Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student

Size: px
Start display at page:

Download "Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student"

Transcription

1 Cas Stuy Vancomycin Answrs Provi by Jffry Stark, Grauat Stunt h antibiotic Vancomycin is liminat almost ntirly by glomrular filtration. For a patint with normal rnal function, th half-lif is about 6 hours. h volum of istribution is 0.9 L/kg. For systmic infctions, vancomycin is givn intravnously an shows a pronounc istribution phas (with a uration of up to on hour aftr aministration. Vancomycin is usually givn via short trm infusions (1 0 with a osing intrval of it 6 or 12 hours. Although, lik many ot antibiotics, vancomycin has a wi taputic margin, th sir stay-stat concntrations ar 20 mg/l (1 post-infusion an 5-10 mg/l at th n of th osing intrval. A 43 yar ol patint (70 kg vlops a woun infction (foun to b Staphylococcus aurus. Sinc this bactria is rsistant to pnicillins, th patint is bgun on vancomycin. Answr th following qustions concrning osag rgimns for this patint. Qustions 1 If vancomycin is givn as an i.v. bolus, which quation will bst scrib th concntration-tim profil? Do w hav sufficint information (givn abov to apply quations of this form? 2 Calculat an appropriat loaing os for this patint using both th i.v. bolus an short-trm infusion quations. Compar th rsults. Ar thy significantly iffrnt? Explain. 3 Using a osing intrval of 12 s, trmin a osing rgimn for this patint. How many o ar rquir to rach stay-stat lvls? What ar th pak (clarly inicat what "pak" rfrs to an trough valus at stay-stat? Disktt #2/Cas Stuis/Vancomycin 1

2 4 Consir th fact that this patint's cratinin claranc is only 30 ml/min an th osing rgimn is 500 mg vry 12 s. What ar th pak an trough valus at stay-stat? h limination rat constant may b calculat using th mpirically riv quation: k ( x (Cratinin Cl , which has units of If th actual pak an trough valus ar 23 mg/l an 14 mg/l (giving 500 mg vry 12 s, what ar k an V for this patint? Suggst a nw osing rgimn (os an osing intrval to provi pak an trough valus of 25 mg/l an 7 mg/l rspctivly. hs qustions ar bas on thos foun in Cas Stuis 9-12 in th whit book. Disktt #2/Cas Stuis/Vancomycin 2

3 1 Sinc vancomycin shows a pronounc istribution phas, a multicompartmnt mol is n. h gnral i.v. bolus quation for a two-compartmnt is: Cp(t a -αt + b -βt W ar not givn th hybri constants α & β; rat w ar givn a singl ovrall limination rat constant k (actually t 1/2. for, w cannot us th two compartmnt mol quation for th following calculations. W must "skip ovr" th istribution (α phas an iscu only plasma lvls on or two hours aftr aministration of th rug. 2 For a singl i.v. bolus os, th concntration is givn by Cp 0 Dos V Sinc w want to obtain stay-stat lvls with on loaing os (LD, Cp LD V which rarrangs to giv LD Cp V Hr, w can us 20 mg/l as th Cp valu, sinc w want to achiv th pak lvl (staystat with a singl os. If w ignor any short-liv paks (α-phas an consir vancomycin has a wi taputic winow, w choos th "pak" lvl for 1 post-infusion. h V (givn as a prkilogram valu can b foun using th patint's wight, 0.9L V 70kg 63L kg Disktt #2/Cas Stuis/Vancomycin 3

4 h loaing os is thn: Cp("pak" 20 mg/l Cp(0 -k t' D V k t ' In th quation abov, t' is th 1 allow for istribution. his quation must b solv for D which will b th loaing os: (20mg / L LD t' (20mg / L(63L 1414mg ( (1 For a singl short trm infusion, th pak lvl is givn by Cp( pak k Dos (1 w is th infusion tim. rcall that w shoul fin "pak" lvls as thos that occur on or two hours aftr th infusion is stopp. hus, w n to multiply th abov quation b -k t', w t' is th post-infusion tim (1. Cp(pak is 20 mg/l (th sir stay-stat lvl an V is 63L as just trmin. k may b foun from th half-lif (t 1/2 6 s; k ln s t 6s 1 / 2 Aftr th abov quation is multipli by -k t', it may b solv for os (or loaing os to giv Cp( pak k LD (1 t ' Disktt #2/Cas Stuis/Vancomycin 4

5 (20mg / L(0.1155(63L(1 ( (1 ( (1 [ mg his valu calculat with th infusion quation is somwhat largr than that calculat using th i.v. bolus quation. For a patint with normal rnal function, a significant amount may b liminat uring th infusion an also in th 1 post-infusion tim (istribution phas. In ths calculations, th infusion os in roughly 6% gratr than th i.v. bolus. 3 Sinc is givn as 12 hours, w n only to trmin th maintnanc os. his is asily on by solving th Cp (max short trm infusion quation for D, Cp ( pak D (1 (1 k t ' Again, w fin th "pak" lvl to b that at 1 hour post-infusion an hav multipli th multipl os pak quation by -k t' (w t' - 1 to account for this. Solving this quation for D givs, Cp D ( pak k (1 (20mg / L( D [1 (1 t ' ( (1 (63L(1[1 ( ( (1 ( mg 1123 mg For 1123 mg vry 12 hours, th "pak" an trough valus ar: Cp (pak 20 mg/l It is unncary to calculat this valu; this valu an th "pak" quation wr us to trmin th os. Disktt #2/Cas Stuis/Vancomycin 5

6 Sinc th osing intrval is 12 hours an 2 hours pa bfor our "pak" lvl (on hour for infusion an on hour for istribution, th trough occurs 10 s aftr th pak. Cp (trough Cp (pak -k t (t 10 s (20 mg/l -( ( mg/l Rcall that 5 half-livs ar n to rach stay-stat lvls. Sinc t 1/2 6 hours, (5 (6s 30 hours ar rquir to rach th stay-stat. With a osing intrval of 12 hours, 3 o will hav bn aministr, 4 Sinc glomrular filtration is th main limination pathway for vancomycin, rnal function is an important factor in trmining an optimal osing rgimn. Rcall that cratinin claranc rflcts GFR (normally 125 ml/min. Lowr cratinin claranc mans that GFR is lowr than normal. In this situation, th amount of os shoul b lowr sinc it is not bing liminat as rapily. o calculat xpct pak an trough lvls for th nw osing rgimn (500 mg vry 12 hours, w will n th actual k. Using th formula givn (Cas Stuy 11 k ( Cl crat ( (30 ml/min Disktt #2/Cas Stuis/Vancomycin 6

7 Disktt #2/Cas Stuis/Vancomycin 7

8 W can now apply th pak an trough xprions us in th prvious qustion. Cp ( pak (63L( D (1 (1 V k (500mg[1 ( (1[1 (1 ( t' (12 (0.0293( mg/l Cp (trough Cp (pak -k t with t 10 hours (25.6 mg/l -( ( mg/l Not how much hig th trough valu is than was calculat prviously whn w aum normal rnal function. 5 With actual ata points w can asily trmin th k (by th slop an V (by plugging th valus into th Cp (pak quation for this patint. k -m (ln 23 ln (2 2 V may b foun using th Cp (pak quation, Disktt #2/Cas Stuis/Vancomycin 8

9 Cp ( pak D (1 (1 k which may b rarrang to giv t' V D ( pak k (1 (1 Cp t ' (500mg [1 (23mg / L( L ( (1 (1 [1 ( ( (1 (12 Hr Dtrmin a nw osing rgimn to giv pak an trough valus of 25 mg/l an 7 mg/l. h first stp is to trmin th osing intrval. h xprion for u th fluctuation factor, F Cp (pak/cp (trough. 25mg / L F mg / L Now, ln F k ln Actually for a short trm infusion, w n to a in th infusion tim for trmining, ln F k 26.7 Sinc aministring mication vry 26.7 s is impractical, w roun th valu to 24 Disktt #2/Cas Stuis/Vancomycin 9

10 h nw maintnanc os can b calculat using an th Cp (pak xprion solv for D, Cp D ( pak k (1 (25mg / L( [1 (1 t ' ( (1 (45.0L(1[1 ( mg his may b roun to D 800 mg hus, th nw osing rgimn is 800 mg vry 24 s. ( (1 (24 Disktt #2/Cas Stuis/Vancomycin 10

Multiple Short Term Infusion Homework # 5 PHA 5127

Multiple Short Term Infusion Homework # 5 PHA 5127 Multipl Short rm Infusion Homwork # 5 PHA 527 A rug is aministr as a short trm infusion. h avrag pharmacokintic paramtrs for this rug ar: k 0.40 hr - V 28 L his rug follows a on-compartmnt boy mol. A 300

More information

Case Study 4 PHA 5127 Aminoglycosides Answers provided by Jeffrey Stark Graduate Student

Case Study 4 PHA 5127 Aminoglycosides Answers provided by Jeffrey Stark Graduate Student Cas Stuy 4 PHA 527 Aminoglycosis Answrs provi by Jffry Stark Grauat Stunt Backgroun Gntamicin is us to trat a wi varity of infctions. Howvr, u to its toxicity, its us must b rstrict to th thrapy of lif-thratning

More information

3) Use the average steady-state equation to determine the dose. Note that only 100 mg tablets of aminophylline are available here.

3) Use the average steady-state equation to determine the dose. Note that only 100 mg tablets of aminophylline are available here. PHA 5127 Dsigning A Dosing Rgimn Answrs provi by Jry Stark Mr. JM is to b start on aminophyllin or th tratmnt o asthma. H is a non-smokr an wighs 60 kg. Dsign an oral osing rgimn or this patint such that

More information

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw

More information

PHA 5128 Answer CASE STUDY 3 Question #1: Model

PHA 5128 Answer CASE STUDY 3 Question #1: Model PHA 5128 Answr CASE STUDY 3 Spring 2008 Qustion #1: Aminoglycosids hav a triphasic disposition, but tobramycin concntration-tim profil hr is dscribd via a 2-compartmnt modl sinc th alpha phas could not

More information

PHA 5127 Answers Homework 2 Fall 2001

PHA 5127 Answers Homework 2 Fall 2001 PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring

More information

PHA Final Exam Fall 2007

PHA Final Exam Fall 2007 PHA 5127 Final Exam Fall 2007 On my honor, I hav nithr givn nor rcivd unauthorizd aid in doing this assignmnt. Nam Plas transfr th answrs onto th bubbl sht. Th qustion numbr rfrs to th numbr on th bubbl

More information

PHA Final Exam Fall 2001

PHA Final Exam Fall 2001 PHA 5127 Final Exam Fall 2001 On my honor, I hav nithr givn nor rcivd unauthorizd aid in doing this assignmnt. Nam Qustion/Points 1. /12 pts 2. /8 pts 3. /12 pts 4. /20 pts 5. /27 pts 6. /15 pts 7. /20

More information

Case Study VI Answers PHA 5127 Fall 2006

Case Study VI Answers PHA 5127 Fall 2006 Qustion. A ptint is givn 250 mg immit-rls thophyllin tblt (Tblt A). A wk ltr, th sm ptint is givn 250 mg sustin-rls thophyllin tblt (Tblt B). Th tblts follow on-comprtmntl mol n hv first-orr bsorption

More information

Case Study 1 PHA 5127 Fall 2006 Revised 9/19/06

Case Study 1 PHA 5127 Fall 2006 Revised 9/19/06 Cas Study Qustion. A 3 yar old, 5 kg patint was brougt in for surgry and was givn a /kg iv bolus injction of a muscl rlaxant. T plasma concntrations wr masurd post injction and notd in t tabl blow: Tim

More information

Unit 6: Solving Exponential Equations and More

Unit 6: Solving Exponential Equations and More Habrman MTH 111 Sction II: Eonntial and Logarithmic Functions Unit 6: Solving Eonntial Equations and Mor EXAMPLE: Solv th quation 10 100 for. Obtain an act solution. This quation is so asy to solv that

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

More information

Mathematics 1110H Calculus I: Limits, derivatives, and Integrals Trent University, Summer 2018 Solutions to the Actual Final Examination

Mathematics 1110H Calculus I: Limits, derivatives, and Integrals Trent University, Summer 2018 Solutions to the Actual Final Examination Mathmatics H Calculus I: Limits, rivativs, an Intgrals Trnt Univrsity, Summr 8 Solutions to th Actual Final Eamination Tim-spac: 9:-: in FPHL 7. Brought to you by Stfan B lan k. Instructions: Do parts

More information

MSLC Math 151 WI09 Exam 2 Review Solutions

MSLC Math 151 WI09 Exam 2 Review Solutions Eam Rviw Solutions. Comput th following rivativs using th iffrntiation ruls: a.) cot cot cot csc cot cos 5 cos 5 cos 5 cos 5 sin 5 5 b.) c.) sin( ) sin( ) y sin( ) ln( y) ln( ) ln( y) sin( ) ln( ) y y

More information

Prod.C [A] t. rate = = =

Prod.C [A] t. rate = = = Concntration Concntration Practic Problms: Kintics KEY CHEM 1B 1. Basd on th data and graph blow: Ract. A Prod. B Prod.C..25.. 5..149.11.5 1..16.144.72 15..83.167.84 2..68.182.91 25..57.193.96 3..5.2.1

More information

Where k is either given or determined from the data and c is an arbitrary constant.

Where k is either given or determined from the data and c is an arbitrary constant. Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

First order differential equation Linear equation; Method of integrating factors

First order differential equation Linear equation; Method of integrating factors First orr iffrntial quation Linar quation; Mtho of intgrating factors Exampl 1: Rwrit th lft han si as th rivativ of th prouct of y an som function by prouct rul irctly. Solving th first orr iffrntial

More information

y = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b)

y = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b) 4. y = y = + 5. Find th quation of th tangnt lin for th function y = ( + ) 3 whn = 0. solution: First not that whn = 0, y = (1 + 1) 3 = 8, so th lin gos through (0, 8) and thrfor its y-intrcpt is 8. y

More information

Note If the candidate believes that e x = 0 solves to x = 0 or gives an extra solution of x = 0, then withhold the final accuracy mark.

Note If the candidate believes that e x = 0 solves to x = 0 or gives an extra solution of x = 0, then withhold the final accuracy mark. . (a) Eithr y = or ( 0, ) (b) Whn =, y = ( 0 + ) = 0 = 0 ( + ) = 0 ( )( ) = 0 Eithr = (for possibly abov) or = A 3. Not If th candidat blivs that = 0 solvs to = 0 or givs an tra solution of = 0, thn withhold

More information

1973 AP Calculus AB: Section I

1973 AP Calculus AB: Section I 97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=

More information

AP Chemistry Multiple Choice Questions - Chapter a. Updated July 3, 2015 Boyceville High School, Mr. Hamm Page 1 of 7

AP Chemistry Multiple Choice Questions - Chapter a. Updated July 3, 2015 Boyceville High School, Mr. Hamm Page 1 of 7 18.2a Upat July 3, 2015 Boycvill High School, Mr. Hamm Pag 1 of 7 407 A solution is prpar y aing 100 ml of 1.0 M HC 2 H 3 O 2 (aq) to 100 ml of 1.0 M NaC 2 H 3 O 2 (aq). Th a solution is stirr an th ph

More information

Additional Math (4047) Paper 2 (100 marks) y x. 2 d. d d

Additional Math (4047) Paper 2 (100 marks) y x. 2 d. d d Aitional Math (07) Prpar b Mr Ang, Nov 07 Fin th valu of th constant k for which is a solution of th quation k. [7] Givn that, Givn that k, Thrfor, k Topic : Papr (00 marks) Tim : hours 0 mins Nam : Aitional

More information

Engineering 323 Beautiful HW #13 Page 1 of 6 Brown Problem 5-12

Engineering 323 Beautiful HW #13 Page 1 of 6 Brown Problem 5-12 Enginring Bautiful HW #1 Pag 1 of 6 5.1 Two componnts of a minicomputr hav th following joint pdf for thir usful liftims X and Y: = x(1+ x and y othrwis a. What is th probability that th liftim X of th

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1

More information

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c.

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c. MA56 utorial Solutions Qustion a Intgrating fator is ln p p in gnral, multipl b p So b ln p p sin his kin is all a Brnoulli quation -- st Sin w fin Y, Y Y, Y Y p Qustion Dfin v / hn our quation is v μ

More information

N1.1 Homework Answers

N1.1 Homework Answers Camrig Essntials Mathmatis Cor 8 N. Homwork Answrs N. Homwork Answrs a i 6 ii i 0 ii 3 2 Any pairs of numrs whih satisfy th alulation. For xampl a 4 = 3 3 6 3 = 3 4 6 2 2 8 2 3 3 2 8 5 5 20 30 4 a 5 a

More information

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula 7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting

More information

INTEGRATION BY PARTS

INTEGRATION BY PARTS Mathmatics Rvision Guids Intgration by Parts Pag of 7 MK HOME TUITION Mathmatics Rvision Guids Lvl: AS / A Lvl AQA : C Edcl: C OCR: C OCR MEI: C INTEGRATION BY PARTS Vrsion : Dat: --5 Eampls - 6 ar copyrightd

More information

Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Thomas Whitham Sith Form Pur Mathmatics Cor rvision gui Pag Algbra Moulus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv blow th ais in th ais. f () f () f

More information

a 1and x is any real number.

a 1and x is any real number. Calcls Nots Eponnts an Logarithms Eponntial Fnction: Has th form y a, whr a 0, a an is any ral nmbr. Graph y, Graph y ln y y Th Natral Bas (Elr s nmbr): An irrational nmbr, symboliz by th lttr, appars

More information

Brief Introduction to Statistical Mechanics

Brief Introduction to Statistical Mechanics Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.

More information

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator. Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r

More information

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall Staning Wav Intrfrnc btwn th incint & rflct wavs Staning wav A string with on n fix on a wall Incint: y, t) Y cos( t ) 1( Y 1 ( ) Y (St th incint wav s phas to b, i.., Y + ral & positiv.) Rflct: y, t)

More information

Sundials and Linear Algebra

Sundials and Linear Algebra Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.

More information

Prelim Examination 2011 / 2012 (Assessing Units 1 & 2) MATHEMATICS. Advanced Higher Grade. Time allowed - 2 hours

Prelim Examination 2011 / 2012 (Assessing Units 1 & 2) MATHEMATICS. Advanced Higher Grade. Time allowed - 2 hours Prlim Eamination / (Assssing Units & ) MATHEMATICS Advancd Highr Grad Tim allowd - hours Rad Carfull. Calculators ma b usd in this papr.. Candidats should answr all qustions. Full crdit will onl b givn

More information

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x ±# ( ). A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic

More information

Chapter 8: Electron Configurations and Periodicity

Chapter 8: Electron Configurations and Periodicity Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how

More information

4037 ADDITIONAL MATHEMATICS

4037 ADDITIONAL MATHEMATICS CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Lvl MARK SCHEME for th Octobr/Novmbr 0 sris 40 ADDITIONAL MATHEMATICS 40/ Papr, maimum raw mark 80 This mark schm is publishd as an aid to tachrs and candidats,

More information

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables.

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables. Chaptr Functions o Two Variabls Applid Calculus 61 Sction : Calculus o Functions o Two Variabls Now that ou hav som amiliarit with unctions o two variabls it s tim to start appling calculus to hlp us solv

More information

Applied Statistics II - Categorical Data Analysis Data analysis using Genstat - Exercise 2 Logistic regression

Applied Statistics II - Categorical Data Analysis Data analysis using Genstat - Exercise 2 Logistic regression Applid Statistics II - Catgorical Data Analysis Data analysis using Gnstat - Exrcis 2 Logistic rgrssion Analysis 2. Logistic rgrssion for a 2 x k tabl. Th tabl blow shows th numbr of aphids aliv and dad

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

Differentiation of Exponential Functions

Differentiation of Exponential Functions Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of

More information

Brief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008

Brief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008 Brif ots on th Frmi-Dirac and Bos-Einstin Distributions, Bos-Einstin Condnsats and Dgnrat Frmi Gass Last Updat: 8 th Dcmbr 8 (A)Basics of Statistical Thrmodynamics Th Gibbs Factor A systm is assumd to

More information

1 1 1 p q p q. 2ln x x. in simplest form. in simplest form in terms of x and h.

1 1 1 p q p q. 2ln x x. in simplest form. in simplest form in terms of x and h. NAME SUMMER ASSIGNMENT DUE SEPTEMBER 5 (FIRST DAY OF SCHOOL) AP CALC AB Dirctions: Answr all of th following qustions on a sparat sht of papr. All work must b shown. You will b tstd on this matrial somtim

More information

Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Thomas Whitham Sith Form Pur Mathmatics Unit C Algbra Trigonomtr Gomtr Calculus Vctor gomtr Pag Algbra Molus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv

More information

Einstein Equations for Tetrad Fields

Einstein Equations for Tetrad Fields Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for

More information

Quasi-Classical States of the Simple Harmonic Oscillator

Quasi-Classical States of the Simple Harmonic Oscillator Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats

More information

Problem Set 6 Solutions

Problem Set 6 Solutions 6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr

More information

(1) Then we could wave our hands over this and it would become:

(1) Then we could wave our hands over this and it would become: MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and

More information

Math 34A. Final Review

Math 34A. Final Review Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right

More information

Chemistry 342 Spring, The Hydrogen Atom.

Chemistry 342 Spring, The Hydrogen Atom. Th Hyrogn Ato. Th quation. Th first quation w want to sov is φ This quation is of faiiar for; rca that for th fr partic, w ha ψ x for which th soution is Sinc k ψ ψ(x) a cos kx a / k sin kx ± ix cos x

More information

Exiting from QE. Fumio Hayashi and Junko Koeda. for presentation at SF Fed Conference. March 28, 2014

Exiting from QE. Fumio Hayashi and Junko Koeda. for presentation at SF Fed Conference. March 28, 2014 Fumio Hayashi an Junko Koa Exiting from QE March 28, 214, 1 / 29 Exiting from QE Fumio Hayashi an Junko Koa for prsntation at SF F Confrnc March 28, 214 To gt start... h^ : Fumio Hayashi an Junko Koa Exiting

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

Grade 12 (MCV4UE) AP Calculus Page 1 of 5 Derivative of a Function & Differentiability

Grade 12 (MCV4UE) AP Calculus Page 1 of 5 Derivative of a Function & Differentiability Gra (MCV4UE) AP Calculus Pag of 5 Drivativ of a Function & Diffrntiabilit Th Drivativ at a Point f ( a h) f ( a) Rcall, lim provis th slop of h0 h th tangnt to th graph f ( at th point a, f ( a), an th

More information

Section 11.6: Directional Derivatives and the Gradient Vector

Section 11.6: Directional Derivatives and the Gradient Vector Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # -4 p. 799 # 4-5 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th

More information

2. Finite Impulse Response Filters (FIR)

2. Finite Impulse Response Filters (FIR) .. Mthos for FIR filtrs implmntation. Finit Impuls Rspons Filtrs (FIR. Th winow mtho.. Frquncy charactristic uniform sampling. 3. Maximum rror minimizing. 4. Last-squars rror minimizing.. Mthos for FIR

More information

( ) Differential Equations. Unit-7. Exact Differential Equations: M d x + N d y = 0. Verify the condition

( ) Differential Equations. Unit-7. Exact Differential Equations: M d x + N d y = 0. Verify the condition Diffrntial Equations Unit-7 Eat Diffrntial Equations: M d N d 0 Vrif th ondition M N Thn intgrat M d with rspt to as if wr onstants, thn intgrat th trms in N d whih do not ontain trms in and quat sum of

More information

Chapter 3 Exponential and Logarithmic Functions. Section a. In the exponential decay model A. Check Point Exercises

Chapter 3 Exponential and Logarithmic Functions. Section a. In the exponential decay model A. Check Point Exercises Chaptr Eponntial and Logarithmic Functions Sction. Chck Point Erciss. a. A 87. Sinc is yars aftr, whn t, A. b. A A 87 k() k 87 k 87 k 87 87 k.4 Thus, th growth function is A 87 87.4t.4t.4t A 87..4t 87.4t

More information

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon. PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also

More information

Calculus concepts derivatives

Calculus concepts derivatives All rasonabl fforts hav bn mad to mak sur th nots ar accurat. Th author cannot b hld rsponsibl for any damags arising from th us of ths nots in any fashion. Calculus concpts drivativs Concpts involving

More information

VTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS

VTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS Diffrntial Equations Unit-7 Eat Diffrntial Equations: M d N d 0 Vrif th ondition M N Thn intgrat M d with rspt to as if wr onstants, thn intgrat th trms in N d whih do not ontain trms in and quat sum of

More information

Chapter 1. Chapter 10. Chapter 2. Chapter 11. Chapter 3. Chapter 12. Chapter 4. Chapter 13. Chapter 5. Chapter 14. Chapter 6. Chapter 7.

Chapter 1. Chapter 10. Chapter 2. Chapter 11. Chapter 3. Chapter 12. Chapter 4. Chapter 13. Chapter 5. Chapter 14. Chapter 6. Chapter 7. Chaptr Binomial Epansion Chaptr 0 Furthr Probability Chaptr Limits and Drivativs Chaptr Discrt Random Variabls Chaptr Diffrntiation Chaptr Discrt Probability Distributions Chaptr Applications of Diffrntiation

More information

Finite Element Analysis

Finite Element Analysis Finit Elmnt Analysis L4 D Shap Functions, an Gauss Quaratur FEA Formulation Dr. Wiong Wu EGR 54 Finit Elmnt Analysis Roamap for Dvlopmnt of FE Strong form: govrning DE an BCs EGR 54 Finit Elmnt Analysis

More information

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation

More information

1997 AP Calculus AB: Section I, Part A

1997 AP Calculus AB: Section I, Part A 997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs x for which f (x) is a ral numbr.. (4x 6 x) dx=

More information

Chapter 6 Folding. Folding

Chapter 6 Folding. Folding Chaptr 6 Folding Wintr 1 Mokhtar Abolaz Folding Th folding transformation is usd to systmatically dtrmin th control circuits in DSP architctur whr multipl algorithm oprations ar tim-multiplxd to a singl

More information

Sec 2.3 Modeling with First Order Equations

Sec 2.3 Modeling with First Order Equations Sc.3 Modling with First Ordr Equations Mathmatical modls charactriz physical systms, oftn using diffrntial quations. Modl Construction: Translating physical situation into mathmatical trms. Clarly stat

More information

6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved.

6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved. 6.1 Intgration by Parts and Prsnt Valu Copyright Cngag Larning. All rights rsrvd. Warm-Up: Find f () 1. F() = ln(+1). F() = 3 3. F() =. F() = ln ( 1) 5. F() = 6. F() = - Objctivs, Day #1 Studnts will b

More information

CS553 Lecture Register Allocation I 3

CS553 Lecture Register Allocation I 3 Low-Lvl Issus Last ltur Intrproural analysis Toay Start low-lvl issus Rgistr alloation Latr Mor rgistr alloation Instrution shuling CS553 Ltur Rgistr Alloation I 2 Rgistr Alloation Prolm Assign an unoun

More information

PHYSICS 489/1489 LECTURE 7: QUANTUM ELECTRODYNAMICS

PHYSICS 489/1489 LECTURE 7: QUANTUM ELECTRODYNAMICS PHYSICS 489/489 LECTURE 7: QUANTUM ELECTRODYNAMICS REMINDER Problm st du today 700 in Box F TODAY: W invstigatd th Dirac quation it dscribs a rlativistic spin /2 particl implis th xistnc of antiparticl

More information

Solutions to Supplementary Problems

Solutions to Supplementary Problems Solution to Supplmntary Problm Chaptr 5 Solution 5. Failur of th tiff clay occur, hn th ffctiv prur at th bottom of th layr bcom ro. Initially Total ovrburn prur at X : = 9 5 + = 7 kn/m Por atr prur at

More information

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA NE APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA Mirca I CÎRNU Ph Dp o Mathmatics III Faculty o Applid Scincs Univrsity Polithnica o Bucharst Cirnumirca @yahoocom Abstract In a rcnt papr [] 5 th indinit intgrals

More information

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration

More information

MATH 319, WEEK 15: The Fundamental Matrix, Non-Homogeneous Systems of Differential Equations

MATH 319, WEEK 15: The Fundamental Matrix, Non-Homogeneous Systems of Differential Equations MATH 39, WEEK 5: Th Fundamntal Matrix, Non-Homognous Systms of Diffrntial Equations Fundamntal Matrics Considr th problm of dtrmining th particular solution for an nsmbl of initial conditions For instanc,

More information

The second condition says that a node α of the tree has exactly n children if the arity of its label is n.

The second condition says that a node α of the tree has exactly n children if the arity of its label is n. CS 6110 S14 Hanout 2 Proof of Conflunc 27 January 2014 In this supplmntary lctur w prov that th λ-calculus is conflunt. This is rsult is u to lonzo Church (1903 1995) an J. arkly Rossr (1907 1989) an is

More information

0 +1e Radionuclides - can spontaneously emit particles and radiation which can be expressed by a nuclear equation.

0 +1e Radionuclides - can spontaneously emit particles and radiation which can be expressed by a nuclear equation. Radioactivity Radionuclids - can spontanously mit particls and radiation which can b xprssd by a nuclar quation. Spontanous Emission: Mass and charg ar consrvd. 4 2α -β Alpha mission Bta mission 238 92U

More information

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin

More information

CS 491 G Combinatorial Optimization

CS 491 G Combinatorial Optimization CS 49 G Cobinatorial Optiization Lctur Nots Junhui Jia. Maiu Flow Probls Now lt us iscuss or tails on aiu low probls. Thor. A asibl low is aiu i an only i thr is no -augnting path. Proo: Lt P = A asibl

More information

3 2x. 3x 2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

3 2x. 3x 2.   Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Math B Intgration Rviw (Solutions) Do ths intgrals. Solutions ar postd at th wbsit blow. If you hav troubl with thm, sk hlp immdiatly! () 8 d () 5 d () d () sin d (5) d (6) cos d (7) d www.clas.ucsb.du/staff/vinc

More information

10. Limits involving infinity

10. Limits involving infinity . Limits involving infinity It is known from th it ruls for fundamntal arithmtic oprations (+,-,, ) that if two functions hav finit its at a (finit or infinit) point, that is, thy ar convrgnt, th it of

More information

1 Minimum Cut Problem

1 Minimum Cut Problem CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms

More information

Hydrogen Atom and One Electron Ions

Hydrogen Atom and One Electron Ions Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial

More information

SECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero.

SECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero. SETION 6. 57 6. Evaluation of Dfinit Intgrals Exampl 6.6 W hav usd dfinit intgrals to valuat contour intgrals. It may com as a surpris to larn that contour intgrals and rsidus can b usd to valuat crtain

More information

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0 unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr

More information

5. B To determine all the holes and asymptotes of the equation: y = bdc dced f gbd

5. B To determine all the holes and asymptotes of the equation: y = bdc dced f gbd 1. First you chck th domain of g x. For this function, x cannot qual zro. Thn w find th D domain of f g x D 3; D 3 0; x Q x x 1 3, x 0 2. Any cosin graph is going to b symmtric with th y-axis as long as

More information

Modeling with first order equations (Sect. 2.3).

Modeling with first order equations (Sect. 2.3). Moling with first orr quations (Sct. 2.3. Main xampl: Salt in a watr tank. Th xprimntal vic. Th main quations. Analysis of th mathmatical mol. Prictions for particular situations. Salt in a watr tank.

More information

Radiation Physics Laboratory - Complementary Exercise Set MeBiom 2016/2017

Radiation Physics Laboratory - Complementary Exercise Set MeBiom 2016/2017 Th following qustions ar to b answrd individually. Usful information such as tabls with dtctor charactristics and graphs with th proprtis of matrials ar availabl in th cours wb sit: http://www.lip.pt/~patricia/fisicadaradiacao.

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

Classical Magnetic Dipole

Classical Magnetic Dipole Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg

More information

10. The Discrete-Time Fourier Transform (DTFT)

10. The Discrete-Time Fourier Transform (DTFT) Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w

More information

Modern Physics. Unit 5: Schrödinger s Equation and the Hydrogen Atom Lecture 5.6: Energy Eigenvalues of Schrödinger s Equation for the Hydrogen Atom

Modern Physics. Unit 5: Schrödinger s Equation and the Hydrogen Atom Lecture 5.6: Energy Eigenvalues of Schrödinger s Equation for the Hydrogen Atom Mdrn Physics Unit 5: Schrödingr s Equatin and th Hydrgn Atm Lctur 5.6: Enrgy Eignvalus f Schrödingr s Equatin fr th Hydrgn Atm Rn Rifnbrgr Prfssr f Physics Purdu Univrsity 1 Th allwd nrgis E cm frm th

More information

Indeterminate Forms and L Hôpital s Rule. Indeterminate Forms

Indeterminate Forms and L Hôpital s Rule. Indeterminate Forms SECTION 87 Intrminat Forms an L Hôpital s Rul 567 Sction 87 Intrminat Forms an L Hôpital s Rul Rcogniz its that prouc intrminat forms Apply L Hôpital s Rul to valuat a it Intrminat Forms Rcall from Chaptrs

More information

Mathematics. Complex Number rectangular form. Quadratic equation. Quadratic equation. Complex number Functions: sinusoids. Differentiation Integration

Mathematics. Complex Number rectangular form. Quadratic equation. Quadratic equation. Complex number Functions: sinusoids. Differentiation Integration Mathmatics Compl numbr Functions: sinusoids Sin function, cosin function Diffrntiation Intgration Quadratic quation Quadratic quations: a b c 0 Solution: b b 4ac a Eampl: 1 0 a= b=- c=1 4 1 1or 1 1 Quadratic

More information

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005 PHYS1444-,Fall 5, Trm Exam #1, Oct., 1, 5 Nam: Kys 1. circular ring of charg of raius an a total charg Q lis in th x-y plan with its cntr at th origin. small positiv tst charg q is plac at th origin. What

More information

Homework #3. 1 x. dx. It therefore follows that a sum of the

Homework #3. 1 x. dx. It therefore follows that a sum of the Danil Cannon CS 62 / Luan March 5, 2009 Homwork # 1. Th natural logarithm is dfind by ln n = n 1 dx. It thrfor follows that a sum of th 1 x sam addnd ovr th sam intrval should b both asymptotically uppr-

More information

EXST Regression Techniques Page 1

EXST Regression Techniques Page 1 EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy

More information

Kernels. ffl A kernel K is a function of two objects, for example, two sentence/tree pairs (x1; y1) and (x2; y2)

Kernels. ffl A kernel K is a function of two objects, for example, two sentence/tree pairs (x1; y1) and (x2; y2) Krnls krnl K is a function of two ojcts, for xampl, two sntnc/tr pairs (x1; y1) an (x2; y2) K((x1; y1); (x2; y2)) Intuition: K((x1; y1); (x2; y2)) is a masur of th similarity (x1; y1) twn (x2; y2) an ormally:

More information