 X X ` G C I E )WUW`Y'TFSPHGU6 g hx s f 4ky'pt et pYq owpt Yt Y~}
University of Toronto - APM - 236
South Carolina Aiken - APLS - 458
S.C. LegislatureOutline of Questions from TextFive Periods of Evolution of the SC Legislature1. Proprietary and Colonial Periods, 16631776 2. Revolutionary and Antebellum Periods, 1776-1860 3. Post-Civil War Period,1865-1868 4. Constitution of 18
South Carolina Aiken - APLS - 458
S.C. GovernorOutline of Questions from TextImportant Governors in SC History William Sayle1st, named by proprietors 1670 John Rutledge1st during and after revolution, signed Constitution Daniel ChamberlainReconstruction Wade Hampton1877,
South Carolina Aiken - APLS - 458
Judicial Systemreal improvement in S.C.!Outline of Questions from TextHow state courts are part of our lives and why more important than federal courts? Deal with everyday matters: traffic court, divorce, custody, civil suits (27x more than feder
South Carolina Aiken - APLS - 458
Introduction to Local Government(lots of themsee #s on p.2) Questions on ChapterDillons Rule Based on ruling from John Dillon of the Iowa Supreme Court Made local government creatures of the state All power came from state Could only do what s
South Carolina Aiken - APLS - 458
MunicipalitiesQuestions on Chapter 269 incorporated cities in SC 40% of population lives in 90% of munis are < 5k in populationWhere people live who are no tin cities or rural areas Suburbs or outskirts of cities in areas that are not incorporat
South Carolina Aiken - APLS - 458
CountiesQuestions on Chapter46 counties SC (average state has 64) > 3,000 in US About 20 city/county consolidations 200 to 8 mil in population (McCormick: 10k; Greenville: 400k 26 to 160,000 sq miles (Aiken Co: 1080; R.I.: 1214)Origin of term and
South Carolina Aiken - APLS - 458
Interest GroupsThe Founding Fathers and Factions (Federalist Number 10) Factions = interest groups + parties Factions a natural outgrowth of freedom and human nature Undermine the public interest Endanger stability Solution is republican princ
South Carolina Aiken - APLS - 458
Parties and ElectionsThe Development of Parties in SC Conditions Not Present in SC Conditions for strong parties: Competition with another party (not SCone party factionalism, Dem and now Rep) Control over nominations (not SCprimaries) Control
South Carolina Aiken - APLS - 458
Local Government Finance1970s changes with a significant impact on local govt finance? Move to home rule in Constitution Local government law of 1975gave responsibility to local to meet citizen needs Population boom in late 1900s created more de
South Carolina Aiken - APLS - 458
Human Resource ManagmentWhat HRM is and why more important than most think Recruiting, testing, evaluation, benefits, and discipline of employees in public sector Important because about 20% of workforce in state (state and local employees) Inc
South Carolina Aiken - APLS - 458
Criminal JusticeExtent to which criminal justice is decentralized, and police powers Decentralized nationally b/c of fear of too strong a central govtgoes back to British experience Most investigations are at local level, not state (SLED) or nati
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughFebruary 5, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Numerical MethodsAs usual, let us construct nite-dierence methods on a grid with space s
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughApril 7, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Nonlinear Schrdinger Equation oThis is a classic nonlinear wave equation. It arises physica
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughJanuary 13, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Boundary ConditionsWe now want to discuss in detail methods for solving the linear diusi
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughFebruary 3, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Hyperbolic equationsNow we will talk about hyperbolic equations. As you may recall, in t
University of Toronto - MAT - 1062
Marina Chugunova, notes from Thursday March 12 1. Finite Element Method Projections in Hilbert Space Denition 1.1. We say that a bilinear functional a(u, v ) denes an inner product in linear space B if it has the following properties ( is an arbitrar
Michigan State University - ISP - 209
ISP 209 : Mystery of the Physical World Course description Laws of physics through demonstrations and analyses of every day phenomena. Optics, mechanical systems and electromagnetic phenomena.4/22/04 ISP 209 - 14B14/22/04ISP 209 - 14B21W
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughMarch 10, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Overview of Projection methodsThroughout this course, we have discussed Fourier modes in t
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughFebruary 10, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Modied equationsAs usual, let us construct nite-dierence methods on a grid with space s
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughJanuary 20, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2StabilityThe main idea is to look at how the solutions of the discrete scheme behave as
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughMarch 26, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Spectral MethodsWe have now argued that we may look at a particular function either in the
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughJanuary 27, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Convergence, Consistency, and Stability examplesdU = f U(t), t dtWe wish to time-step t
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughFebruary 12, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Convergence rate for the explicit upwind and Lax-Friedrichs schemes1 for x < 0 0 otherwi
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughMarch 17, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2The Ritz-Galerkin Approximation Problem(1)We seek approximate solutions ofu V, a(u, v)
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughMarch 24, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2An ExampleSpectral methods are similar to nite element methods in that they involve repres
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDE Problem Set 5 Thursday March 19, 2008 due: Thursday April 2, 2008 1. You want to nd approximate solutions of x (0, L), t > 0 ut = Duxx u(x, 0) = u (x) x [0, L] 0 u(0, t) = 0 t>0 u(L, t) = 0 t>0
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDE Problem Set 4 Thursday, Feb 26, 2009 due: Tuesday, March 17 in class 1. For each of the following initial value problems, nd the solution u(x, t): (a) ut + xux = 0 x R, t > 0 u(x, 0) = sin(x) xR (b) ut
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDE Problem Set 3 Thursday, February 12, 2008 due: Thursday, February 26 in class 1. In the rst homework set, you computed the solution of the heat equation on an interval [L, L] with initial data u0 (x) =
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughMarch 31, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Further SourcesFor more information on spectral and pseudospectral methods, have a look at
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughApril 9, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Lets compute!In the following, we will use Richardson Extrapolation. This is a method of ac
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughJanuary 15, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Time discretization ut = Duxx for x [XL , XR ], t > 0 u(X , t) = u (t) L L u(XR , t)
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughMarch 12, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Finite Element MethodsFor nite element methods we need a Hilbert Space. This is a complete
University of Toronto - MAT - 1062
Mat1062: Introductory Numerical Methods for PDEMary PughMarch 3, 20091OwnershipThese notes are the joint property of Rob Almgren and Mary Pugh.2Numerical methodsFor more on numerical methods for hyperbolic conservation laws see \Numeri
University of Toronto - APM - 236
University of Toronto - APM - 236
University of Toronto - APM - 236
8 9FT h P HF i E Ca H H B H P HF E C x@SImDCB fUDtQSdca E eaP RPq Pqa i Eqay HF 9FT h P HF T 8 i E Ea q qP u e h E Ca FT h P HF TF i E Ea qq qP u xDPfs{ifzc0G@T xckiF jQ@mabc@2QI5IS@Q@#mae p n @DTIQ@sT mcH Qn0aQQrn0U0aQ~vq i C BF hT F ia T
University of Toronto - APM - 236
University of Toronto - APM - 236
IIH S Y P#%S I S Y EG%VS I S Y EG%VS I S Y EG%VS I S Y EG%VS I S Y EG%VS 1 f dS PehaE f dS 9PehaE f dS uPehaE f dS PehaE H f dS ~PehaE hh W U` h` f VPecehD f f h W S Y U &eaehdg%VGXWc6o y r y p w j Ey 6y s6x!x!y i u x~
University of Toronto - APM - 236
University of Toronto - APM - 236
APM 236Second MidtermMarch 10, 2004100 points possibleYou may not use calculators, cell phones, or PDAs during the exam. Partial credit is possible. Please read the entire test before starting. READ EACH PROBLEM CAREFULLY.The test ends at 7
University of Toronto - APM - 236
APM 236Second MidtermMarch 10, 2004100 points possibleYou may not use calculators, cell phones, or PDAs during the exam. Partial credit is possible. Please read the entire test before starting. READ EACH PROBLEM CAREFULLY.The test ends at 7
University of Toronto - MAT - 187
iw 9'e}q}k'VA%VQ}rrzvQXCVAA ESEA4bIF q e e j v e o l e x e x e x l i u e o i & @ ( 1 y l " q"Eu A z`G`$8 w w v w f e e x e i e o i l e w x e o e & @ ( 1 C{u A"gftv"u }t}"q"AQ
University of Toronto - MAT - 187
&}Cg y u " y s u s py y py 1ljftd1p~&8ils~&jjtq q t~&~181ts8 ) x pDp1w9@ u yu g u # w ' &}~u y AD "l u y u g u # w ' t~&~a818t1) x pDp1w5 m g y s u s py y py 8p1ljftdwCplwXj8~&jjtq
University of Toronto - MAT - 187
! `#ie! 4@oA 0 4@oA 0 ci 4@oA 0 ! 5 `$` E Y W Y T Y W Y C g`3z`3sB YEb dXE P x G xs u E Cq Y E b Uaff{3dXE W Y b E C q ~3dcFnaT YW Bb EWebE `Dd`nnXfT W BC ~DxT Y C B CE k6S3D3E p j Ak 0 d4@$o 0 y ) ' 9gmAk1 f'
University of Toronto - MAT - 187
! `#ih! t 4@sA 0 i 4@sA 0 l cqi 4@sA 0 l p ! l 5 `$` E Y W Y T Y W Y C g`3`3sB YEb dXE P x G x{ } E f Cy Y E b Uaffeq3dXE W Y b E C y 3dcFaT YW Bb EWebE `Dd`XfT W BC DxT Y C B CE y6S3D3E x Ay 0 d4@$s 0 m ) ' 9vAy1 u
University of Toronto - MAT - 187
I g s l i u u u i f s l f # 9 ' 0 7i &y{n{h&IW@"WxRx{oow Ryw`BW@y DTD@3Et t s t u f l f Bxs @$dqI}y{s {x`iR`R@ i wv $Bs H 7H } k}{yxy@Bxswqs ` DTD@3S i w t u l # 9
University of Toronto - MAT - 187
! `#pf! f4@oA 0 4@oA 0 p 4@oA 0 ! 5 `$` d E Y W Y T Y W Y C h`3z`f3tB dYE nXE P y G ys u E d Cq Y E Uagg{3nXE d W Y E C d q ~3nFfeaT dYW Bd EdWcE f`Dnf`eeXgT dW BC ~DdydT Y C B CE w6S3D3E p k Aw 0 n4@$o 0 fy ) '
University of Toronto - MAT - 187
w h # B ' 0 AHAwE vTvE3HI u h # B ' 0 A E vTvE3S QId U 4 U RP}t w&Eox`9gqEFo&v A&$RgRv R`AkTuEW`vs d$xh m m j s m s y h y h s s y e u y m v u y m m y n u i u j m u y e ~h { |
University of Toronto - MAT - 187
$ $zgd &1 @ yp q f f m w f w o f y w s w s w p f h f y # w ' td 1$kzr$qd quq8r`$r8V11y &1k er~&~r~1gtdqkd 1u~s gCg1Ru97 C " gh r~&~h& zr13rqBq~&iiseBrp8xr11r gCg1Ru5 s w s w m f y h o w
N. Arizona - CIS - 120
DevelopingSpreadsheetApplications1CHAPTER3:DEVELOPINGSPREADSHEETAPPLICATIONSEnd user applications canvary greatly inscope and complexity.Some applications simply require the development ofasinglespreadsheet foronetime use byasingle user.Atthe
University of Toronto - MAT - 187
# w & yFB yCft # w & & %Y yCf g x # w & A 3 qBu@P ~%|8f% PYq fCfT3 A9z D ) D BYEdWW qu}ghr6iyguo (uTBBf B6(qCqept6}fc %Thtr x er ex k x ex xc v i x ixr c c v i e x v ir r ex o m r i x
University of Toronto - MAT - 187
fq bw # v ' g~&|~1v1py eAe1Qs75 g~|77py 1py eAe1Qs@ # v ' 85y B 2 B 9WCcUU q&1|fgqGi1xf&o g&$99e 9GgpApd1psG|eb $gsq w dq y dw k w dw wb u h w hwq b b u h y d w u hq q y dw o m yq h w d y dw q ywq
University of Toronto - MAT - 187
% C ' 9 8rH % C ' G ' D{ 8rHi} e s % C ' P Q Hw9}&IY DArD Y{v r8rH"Q PE~a R 4 RS 9{pS v&HmtxWBpHm&}u n&"99r 9Wniw8wqHTWri D"tex kx k h r k i u e ux e i i u q ux x k u t x u kx k
University of Toronto - MAT - 187
g !" 3 5 q q " b !" 3 ) ! ! rX6$%es#44A1r%6$%D6)46$u) A#hEbX6$%"4D6)1uA#r h@4D16$u 1X6$A8@ k # k k r ! 5 ! 3 ) ! H ) ! 5 d ! ) q !" 3 5 ! ! q $@D1y@i yFm m h 4zm tAX6$%g@ k # k 16$gta6Bg erg1hB u y & " ! " 3 5 ! ! q ! C
University of Toronto - MAT - 187
k ` w s y d p g wy dw d m f w p h fy fy o f fy # x ' I ~`qiV@d RBqd8@krg@)&ihus @uyhi~Hq31irkH&r11r gBg1x85 s h y d p g w f m f w p h fy y | # x ' i&iqdrugitdkuyhi~HqE1rf bgBg1RuA 95{ C 2 C @X
University of Toronto - MAT - 187
g % B ' 0 )Yyy tRt3I )Hy y tRt3Q g % B ' 0 PI~b S 4 SU E#rU wzovY9fqozHv )zEfEt EY)kyRysVYtq &vg m m j s m q w g w g q q w d s w m v u w m m w n u h s j m s w d ~ % " }f { | C
University of Toronto - MAT - 187
A E9rD33 # C ' Tz E9rD3h| # C ' ' # C ' P Q d Dw DW I | BBw Yzu r9rD33$Q PF}b R 4 AzR uDltxW"oDEl|t m$AAr AWmhw9wqDTWrp &$tdx jx j g q j p u d ux d p p u q ux x j t s x u jx j
Rutgers - RCI - 486
Lecture 21. EDA (EXPLORATORY DATA ANALYSIS by J.Tukey).Learn how to explore data and find valuable information, structures and relationships among variables. Find the structure of the majority of the data but also detect exceptional observations, r
Rose-Hulman - CSSE - 372
Communications Matrix ExampleCustome r Manager sContracto rProject Noteboo kSponsorVPEng.Team Member sCEOCFOProjectPlan Executive Summary Statusreports Statusmeeting minutes EarnedValue Timephased budget Resource utilization Issue/Pro