ESCI 485 Air/sea Interaction Lesson 6 Wind Driven Circulation Dr. DeCaria
|
|
|
- Valentine Morris
- 5 years ago
- Views:
Transcription
1 ESCI 485 Air/sea Iteractio Lesso 6 Wid Drive Circulatio Dr. DeCaria Refereces: Itroductor Damical Oceaograp, Pod ad Pickard Priciples of Ocea Psics, Apel STOEL S SOLUTION FOR WESTWARD INTENSIFICATION Te surface circulatio i a ocea basi is drive b te wid. Caracteristic of tese circulatios (or gres) is tat te are aticcloic. A strikig feature of tese gres i te strog poleward currets o te wester side of te ocea basis (off of te east coast of te cotiets). To tr to uderstad te cause of tis westward itesificatio, Stommel i 1948 proposed te followig. ο Use te sallow water equatios of motio for a fluid of costat dept H. (Tis presumes tat te fluid is barotropic). ο Let f = f + β ο Iclude frictio supplied at te bottom of te fluid. Te frictio is assumed to be liear wit speed. u η + V u = g + ( f + β ) v γ u + t ρh v η + V v = g ( f + β ) u + γ v + t ρh Form a vorticit equatio b cross-differetiatig tese equatios Te equatio formed i tis wa is ζ v u = t t t. () ζ 1 == V ζ β v γ ζ + t ρh Tis vorticit equatio sas tat te relative vorticit of a fluid parcel ca be caged via tree was: ο ovig te parcel ort or sout (te beta effect). Sice absolute vorticit is coserved, movig te parcel ort toward iger plaetar vorticit will decrease te relative vorticit. (1)
2 ο Frictio Te frictio tries to move te vorticit toward zero. If te vorticit is positive, frictio will decrease it. If te vorticit is egative, frictio will icrease it. ο Wid stress Te curl of te wid stress will add vorticit if te curl is positive, or decrease vorticit if te curl is egative. If te flow is o-diverget te velocit compoets ca be give i terms of a stream fuctio,, suc tat u = v = ζ =. Tis lets us write te vorticit equatio as 1 = V ( ) β γ +. (3) t ρh Stommel looked at te stead state solutio to Eq. (3), so tat te local time derivative could be igored. He also assumed te advectio term was egligible i te total derivative. Tis simplified te equatio to β 1 + =. (4) γ γρ H Stommel assumed a simplistic form for te wid stress, give as π = cos = so tat π π = si. Te equatio for te stream fuctio is te β π + = γ γρ H π si. (5) Stommel ivestigated te solutio of Eq. (5) for a rectagular ocea of costat dept for te case of a rotatig Eart for two cases: costat Coriolis parameter
3 (te f-plae approimatio; β = ); Coriolis parameter cagig wit latitude at a costat rate (te β -plae approimatio). O te f-plae, te solutio for te streamfuctio looks like ο Tere is o westward itesificatio i tis case. O te β -plae te solutio for te streamfuctio looks like Te cage i Coriolis parameter wit latitude (β) is te ke to westward itesificatio. 3
4 UNK S SOLUTION FOR WESTWARD INTENSIFICATION Stommel s solutio, toug correctl allowig a wester boudar curret, was ver simplistic. ο Stommel assumed a barotropic ocea wit frictio supplied at te bottom. I te real ocea most of te curret is i te upper laers, ad tere is ver little flow at te bottom. uk (195) used te more complete equatios of motio ad a more realistic frictio term due to turbulet flues (Reolds stresses). Tese equatios are Du Dt Dv Dt 1 p = + ρ 1 p = ρ ( f + β ) ( f + β ) v + A u + A 1 u r 1 v r (6) were r ad r are te vertical Reolds stresses. A vorticit equatio is agai formed b cross differetiatio, ad gives ζ 1 = V ζ β v + A ς r t ( ) (7) Like Stommel, uk was iterested i te stead state solutio. He also assumed tat te advective terms were egligible. Terefore is equatio becomes. = β v + A 1 ς Itegratig troug te dept of te ocea ields β Usig te streamfuctio we get β ( ) 1 vdz + A ς dz ( ) =. ρ dz + A 1 dz ρ Defiig te mass trasport stream fuctio as we ed up wit a fourt-order equatio r. ( ) = ρ dz (8). 4
5 5 β = A 4. (9) If uk s equatio is used wit te simplified wid stress cos = = π te te fial equatio becomes = A π π β si 4. (1) If tis equatio is solved o te f-plae (β = ) te te results (sow below) are similar to tat of Stommel, sowig a smmetric gre.
6 O te β-plae te solutio for te streamfuctio is sligtl differet from Stommel s, but still sows te westward itesificatio of te boudar curret. uk actuall used observed wid stresses istead of te simplified wid stress, but is results were ver similar to tose above. He also solved for te case of a triagular ocea basi, wic more realisticall represets te Atlatic Ocea. uk s results sow a iterestig feature i tat tere is a soutward flowig coutercurret just to te east of te wester boudar curret. Tis coutercurret is ideed a real feature tat is observed east of te Gulf Stream. Te idealized currets for a rectagular ocea basi are sow below. Te major features of te circulatio are: 6
7 A ccloicall rotatig subpolar gre A aticcloicall rotatig subtropical gre Two westward flowig equatorial currets smmetric wit te ITCZ (ot te Equator). A eastward flowig equatorial couter curret betwee te equatorial currets. Strog, wester boudar currets i te subtropical ad subpolar gres, cotrasted wit weaker retur flows east of te gre ceters. 7
Salmon: Lectures on partial differential equations. 3. First-order linear equations as the limiting case of second-order equations
3. First-order liear equatios as the limitig case of secod-order equatios We cosider the advectio-diffusio equatio (1) v = 2 o a bouded domai, with boudary coditios of prescribed. The coefficiets ( ) (2)
d y f f dy Numerical Solution of Ordinary Differential Equations Consider the 1 st order ordinary differential equation (ODE) . dx
umerical Solutio o Ordiar Dieretial Equatios Cosider te st order ordiar dieretial equatio ODE d. d Te iitial coditio ca be tae as. Te we could use a Talor series about ad obtai te complete solutio or......!!!
The General Circulation of the Oceans
The General Circulation of the Oceans In previous classes we discussed local balances (Inertial otion, Ekman Transport, Geostrophic Flows, etc.), but can we eplain the large-scale general circulation of
Atomic Physics 4. Name: Date: 1. The de Broglie wavelength associated with a car moving with a speed of 20 m s 1 is of the order of. A m.
Name: Date: Atomic Pysics 4 1. Te de Broglie wavelegt associated wit a car movig wit a speed of 0 m s 1 is of te order of A. 10 38 m. B. 10 4 m. C. 10 4 m. D. 10 38 m.. Te diagram below sows tree eergy
2. Temperature, Pressure, Wind, and Minor Constituents.
2. Temperature, Pressure, Wind, and Minor Constituents. 2. Distributions of temperature, pressure and wind. Close examination of Figs..7-.0 of MS reveals te following features tat cry out for explanation:
NUMERICAL DIFFERENTIAL 1
NUMERICAL DIFFERENTIAL Ruge-Kutta Metods Ruge-Kutta metods are ver popular ecause o teir good eiciec; ad are used i most computer programs or dieretial equatios. Te are sigle-step metods as te Euler metods.
LIMITS AND DERIVATIVES
Capter LIMITS AND DERIVATIVES. Overview.. Limits of a fuctio Let f be a fuctio defied i a domai wic we take to be a iterval, say, I. We sall study te cocept of it of f at a poit a i I. We say f ( ) is
An Insight into Differentiation and Integration
Differetiatio A Isigt ito Differetiatio a Itegratio Differetiatio is basically a task to fi out ow oe variable is cagig i relatio to aoter variable, te latter is usually take as a cause of te cage. For
LIMITS AND DERIVATIVES NCERT
. Overview.. Limits of a fuctio Let f be a fuctio defied i a domai wic we take to be a iterval, say, I. We sall study te cocept of it of f at a poit a i I. We say f ( ) is te epected value of f at a give
Notes on the GSW function gsw_geostrophic_velocity (geo_strf,long,lat,p)
Notes o gsw_geostrophic_velocity Notes o the GSW fuctio gsw_geostrophic_velocity (geo_strf,log,lat,p) Notes made 7 th October 2, ad updated 8 th April 2. This fuctio gsw_geostrophic_velocity(geo_strf,log,lat,p)
Differentiation Techniques 1: Power, Constant Multiple, Sum and Difference Rules
Differetiatio Teciques : Power, Costat Multiple, Sum ad Differece Rules 97 Differetiatio Teciques : Power, Costat Multiple, Sum ad Differece Rules Model : Fidig te Equatio of f '() from a Grap of f ()
The Vorticity Equation in a Rotating Stratified Fluid
Capter 7 Te Vorticity Equation in a Rotating Stratified Fluid Te vorticity equation for a rotating, stratified, viscous fluid Te vorticity equation in one form or anoter and its interpretation provide
Partial Differential Equations
EE 84 Matematical Metods i Egieerig Partial Differetial Eqatios Followig are some classical partial differetial eqatios were is assmed to be a fctio of two or more variables t (time) ad y (spatial coordiates).
ESCI 485 Air/sea Interaction Lesson 5 Oceanic Boundary Layer
ESCI 485 Air/sea Interaction Lesson 5 Oceanic Boundar Laer References: Descriptive Phsical Oceanograph, Pickard and Emer Introductor Dnamical Oceanograph, Pond and Pickard Principles of Ocean Phsics, Apel
DEGENERACY AND ALL THAT
DEGENERACY AND ALL THAT Te Nature of Termodyamics, Statistical Mecaics ad Classical Mecaics Termodyamics Te study of te equilibrium bulk properties of matter witi te cotext of four laws or facts of experiece
The Advection-Diffusion equation!
ttp://www.d.edu/~gtryggva/cf-course/! Te Advectio-iffusio equatio! Grétar Tryggvaso! Sprig 3! Navier-Stokes equatios! Summary! u t + u u x + v u y = P ρ x + µ u + u ρ y Hyperbolic part! u x + v y = Elliptic
is proportional to the amount by which this velocity is not parallel to the direction of the thermal wind shear v z = v v, (V_rotate_03)
97 Whe globally itegrated over complete desity surfaces, the total trasport due to these o- liear processes ca be calculated. I gree is the mea diaeutral trasport from the ill- defied ature of eutral surfaces,
A New Hybrid in the Nonlinear Part of Adomian Decomposition Method for Initial Value Problem of Ordinary Differential Equation
Joural of Matematics Researc; Vol No ; ISSN - E-ISSN - Publised b Caadia Ceter of Sciece ad Educatio A New Hbrid i te Noliear Part of Adomia Decompositio Metod for Iitial Value Problem of Ordiar Differetial
Problem Cosider the curve give parametrically as x = si t ad y = + cos t for» t» ß: (a) Describe the path this traverses: Where does it start (whe t =
Mathematics Summer Wilso Fial Exam August 8, ANSWERS Problem 1 (a) Fid the solutio to y +x y = e x x that satisfies y() = 5 : This is already i the form we used for a first order liear differetial equatio,
A Simplified General Circulation Model for a Baroclinic Ocean with Topography. Part I: Theory, Waves, and Wind-Driven Circulations
DECEMBER 3 OLBERS AND EDEN 719 A Simplified Geeral Circulatio Model for a Barocliic Ocea wit Topograpy. Part I: Teory, Waves, ad Wid-Drive Circulatios DIRK OLBERS Alfred Wegeer Istitute for Polar ad Marie
The Verlet Algorithm for Molecular Dynamics Simulations
Cemistry 380.37 Fall 2015 Dr. Jean M. Standard November 9, 2015 Te Verlet Algoritm for Molecular Dynamics Simulations Equations of motion For a many-body system consisting of N particles, Newton's classical
2.3 Warmup. Graph the derivative of the following functions. Where necessary, approximate the derivative.
. Warmup Grap te erivative of te followig fuctios. Were ecessar, approimate te erivative. Differetiabilit Must a fuctio ave a erivative at eac poit were te fuctio is efie? Or If f a is efie, must f ( a)
Taylor expansion: Show that the TE of f(x)= sin(x) around. sin(x) = x - + 3! 5! L 7 & 8: MHD/ZAH
Taylor epasio: Let ƒ() be a ifiitely differetiable real fuctio. A ay poit i the eighbourhood of 0, the fuctio ƒ() ca be represeted by a power series of the followig form: X 0 f(a) f() f() ( ) f( ) ( )
3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,
![3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,](/thumbs/82/85448051.jpg "3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,")
3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [
L 5 & 6: RelHydro/Basel. f(x)= ( ) f( ) ( ) ( ) ( ) n! 1! 2! 3! If the TE of f(x)= sin(x) around x 0 is: sin(x) = x - 3! 5!
aylor epasio: Let ƒ() be a ifiitely differetiable real fuctio. At ay poit i the eighbourhood of =0, the fuctio ca be represeted as a power series of the followig form: X 0 f(a) f() ƒ() f()= ( ) f( ) (
ANALYSIS OF THERMOELASTIC STRESSES IN LAYERED PLATES
6t Iteratioal DAAAM Baltic Coferece "INDUSTRIAL ENGINEERING" 4-6 April 8, Talli, Estoia ANALYSIS OF THERMOELASTIC STRESSES IN LAYERED PLATES Kõo, J. & Valgur, J. Abstract: Tis paper deals wit termoelastic
PHYS 321 Solutions to Practice Final (December 2002).
PHYS Solutios to Practice Fial (December ) Two masses, m ad m are coected by a sprig of costat k, leadig to the potetial V( r) = k( r ) r a) What is the Lagragia for this system? (Assume -dimesioal motio)
Ocean dynamics: the wind-driven circulation
Ocean dynamics: the wind-driven circulation Weston Anderson March 13, 2017 Contents 1 Introduction 1 2 The wind driven circulation (Ekman Transport) 3 3 Sverdrup flow 5 4 Western boundary currents (western
4 Conditional Distribution Estimation
4 Coditioal Distributio Estimatio 4. Estimators Te coditioal distributio (CDF) of y i give X i = x is F (y j x) = P (y i y j X i = x) = E ( (y i y) j X i = x) : Tis is te coditioal mea of te radom variable
An Inertial Model of the Interaction of Ekman Layers and Planetary Islands
1398 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 43 A Iertial Model of the Iteractio of Ekma Layers ad Plaetary Islads JOSEPH PEDLOSKY Departmet of Physical Oceaography, Woods Hole
On the convergence, consistence and stability of a standard finite difference scheme
AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH 2, Sciece Huβ, ttp://www.sciub.org/ajsir ISSN: 253-649X, doi:.525/ajsir.2.2.2.74.78 O te covergece, cosistece ad stabilit of a stadard fiite differece
Fourier Techniques lecture by Håkon Hoel
CSC Nada DN55 Sprig - Differetial Equatios II JOp p (7) Fourier Teciques lecture by Håo Hoel Fourier series... Applicatios to liear PDE... 3 Numerical metods...3 3. Vo Neuma aalysis...4 3. Spectral metods...6
The wind-driven models of Stommel and Munk employed a linearization involving a small parameter, the Rossby number, which we need to reconsider.
Equatorial twists to mid-latitude dnamics As we saw or Stommel s or Munk s wind-driven gres and or Sverdrup s balance, there was no particular problem with the equator. In act, Stommel solved his gre or
x x x Using a second Taylor polynomial with remainder, find the best constant C so that for x 0,
Math Activity 9( Due with Fial Eam) Usig first ad secod Taylor polyomials with remaider, show that for, 8 Usig a secod Taylor polyomial with remaider, fid the best costat C so that for, C 9 The th Derivative
7.8 Transient motion in a two-layered sea
1 Lecture Notes on Fluid Dynamics (1.63J/2.21J by Ciang C. Mei, 2002 7-8-2layer.tex Refs: Csandy: Circulation in te Coastal Ocean Cusman-Rosin, Intro to Geopysical Fluid Dynamics 7.8 Transient motion in
Most text will write ordinary derivatives using either Leibniz notation 2 3. y + 5y= e and y y. xx tt t
Itroductio to Differetial Equatios Defiitios ad Termiolog Differetial Equatio: A equatio cotaiig the derivatives of oe or more depedet variables, with respect to oe or more idepedet variables, is said
MATHEMATICS. 61. The differential equation representing the family of curves where c is a positive parameter, is of
MATHEMATICS 6 The differetial equatio represetig the family of curves where c is a positive parameter, is of Order Order Degree (d) Degree (a,c) Give curve is y c ( c) Differetiate wrt, y c c y Hece differetial
x x x 2x x N ( ) p NUMERICAL METHODS UNIT-I-SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS By Newton-Raphson formula
NUMERICAL METHODS UNIT-I-SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS. If g( is cotiuous i [a,b], te uder wat coditio te iterative (or iteratio metod = g( as a uique solutio i [a,b]? '( i [a,b].. Wat
CHAPTER 11 Limits and an Introduction to Calculus
CHAPTER Limits ad a Itroductio to Calculus Sectio. Itroductio to Limits................... 50 Sectio. Teciques for Evaluatig Limits............. 5 Sectio. Te Taget Lie Problem................. 50 Sectio.
Numerical Differentiation
Numerical Differentiation Finite Difference Formulas for te first derivative (Using Taylor Expansion tecnique) (section 8.3.) Suppose tat f() = g() is a function of te variable, and tat as 0 te function
MTH-112 Quiz 1 Name: # :
MTH- Quiz Name: # : Please write our name in te provided space. Simplif our answers. Sow our work.. Determine weter te given relation is a function. Give te domain and range of te relation.. Does te equation
y = f x x 1. If f x = e 2x tan -1 x, then f 1 = e 2 2 e 2 p C e 2 D e 2 p+1 4
. If f = e ta -, the f = e e p e e p e p+ 4 f = e ta -, so f = e ta - + e, so + f = e p + e = e p + e or f = e p + 4. The slope of the lie taget to the curve - + = at the poit, - is - 5 Differetiate -
Chapter 4. Fourier Series
Chapter 4. Fourier Series At this poit we are ready to ow cosider the caoical equatios. Cosider, for eample the heat equatio u t = u, < (4.) subject to u(, ) = si, u(, t) = u(, t) =. (4.) Here,
TECHNIQUES OF INTEGRATION
7 TECHNIQUES OF INTEGRATION Simpso s Rule estimates itegrals b approimatig graphs with parabolas. Because of the Fudametal Theorem of Calculus, we ca itegrate a fuctio if we kow a atiderivative, that is,
ChE 471 Lecture 10 Fall 2005 SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS
SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS I a exothermic reactio the temperature will cotiue to rise as oe moves alog a plug flow reactor util all of the limitig reactat is exhausted. Schematically
Quiz. Use either the RATIO or ROOT TEST to determine whether the series is convergent or not.
Quiz. Use either the RATIO or ROOT TEST to determie whether the series is coverget or ot. e .6 POWER SERIES Defiitio. A power series i about is a series of the form c 0 c a c a... c a... a 0 c a where
Essential Microeconomics EXISTENCE OF EQUILIBRIUM Core ideas: continuity of excess demand functions, Fixed point theorems
Essetial Microecoomics -- 5.3 EXISTENCE OF EQUILIBRIUM Core ideas: cotiuity of excess demad fuctios, Fixed oit teorems Two commodity excage ecoomy 2 Excage ecoomy wit may commodities 5 Discotiuous demad
Fundamental Concepts: Surfaces and Curves
UNDAMENTAL CONCEPTS: SURACES AND CURVES CHAPTER udametal Cocepts: Surfaces ad Curves. INTRODUCTION This chapter describes two geometrical objects, vi., surfaces ad curves because the pla a ver importat
Further Methods for Advanced Mathematics (FP2) WEDNESDAY 9 JANUARY 2008
ADVANCED GCE 7/ MATHEMATICS (MEI) Furter Metods for Advaced Matematics (F) WEDNESDAY 9 JANUARY 8 Additioal materials: Aswer Booklet (8 pages) Grap paper MEI Eamiatio Formulae ad Tables (MF) Afteroo Time:
Experiment (2) Upsetting Test of Forgeability of Metal 1. Objective: 2. Background: 3. Theory
Eperimet () Upsettig Test of Forgeabilit of Metal Dr. Moammad Al-taat Departmet of Idustrial Egieerig. Uiversit of Jorda. Lab. Of Maufacturig Processes. Course No: 9064. Objective: Te forgeabilit of a
The Derivative as a Function
Section 2.2 Te Derivative as a Function 200 Kiryl Tsiscanka Te Derivative as a Function DEFINITION: Te derivative of a function f at a number a, denoted by f (a), is if tis limit exists. f (a) f(a + )
Chapter 10: Power Series
Chapter : Power Series 57 Chapter Overview: Power Series The reaso series are part of a Calculus course is that there are fuctios which caot be itegrated. All power series, though, ca be itegrated because
Consider that special case of a viscous fluid near a wall that is set suddenly in motion as shown in Figure 1. The unsteady Navier-Stokes reduces to
Exact Solutios to the Navier-Stokes Equatio Ustead Parallel Flows (Plate Suddel Set i Motio) Cosider that special case of a viscous fluid ear a wall that is set suddel i motio as show i Figure. The ustead
Chapter 10 An Introduction to Calculus: Limits, Derivatives, and Integrals
86 Capter 0 A Itroductio to Calculus: Limits, Derivatives, ad Itegrals Capter 0 A Itroductio to Calculus: Limits, Derivatives, ad Itegrals Sectio 0. Limits ad Motio: Te Taget Problem Eploratio.. v ave
SOLUTION SET VI FOR FALL [(n + 2)(n + 1)a n+2 a n 1 ]x n = 0,
![SOLUTION SET VI FOR FALL [(n + 2)(n + 1)a n+2 a n 1 ]x n = 0,](/thumbs/94/119566625.jpg "SOLUTION SET VI FOR FALL [(n + 2)(n + 1)a n+2 a n 1 ]x n = 0,")
4. Series Solutios of Differetial Equatios:Special Fuctios 4.. Illustrative examples.. 5. Obtai the geeral solutio of each of the followig differetial equatios i terms of Maclauri series: d y (a dx = xy,
Exam 1 Solutions. x(x 2) (x + 1)(x 2) = x
Eam Solutions Question (0%) Consider f() = 2 2 2 2. (a) By calculating relevant its, determine te equations of all vertical asymptotes of te grap of f(). If tere are none, say so. f() = ( 2) ( + )( 2)
MVT and Rolle s Theorem
AP Calculus CHAPTER 4 WORKSHEET APPLICATIONS OF DIFFERENTIATION MVT and Rolle s Teorem Name Seat # Date UNLESS INDICATED, DO NOT USE YOUR CALCULATOR FOR ANY OF THESE QUESTIONS In problems 1 and, state
ALLOCATING SAMPLE TO STRATA PROPORTIONAL TO AGGREGATE MEASURE OF SIZE WITH BOTH UPPER AND LOWER BOUNDS ON THE NUMBER OF UNITS IN EACH STRATUM
ALLOCATING SAPLE TO STRATA PROPORTIONAL TO AGGREGATE EASURE OF SIZE WIT BOT UPPER AND LOWER BOUNDS ON TE NUBER OF UNITS IN EAC STRATU Lawrece R. Erst ad Cristoper J. Guciardo Erst_L@bls.gov, Guciardo_C@bls.gov
CHAPTER 8 SYSTEMS OF PARTICLES
CHAPTER 8 SYSTES OF PARTICLES CHAPTER 8 COLLISIONS 45 8. CENTER OF ASS The ceter of mass of a system of particles or a rigid body is the poit at which all of the mass are cosidered to be cocetrated there
ME 501A Seminar in Engineering Analysis Page 1
Accurac, Stabilit ad Sstems of Equatios November 0, 07 Numerical Solutios of Ordiar Differetial Equatios Accurac, Stabilit ad Sstems of Equatios Larr Caretto Mecaical Egieerig 0AB Semiar i Egieerig Aalsis
Estimating the Population Mean using Stratified Double Ranked Set Sample
Estimatig te Populatio Mea usig Stratified Double Raked Set Sample Mamoud Syam * Kamarulzama Ibraim Amer Ibraim Al-Omari Qatar Uiversity Foudatio Program Departmet of Mat ad Computer P.O.Box (7) Doa State
Castiel, Supernatural, Season 6, Episode 18
13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio
MATH Exam 1 Solutions February 24, 2016
MATH 7.57 Exam Solutios February, 6. Evaluate (A) l(6) (B) l(7) (C) l(8) (D) l(9) (E) l() 6x x 3 + dx. Solutio: D We perform a substitutio. Let u = x 3 +, so du = 3x dx. Therefore, 6x u() x 3 + dx = [
3. GRADUALLY-VARIED FLOW (GVF) AUTUMN EGL (energy grade line) weir change of slope
3. GRADUALLY-ARIED FLOW (GF) AUTUMN 17 3.1 Normal Flow vs Gradually-aried Flow /g EGL (eergy grade lie) ictio slope Geometric slope S I ormal flow te dowslope compoet of weigt balaces bed frictio. As a
Kernel Density Estimation
Kernel Density Estimation Univariate Density Estimation Suppose tat we ave a random sample of data X 1,..., X n from an unknown continuous distribution wit probability density function (pdf) f(x) and cumulative
Math 1241 Calculus Test 1
February 4, 2004 Name Te first nine problems count 6 points eac and te final seven count as marked. Tere are 120 points available on tis test. Multiple coice section. Circle te correct coice(s). You do
Numerical Analysis MTH603. dy dt = = (0) , y n+1. We obtain yn. Therefore. and. Copyright Virtual University of Pakistan 1
Numerical Analysis MTH60 PREDICTOR CORRECTOR METHOD Te metods presented so far are called single-step metods, were we ave seen tat te computation of y at t n+ tat is y n+ requires te knowledge of y n only.
Free Surface Hydrodynamics
Water Sciece ad Egieerig Free Surface Hydrodyamics y A part of Module : Hydraulics ad Hydrology Water Sciece ad Egieerig Dr. Shreedhar Maskey Seior Lecturer UNESCO-IHE Istitute for Water Educatio S. Maskey
Analytic Continuation
Aalytic Cotiuatio The stadard example of this is give by Example Let h (z) = 1 + z + z 2 + z 3 +... kow to coverge oly for z < 1. I fact h (z) = 1/ (1 z) for such z. Yet H (z) = 1/ (1 z) is defied for
Math Spring 2013 Solutions to Assignment # 3 Completion Date: Wednesday May 15, (1/z) 2 (1/z 1) 2 = lim
Mat 311 - Spring 013 Solutions to Assignment # 3 Completion Date: Wednesday May 15, 013 Question 1. [p 56, #10 (a)] 4z Use te teorem of Sec. 17 to sow tat z (z 1) = 4. We ave z 4z (z 1) = z 0 4 (1/z) (1/z
Section 3.1: Derivatives of Polynomials and Exponential Functions
Section 3.1: Derivatives of Polynomials and Exponential Functions In previous sections we developed te concept of te derivative and derivative function. Te only issue wit our definition owever is tat it
Diagnosis of Kinematic Vertical Velocity in HYCOM. By George Halliwell, 28 November ( ) = z. v (1)
Diagosis of Kiematic Vertical Velocity i HYCOM By George Halliwell 28 ovember 2004 Overview The vertical velocity w i Cartesia coordiates is determied by vertically itegratig the cotiuity equatio dw (
The total error in numerical differentiation
AMS 147 Computational Metods and Applications Lecture 08 Copyrigt by Hongyun Wang, UCSC Recap: Loss of accuracy due to numerical cancellation A B 3, 3 ~10 16 In calculating te difference between A and
Honors Calculus Homework 13 Solutions, due 12/8/5
Hoors Calculus Homework Solutios, due /8/5 Questio Let a regio R i the plae be bouded by the curves y = 5 ad = 5y y. Sketch the regio R. The two curves meet where both equatios hold at oce, so where: y
LECTURE 2 LEAST SQUARES CROSS-VALIDATION FOR KERNEL DENSITY ESTIMATION
Jauary 3 07 LECTURE LEAST SQUARES CROSS-VALIDATION FOR ERNEL DENSITY ESTIMATION Noparametric kerel estimatio is extremely sesitive to te coice of badwidt as larger values of result i averagig over more
Chapter 4 : Laplace Transform
4. Itroductio Laplace trasform is a alterative to solve the differetial equatio by the complex frequecy domai ( s = σ + jω), istead of the usual time domai. The DE ca be easily trasformed ito a algebraic
i 0 8) If 0 < x < 1, what is the value of x n+1 as n approaches infinity? 9) Infinite Power Series Formula.
Discovery Seet # Series Notatio ) Expad ad te evaluate eac series. 9 a) i i 4 4 b) i 4 e) i i 4 f) 5+5i i c) i+5 g) 4+5i d) i ) 5i i i 8 ) Rewrite te series i Σ otatio, ad te evaluate. a) 5++5++5+ b) 7+++6
x a x a Lecture 2 Series (See Chapter 1 in Boas)
Lecture Series (See Chapter i Boas) A basic ad very powerful (if pedestria, recall we are lazy AD smart) way to solve ay differetial (or itegral) equatio is via a series expasio of the correspodig solutio
Bernoulli Polynomials Talks given at LSBU, October and November 2015 Tony Forbes
Beroulli Polyoials Tals give at LSBU, October ad Noveber 5 Toy Forbes Beroulli Polyoials The Beroulli polyoials B (x) are defied by B (x), Thus B (x) B (x) ad B (x) x, B (x) x x + 6, B (x) dx,. () B 3
Math 12 Final Exam, May 11, 2011 ANSWER KEY. 2sinh(2x) = lim. 1 x. lim e. x ln. = e. (x+1)(1) x(1) (x+1) 2. (2secθ) 5 2sec2 θ dθ.
Math Fial Exam, May, ANSWER KEY. [5 Poits] Evaluate each of the followig its. Please justify your aswers. Be clear if the it equals a value, + or, or Does Not Exist. coshx) a) L H x x+l x) sihx) x x L
A Pseudo Spline Methods for Solving an Initial Value Problem of Ordinary Differential Equation
Joural of Matematics ad Statistics 4 (: 7-, 008 ISSN 549-3644 008 Sciece Publicatios A Pseudo Splie Metods for Solvig a Iitial Value Problem of Ordiary Differetial Equatio B.S. Ogudare ad G.E. Okeca Departmet
Chapter 10 An Introduction to Calculus: Limits, Derivatives, and Integrals
c0_p88_.qd /7/0 :6 PM Page 88 88 Capter 0 A Itroductio to Calculus: Limits, Derivatives, ad Itegrals Capter 0 A Itroductio to Calculus: Limits, Derivatives, ad Itegrals Sectio 0. Limits ad Motio: Te Taget
Boundary layer problem on conveyor belt. Gabriella Bognár University of Miskolc 3515 Miskolc-Egyetemváros, Hungary
Boudary layer problem o coveyor belt Gabriella Bogár Uiversity of Miskolc 355 Miskolc-Egyetemváros, Hugary e-mail: matvbg@ui-miskolc.hu Abstract: A techologically importat source of the boudary layer pheomeo
Stability analysis of numerical methods for stochastic systems with additive noise
Stability aalysis of umerical metods for stoctic systems wit additive oise Yosiiro SAITO Abstract Stoctic differetial equatios (SDEs) represet pysical peomea domiated by stoctic processes As for determiistic
Appendix: The Laplace Transform
Appedix: The Laplace Trasform The Laplace trasform is a powerful method that ca be used to solve differetial equatio, ad other mathematical problems. Its stregth lies i the fact that it allows the trasformatio
On Exact Finite-Difference Scheme for Numerical Solution of Initial Value Problems in Ordinary Differential Equations.
O Exact Fiite-Differece Sceme for Numerical Solutio of Iitial Value Problems i Ordiar Differetial Equatios. Josua Suda, M.Sc. Departmet of Matematical Scieces, Adamawa State Uiversit, Mubi, Nigeria. E-mail:
Lecture 4. We also define the set of possible values for the random walk as the set of all x R d such that P(S n = x) > 0 for some n.
Radom Walks ad Browia Motio Tel Aviv Uiversity Sprig 20 Lecture date: Mar 2, 20 Lecture 4 Istructor: Ro Peled Scribe: Lira Rotem This lecture deals primarily with recurrece for geeral radom walks. We preset
Optimal Estimator for a Sample Set with Response Error. Ed Stanek
Optial Estiator for a Saple Set wit Respose Error Ed Staek Itroductio We develop a optial estiator siilar to te FP estiator wit respose error tat was cosidered i c08ed63doc Te first 6 pages of tis docuet
Exact Solutions of Non-Newtonian Fluid Flow. between Two Moving Parallel Disks. and Stability Analysis
Applied Mathematical Scieces, Vol. 6,, o. 37, 87-835 Eact Solutios of No-Newtoia Fluid Flow betwee Two Movig Parallel Disks ad Stabilit Aalsis M. Kempegowda ad P. M. Balagodar Departmet of Mathematics,
MATH2007* Partial Answers to Review Exercises Fall 2004
MATH27* Partial Aswers to Review Eercises Fall 24 Evaluate each of the followig itegrals:. Let u cos. The du si ad Hece si ( cos 2 )(si ) (u 2 ) du. si u 2 cos 7 u 7 du Please fiish this. 2. We use itegratio
2018 MAΘ National Convention Mu Individual Solutions ( ) ( ) + + +
8 MΘ Natioal ovetio Mu Idividual Solutios b a f + f + + f + + + ) (... ) ( l ( ) l ( ) l ( 7) l ( ) ) l ( 8) ) a( ) cos + si ( ) a' ( ) cos ( ) a" ( ) si ( ) ) For a fuctio to be differetiable at c, it
Open Access The Rough Model Method (RMM) Application to The Computation of Normal Depth in Circular Conduit
Sed Orders for Reprits to reprits@betamsciece.et Te Ope Civil Egieerig Joural, 04, 8, 7-6 7 Ope Access Te Roug Model Metod (RMM) Applicatio to Te Computatio of Normal ept i Circular Coduit Bacir Acour
NUMERICAL DIFFERENTIATION
NUMERICAL IFFERENTIATION FIRST ERIVATIVES Te simplest difference formulas are based on using a straigt line to interpolate te given data; tey use two data pints to estimate te derivative. We assume tat
(4 pts.) (4 pts.) (4 pts.) b) y(x,t) = 1/(ax 2 +b) This function has no time dependence, so cannot be a wave.
12. For each of the possible wave forms below, idicate which satisf the wave equatio, ad which represet reasoable waveforms for actual waves o a strig. For those which do represet waves, fid the speed
EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 4 - CALCULUS
EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 4 - CALCULUS TUTORIAL 1 - DIFFERENTIATION Use the elemetary rules of calculus arithmetic to solve problems that ivolve differetiatio
Name: Math 10550, Final Exam: December 15, 2007
Math 55, Fial Exam: December 5, 7 Name: Be sure that you have all pages of the test. No calculators are to be used. The exam lasts for two hours. Whe told to begi, remove this aswer sheet ad keep it uder
1 The Euler Forward scheme (schéma d Euler explicite)
TP : Fiite differece metod for a Europea optio M2 Modélisatio aléatoire - Uiversité Deis-Diderot Cours EDP e Fiace et Métodes Numériques December 8, 2017 1 Te Euler Forward sceme (scéma d Euler explicite)
LIMITS MULTIPLE CHOICE QUESTIONS. (a) 1 (b) 0 (c) 1 (d) does not exist. (a) 0 (b) 1/4 (c) 1/2 (d) 1/8. (a) 1 (b) e (c) 0 (d) none of these
DSHA CLASSES Guidig you to Success LMTS MULTPLE CHOCE QUESTONS.... 5. Te value of + LEVEL (Objective Questios) (a) e (b) e (c) e 5 (d) e 5 (a) (b) (c) (d) does ot et (a) (b) / (c) / (d) /8 (a) (b) (c)
10/ Statistical Machine Learning Homework #1 Solutions
Caregie Mello Uiversity Departet of Statistics & Data Sciece 0/36-70 Statistical Macie Learig Hoework # Solutios Proble [40 pts.] DUE: February, 08 Let X,..., X P were X i [0, ] ad P as desity p. Let p
Chapter 5 Problem Solutions
Capter 5 Proble Solutios Wic of te wave fuctios i Fig 55 caot ave psical sigificace i te iterval sow? W ot? Figure b is double valued ad is ot a fuctio at all ad caot ave psical sigificace Figure c as