Multiple Short Term Infusion Homework # 5 PHA 5127

Size: px
Start display at page:

Download "Multiple Short Term Infusion Homework # 5 PHA 5127"

Transcription

1 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 mg os of this rug is givn as a short trm infusion ovr 30 minuts. What is th infusion rat? What will b th plasma concntration at th n of th infusion? 2 How long will it tak for th plasma concntration to fall to 5.0 mg/l? 3 If anothr infusion is start 5.5 hours aftr th first infusion was stopp, what will th plasma concntration b just bfor th scon infusion? 4* What will th pak lvl b at th n of th scon infusion? 5* If th osing intrval is kpt at 6 hours, what will th trough lvl b bfor th thir infusion is start? 6 Calculat th pak an trough plasma lvls at stay-stat for this osing rgimn. 7 How long will it tak to rach stay-stat lvls? How many infusions ar rquir to rach stay-stat conitions? 8 o you think a loaing os woul b bnficial in this xampl? Suggst a loaing os. (Aum that th avrag stay-stat lvl is wll within th thraputic winow for this rug. 9* h sir pak an trough lvls at stay-stat ar 2 mg/l an 3 mg/l rspctivly. How oftn must th rug b infus to achiv ths lvls? How shoul th os b ajust for this nw rgimn? Aum that th infusion tim is kpt at 30 minuts (0.5 hr. *ifficult but o-abl. isktt #2/Problms/Homwork/Multipl short trm.oc

2 h infusion rat is simply th amount of rug (or volum of solution of givn concntration aministr pr unit tim, 300mg k 0 0mg 30min / min Aftr a singl infusion, th pak lvl is givn by: Cl k (max ( whr Cl k 300 mg (0.40hr x0.5hr [ (0.40hr (28L(0.5hr 9.7 mg/l V 2 Concntrations at any tim point t' aftr stopping th infusion may b calculat by multiplying (max by -k t', whr t' is th amount of tim that has laps sinc stopping th infusion: (t' (max -k t' his is poibl for a rug following a on-compartmnt boy mol with st orr limination. his is analogous to th quation w us for a singl i.v. bolus injction, (t 0 -k t Only hr w ar trating (max as th (0 Exampl: Calculat 30 minuts (0.5 hr aftr stopping th infusion t k t' ( ' (max whr t' 0. 5 hr (9.7mg / L 7.95 mg/l (0.4hr x0.5hr isktt #2/Problms/Homwork/Multipl short trm.oc 2

3 o trmin how much tim is rquir for th concntration to rop to 5.0 mg/l, w must solv th (t' xprion abov for t': (t' (max -k t' whr (t' 5.0 mg/l (max ( t' t ' tak th natural logarithm of ach sli, k ( t' ln (max t' t' is thn givn by t' k ( t' ln (max 5.0mg / L ln 0.4hr 9.7mg / L 60 min.66hr x 00 min hr 3 Hr w n to calculat th trough lvl just bfor th 2 n os. h osing intrval is apparntly 6 hours: isktt #2/Problms/Homwork/Multipl short trm.oc 3

4 I hav fin t' now as th tim btwn th stop of th first infusion an th start of th 2 n infusion. his may b xpr in trms of th infusion tim an th osing intrval : t' - ( hr 5.5 hr h quation for calculating (min is (min (max k (9.7 mg / L.08 mg/l ( (0.40hr x5.5hr 4 his calculation is mor involv than th prvious ons. W bgin anothr infusion which will incras th concntration. Howvr, w o not bgin with 0. At th start of th 2 n infusion, th plasma lvl is.08 mg/l. w must consir this concntration (which will continu to cras by st orr limination an a it to th incras in provi by th 2 n infusion: (max (min 2 + ( k V u to th complxity of ths quations, w oftn limit our iscuion to concntrations following on os or at stay-stat. (max `(min 2 + ( k V isktt #2/Problms/Homwork/Multipl short trm.oc 4

5 (.08mg / L (0.4hr x0.5hr 300mg + [ (0.40hr (28L(0.5hr (0.40 hr x0.5hr ( mg/l 0.59 mg/l 5 If th osing intrval 6 an th infusion tim 0.5 o not chang, ( - ( hours transpir btwn th pak lvl (at th n of th infusion an th trough (just bfor anothr infusion bgins. his is tru for th st os, th 2 n os, an th nth os. (min (max -k ( - n (min n (max -k ( - (min (max -k ( - h trough lvl aftr th 2 n os is thn 2 (min 2 (max -k ( - (0.59 mg/l -(0.40hr -x(6-0.5hr.7 mg/l 6 At stay-stat, th (max is (max Cl ( ( this is list as "Pak (multipl os on your quation sht. W know this is a multipl osing xprion at stay-stat sinc th accumulation factor quation. r ( appars in th isktt #2/Problms/Homwork/Multipl short trm.oc 5

6 Rcall: h accumulation factor tlls you how much th plasma concntration incras at stay-stat compar to th first os. Compar th two quations: (max ( vs Cl (max Cl ( ( h stay-stat max for this osing rgimn is thn 300mg [ (max x (0.40hr (28L(0.5hr [ 0.68 mg/l (0.40hr (0.40hr (0.5hr (6hr h trough at stay-stat is (min (max ( (0.68mg / L.8 mg/l (0.40hr x5.5hr 7 It taks roughly 5-7 half-livs to rach stay-stat for a givn osing rgimn. h half-lif for this rug is t ln k 0.40hr / 2 hus, to rach stay-stat lvls, 5 x.73 hours 8.65 hours.73 hours ar rquir. Sinc th osing intrval is 6 hours, 0 st os 6 2 n os * r os 2 o ar rquir to rach stay-stat. hat is, w ar at stay-stat lvls just aftr th 2 n infusion. isktt #2/Problms/Homwork/Multipl short trm.oc 6

7 8 Sinc lvls ar not that much iffrnt than thos aftr th st os (an sinc th stay-stat is rach aftr th 2 n os, a loaing os may not b n hr. Of cours, this woul pn on th thraputic winow. If w n th plasma concntration to b 0.68 mg/l aftr th st infusion, w woul n to incras th amount of rug aministr slightly. h short-trm infusion quation for singl osing is (max ( Cl (0.68mg / L(0.4hr (0.40hr [ x28l(0.5hr x0.5hr 330 mg his is solv for (which will b th loaing os an (max is rplac by (max: L (max Cl ( 9 Hr w want (max 2 mg/l an (min 3 mg/l. th fluctuation factor F is thn (max 2mg / L F 4 (min 3mg / L W can trmin th osing intrval using this fluctuation factor: F ln k + his quation is list unr "calculat rcommn osing intrval" on your quation sht. It is similar to th xprion us in i.v. bolus quations xcpt for short-trm infusions, th infusion tim must b a on. If is still 0.5 hr, ln hr 4 hours 0.40hr isktt #2/Problms/Homwork/Multipl short trm.oc 7

8 Having trmin th osing intrval, w can calculat th os n to rach ths staystat lvls. W can o this by solving th (max xprion for os : (max k V ( ( which rarrangs to giv (max k V ( ( (2mg / L(0.40hr (28L(0.5hr[ (0.40hr x0.5hr [ (0.40hr 296 mg hus, giving th sam os (296 mg 300 mg mor frquntly rai th concntrations slightly* an th fluctuation is cras**. x4hr *300 mg vry 4 hours 6 x mg vry 24hours vs th initial osing rgimn which was 300 mg vry 6 hours 4 x 300 mg 200 mg vry 24 hours. Obviously, giving mor rug uring th sam tim intrval will incras plasma lvls. **If th osing intrval is cras, thr is l tim btwn o for limination to tak plac. hus, (max an (min will b closr togthr with l fluctuation. isktt #2/Problms/Homwork/Multipl short trm.oc 8

Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student

Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student 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.

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

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

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 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 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

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 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

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

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

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

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

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

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

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

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

High Energy Physics. Lecture 5 The Passage of Particles through Matter

High Energy Physics. Lecture 5 The Passage of Particles through Matter High Enrgy Physics Lctur 5 Th Passag of Particls through Mattr 1 Introduction In prvious lcturs w hav sn xampls of tracks lft by chargd particls in passing through mattr. Such tracks provid som of th most

More information

Introduction to Condensed Matter Physics

Introduction to Condensed Matter Physics Introduction to Condnsd Mattr Physics pcific hat M.P. Vaughan Ovrviw Ovrviw of spcific hat Hat capacity Dulong-Ptit Law Einstin modl Dby modl h Hat Capacity Hat capacity h hat capacity of a systm hld at

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat

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

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

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!

More information

Elements of Statistical Thermodynamics

Elements of Statistical Thermodynamics 24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,

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

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!

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

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

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

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

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

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

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

(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

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

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

nd the particular orthogonal trajectory from the family of orthogonal trajectories passing through point (0; 1).

nd the particular orthogonal trajectory from the family of orthogonal trajectories passing through point (0; 1). Eamn EDO. Givn th family of curvs y + C nd th particular orthogonal trajctory from th family of orthogonal trajctoris passing through point (0; ). Solution: In th rst plac, lt us calculat th di rntial

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

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

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

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th

More information

Derivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian

Derivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian Drivation of Elctron-Elctron Intraction Trms in th Multi-Elctron Hamiltonian Erica Smith Octobr 1, 010 1 Introduction Th Hamiltonian for a multi-lctron atom with n lctrons is drivd by Itoh (1965) by accounting

More information

64. A Conic Section from Five Elements.

64. A Conic Section from Five Elements. . onic Sction from Fiv Elmnts. To raw a conic sction of which fiv lmnts - points an tangnts - ar known. W consir th thr cass:. Fiv points ar known.. Four points an a tangnt lin ar known.. Thr points an

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

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

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

Continuous probability distributions

Continuous probability distributions Continuous probability distributions Many continuous probability distributions, including: Uniform Normal Gamma Eponntial Chi-Squard Lognormal Wibull EGR 5 Ch. 6 Uniform distribution Simplst charactrizd

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

On the Hamiltonian of a Multi-Electron Atom

On the Hamiltonian of a Multi-Electron Atom On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making

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

A Propagating Wave Packet Group Velocity Dispersion

A Propagating Wave Packet Group Velocity Dispersion Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to

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

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

A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES

A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES ADRIAAN DANIËL FOKKER (1887-197) A translation of: Ein invariantr Variationssatz für i Bwgung mhrrr lctrischr Massntilshn Z. Phys. 58, 386-393

More information

Mor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

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

SPH4U Electric Charges and Electric Fields Mr. LoRusso

SPH4U Electric Charges and Electric Fields Mr. LoRusso SPH4U lctric Chargs an lctric Fils Mr. LoRusso lctricity is th flow of lctric charg. Th Grks first obsrv lctrical forcs whn arly scintists rubb ambr with fur. Th notic thy coul attract small bits of straw

More information

Pipe flow friction, small vs. big pipes

Pipe flow friction, small vs. big pipes Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction

More information

University of Illinois at Chicago Department of Physics. Thermodynamics & Statistical Mechanics Qualifying Examination

University of Illinois at Chicago Department of Physics. Thermodynamics & Statistical Mechanics Qualifying Examination Univrsity of Illinois at Chicago Dpartmnt of hysics hrmodynamics & tatistical Mchanics Qualifying Eamination January 9, 009 9.00 am 1:00 pm Full crdit can b achivd from compltly corrct answrs to 4 qustions.

More information

INTRODUCTION TO AUTOMATIC CONTROLS INDEX LAPLACE TRANSFORMS

INTRODUCTION TO AUTOMATIC CONTROLS INDEX LAPLACE TRANSFORMS adjoint...6 block diagram...4 clod loop ytm... 5, 0 E()...6 (t)...6 rror tady tat tracking...6 tracking...6...6 gloary... 0 impul function...3 input...5 invr Laplac tranform, INTRODUCTION TO AUTOMATIC

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

Chapter 10. The singular integral Introducing S(n) and J(n)

Chapter 10. The singular integral Introducing S(n) and J(n) Chaptr Th singular intgral Our aim in this chaptr is to rplac th functions S (n) and J (n) by mor convnint xprssions; ths will b calld th singular sris S(n) and th singular intgral J(n). This will b don

More information

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17) MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl

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

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

Need to understand interaction of macroscopic measures

Need to understand interaction of macroscopic measures CE 322 Transportation Enginring Dr. Ahmd Abdl-Rahim, h. D.,.E. Nd to undrstand intraction o macroscopic masurs Spd vs Dnsity Flow vs Dnsity Spd vs Flow Equation 5.14 hlps gnraliz Thr ar svral dirnt orms

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

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

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

Statistical Thermodynamics: Sublimation of Solid Iodine

Statistical Thermodynamics: Sublimation of Solid Iodine c:374-7-ivap-statmch.docx mar7 Statistical Thrmodynamics: Sublimation of Solid Iodin Chm 374 For March 3, 7 Prof. Patrik Callis Purpos:. To rviw basic fundamntals idas of Statistical Mchanics as applid

More information

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds.

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds. 1 Th diagram shows th lctronic configurations of six diffrnt atoms. A B C D E F (a) You may us th Priodic Tabl on pag 2 to hlp you answr this qustion. Answr ach part by writing on of th lttrs A, B, C,

More information

Digital Signal Processing, Fall 2006

Digital Signal Processing, Fall 2006 Digital Signal Prossing, Fall 006 Ltur 7: Filtr Dsign Zhng-ua an Dpartmnt of Eltroni Systms Aalborg Univrsity, Dnmar t@om.aau. Cours at a glan MM Disrt-tim signals an systms Systm MM Fourir-omain rprsntation

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

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

Appendix 2.3 General Solutions for the Step Response of Third- and Fourth-Order Systems (with some unpleasant surprises!)

Appendix 2.3 General Solutions for the Step Response of Third- and Fourth-Order Systems (with some unpleasant surprises!) P.Stariè, E.Margan Appnix 2. A2..1 A2..2 Contnts: Appnix 2. Gnral Solutions for th Stp Rspons of Thir- an Fourth-Orr Systms (with som unplasant surpriss!) Thr is no such thing as instant xprinc! ( Oppnhimr

More information

Numerical methods, Mixed exercise 10

Numerical methods, Mixed exercise 10 Numrial mthos, Mi ris a f ( ) 6 f ( ) 6 6 6 a = 6, b = f ( ) So. 6 b n a n 6 7.67... 6.99....67... 6.68....99... 6.667....68... To.p., th valus ar =.68, =.99, =.68, =.67. f (.6).6 6.6... f (.6).6 6.6.7...

More information

PROBLEM SET Problem 1.

PROBLEM SET Problem 1. PROLEM SET 1 PROFESSOR PETER JOHNSTONE 1. Problm 1. 1.1. Th catgory Mat L. OK, I m not amiliar with th trminology o partially orr sts, so lt s go ovr that irst. Dinition 1.1. partial orr is a binary rlation

More information

SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY

SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY P. Poornima¹, Santosh Kumar Jha² 1 Associat Profssor, 2 Profssor, ECE Dpt., Sphoorthy Enginring Collg Tlangana, Hyraba (Inia) ABSTRACT This papr prsnts

More information

Title: Vibrational structure of electronic transition

Title: Vibrational structure of electronic transition Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum

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

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

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

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

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

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 = 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

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

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

MEMORIAL UNIVERSITY OF NEWFOUNDLAND

MEMORIAL UNIVERSITY OF NEWFOUNDLAND MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS Midtrm Examination Statistics 2500 001 Wintr 2003 Nam: Studnt No: St by Dr. H. Wang OFFICE USE ONLY Mark: Instructions: 1. Plas

More information

Introduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013

Introduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013 18.782 Introduction to Arithmtic Gomtry Fall 2013 Lctur #20 11/14/2013 20.1 Dgr thorm for morphisms of curvs Lt us rstat th thorm givn at th nd of th last lctur, which w will now prov. Thorm 20.1. Lt φ:

More information

Diploma Macro Paper 2

Diploma Macro Paper 2 Diploma Macro Papr 2 Montary Macroconomics Lctur 6 Aggrgat supply and putting AD and AS togthr Mark Hays 1 Exognous: M, G, T, i*, π Goods markt KX and IS (Y, C, I) Mony markt (LM) (i, Y) Labour markt (P,

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

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

the output is Thus, the output lags in phase by θ( ωo) radians Rewriting the above equation we get

the output is Thus, the output lags in phase by θ( ωo) radians Rewriting the above equation we get Th output y[ of a frquncy-sctiv LTI iscrt-tim systm with a frquncy rspons H ( xhibits som ay rativ to th input caus by th nonro phas rspons θ( ω arg{ H ( } of th systm For an input A cos( ωo n + φ, < n

More information

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.

More information

SER/BER in a Fading Channel

SER/BER in a Fading Channel SER/BER in a Fading Channl Major points for a fading channl: * SNR is a R.V. or R.P. * SER(BER) dpnds on th SNR conditional SER(BER). * Two prformanc masurs: outag probability and avrag SER(BER). * Ovrall,

More information

Section 3: Antiderivatives of Formulas

Section 3: Antiderivatives of Formulas Chptr Th Intgrl Appli Clculus 96 Sction : Antirivtivs of Formuls Now w cn put th is of rs n ntirivtivs togthr to gt wy of vluting finit intgrls tht is ct n oftn sy. To vlut finit intgrl f(t) t, w cn fin

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