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mat1000_hw8
Course: MAT 1000, Fall 2009School: University of Toronto
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Word Count: 716
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University of Toronto - MAT - 1000
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University of Toronto - MAT - 1000
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University of Toronto - MAT - 1000
U 0 U " 0 S T R Q P( )& $G IE FG HE F D C 8 B$@8 75 A9 6& 4 320 1( )' &$ % # "! ( 8f 98j&dY 9dnj $ $ d9( jY($~ ddk hj8 j t88 ~$i 4j
Washington - WEEK - 492
Drug Regimen ReviewINTRODUCTIONA Systematic Approach toREVISITING D R U G REGIMEN REVIEW PART IIIThis article is the third in a threepart series exploring drug regimen review (DRR) over the last 30 years. In the first part, we explored the ear
University of Toronto - MAT - 1060
09h3#ts@!)9'uC'q'!tc2@r2yS#h!#n%q'%9! A A h & & 7 4 &$ 7 7 A A & D A A A 3 0 & A$ g &$ ( 7 & m`W d sikq& W g d & $ A & A ( & & v A v & 1 7 3 A !)'%t!t@)2'!tt'sc%#!xv!gW ! ( D dh 2xs D 3 " e
Washington - WEEK - 492
Thomas R. Clark Joseph Gruber Mark SeyTHE CONSULTANT PHARMACIST MARCH 2003 VOL. 18, NO. 3Nearly three decades after implementation of the federal drug regimen review mandate, DRR remains at the heart of long-term care pharmacy practice. Here, wel
Washington - WEEK - 492
Art or Science?Although it has been a core component of consultant pharmacy practice for more than 30 years, drug regimen review (DRR) continues to evolve to accommodate many new additions to the increasingly complex medication armamentarium, and th
Washington - WEEK - 492
Washington - WEEK - 492
Washington - WEEK - 492
Washington - WEEK - 492
University of Toronto - MAT - 1060
Noncharacteristic boundary conditions In the book, the boundary is locally straightened and the noncharacteristic boundary condition is given in (35) on page 105. However, the noncharacteristic boundary condition can also be given for the unattened b
University of Toronto - MAT - 1060
Homework due Monday December 6, in my mailbox by 5pm.1. Integral Solutions Consider the Riemann problem given by (53) on page 154. Formula (56) is alleged to be an integral solution. Prove this is true. 2. the Lax-Oleinik formula Formulas (54) and (
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDE Problem Set 5 Friday March 21, 2008 due: Tuesday April 1, 2008 1. We want to solve the Poisson equation u = f in the unit square = [0, 1]2 , with u = 0 on the boundaries of the square. It is easy to see that th
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDE Problem Set 1 Thursday January 17, 2008 due: Tuesday January 29 To save gures you can use the command print -dps gure1.ps. 1. Given the heat equation ut = uxx on [0, L] with linear homogeneous boundary condition
University of Toronto - MAT - 1062
1Ownership 2General classication u x, y, . . . F x, y, . .
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary PughFebruary 7, 20081OwnershipThese notes are primarily those of Rob Almgren who taught an analogous course in 2003. Whatever you learn of value from them is due to him. All mistakes and sources of
University of Toronto - MAT - 1062
Homework problems: September 25, 20071. Let u(x, y, t) be a solution of the heat equation ut = 2 (uxx + uyy ). Let U be the function dened by U (X (x, y ), Y (x, y ), t) = u(x, y, t) (a) If X (x, y ) = x + 3 and Y (x, y ) = y 1, what PDE does U (X,
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDE Problem Set 3 Tuesday, February 12, 2008 due: Thursday, February 28 in class 1. In this problem, you will do the von Neumann stability analysis of a variety of schemes on hZ. For each scheme, nd whether or not t
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDE Problem Set 2 Tuesday, January 29, 2008 due: Thursday February 7 in class 1. In the January 29 lecture notes, I gave a table which showed how the sup-norm error decreased as h decreased. Present this table where
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh April 8, 2008Burgers EquationIts clear how to use spectral methods for any linear constant coecient partial dierential equation on a periodic domain. We now turn to nonlinear equations. As a sample
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary PughJanuary 29, 20081How to use truncation errors to test your codeLet's step back and look at what we've done in proving convergence for the explicit euler scheme for the heat equation ut = Duxx .
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh April 3, 2008Nonlinear EquationsFrom the above, its clear how to use spectral methods for any linear constant coecient partial dierential equation on a periodic domain. We now turn to nonlinear equa
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh March 20, 2008OwnershipThese notes are built upon those of Rob Almgren who taught an analogous course in 2003. Whatever you learn of value from them is due to him. All mistakes and sources of confus
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh February 28, 20081Phase errorAnother way to understand the error in the discrete computation is to consider solutions of the form u(x, t) = U (t) exp(ix), for R. The true solution has U (t) = e
University of Toronto - MAT - 1062
1Ownership 2Convergence, Consistency, and Stability dU = f U(t), t dt t [0, T ]U(0) = U0. U(t) RN f RN [
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh March 27, 20081Computing DerivativesNow, suppose that we want to compute approximate values vj u (xj ) of the derivative at the grid points xj , given only the values uj of the function at the g
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh April 1, 2008For more information on spectral and pseudospectral methods, have a look at Spectral Methods: Fundamentals in Single Domains by C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zhang.
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh February 14, 20081OwnershipThese notes are built upon those of Rob Almgren who taught an analogous course in 2003. Whatever you learn of value from them is due to him. All mistakes and sources of
University of Toronto - MAT - 1062
1Ownership 2Boundary Conditions ut = D uxx u(x, t) u0(x) t = 0 X x X X x X .u(x, 0) = u0(x),
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh March 13, 20081Overview of Projection methodsThroughout this course, we have discussed Fourier modes in the context of stability. Generally, we assume that a PDE or a discrete scheme has a soluti
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh March 6, 2008OwnershipThese notes are built upon those of Rob Almgren who taught an analogous course in 2003. Whatever you learn of value from them is due to him. All mistakes and sources of confusi
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh February 26, 20081Modied equationsThe modied equation or eective equation is a way to understand qualitatively the eect of discretization errors on the behaviour of the solution. The idea is that
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDEMary Pugh March 18, 20081Convergence of the Approximate SolutionsV = {v (x) real-valued functions on R1 0We recall the weak problem: We have the Hilbert space1 0v (x)2 dx < ,v (x)2 dx < , v (0) = 0
University of Toronto - MAT - 1062
University of TorontoDepartment of Mathematics Mat1062H Computational Methods for PDEs Winter 2008Instructor: Web page: Lecture: Oce Hours: Mary Pugh mpugh@math.utoronto.ca http:/www.math.utoronto.ca/mpugh/Teaching/Mat1062/mat1062.html Tu, 11:10am1
University of Toronto - MAT - 1062
Mat1062: Computational Methods for PDE Problem Set 2 Thursday, January 29, 2008 due: Thursday February 12 in class 1. Revisit the local truncation error analysis for the Forward Euler method. For general , we found that that the local truncation erro
University of Toronto - APM - 236
ee S RV eV c G)b`beD c c e S P U R 'bWbesd&G$TS`xn ti r q w g v v r g r p)w lDwDlpj w w r w g v gi w i g i g t g v i g r m g u r w i r n j vi w r w g} 4l74lhpl2p)4pzvplDwIh2vwd44l&DdGl~wIu wthGd{llzwylxwl@)Dwhopv&)ts
University of Toronto - APM - 236
~ mk fv b`{bj 96 i u 9 i kg 9|ftocj 9 i kg 69|ftocj 9 i kg 9|ftocj 9 i kg 9|ftocj 9 i kg t9|ftocj Q i kg 9|ftocj ~ i ~ kg 9|ftocj 9 i kg 9|ftocj p V uYG % Hou % t f}
University of Toronto - APM - 236
University of Toronto - APM - 236
ee S RV eV c G)b`beD c c e S P U R 'bWbesd&G$TS`xn ti r q w g v v r g r p)w lDwDlpj w w r w g v gi w i g i g t g v i g r m g u r w i r n j vi w r w g} 4l74lhpl2p)4pzvplDwIh2vwd44l&DdGl~wIu wthGd{llzwylxwl@)Dwhopv&)ts
University of Toronto - APM - 236
University of Toronto - APM - 236
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
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