How to create a. Rain Garden. in 6 easy steps
|
|
- Anthony Nelson
- 5 years ago
- Views:
Transcription
1 How o cree Rin Grden in 6 esy seps
2 1 design Firs nd foremos, his is grden for your yrd. So pick rcive plns h you like. Mos of he plns lised like full sun o pril shde. Rin grdens cn lso work in shdy res, bu more creful pln selecion is required. A rin grden is designed o dry ou beween sorm evens. I is no welnd inended o permnenly hold wer. Plns h like verge-o-mois condiions ypiclly do well. If you choose plns h prefer we-o-sured condiions, you my need o wer hem during he summer. Use rock wlls, rbors, or oher borders o help define he boundries of he grden. Sr smll, see wh works, nd expnd your grden he nex yer.
3 2 locion Build rin grdens ner downspous, drivewys, or oher low poins h collec wer in your yrd. Pick locion where you cn dig shllow depression of he deph nd shpe you wn. You my need o dig i ou in he cener, nd build smll dm on he downhill side of he grden o help hold he wer. Consider where he wer will ener he grden, nd where i will drin ou when i overflows. Try o mke sure i does no drin in n unwned direcion, such s owrds he neighbor s fvorie siing spo. Do no insll he grden on op of sepic nk lech fields or over uiliy lines. Cll he locl uiliy clernce service o idenify buried uiliy lines before digging. Try o pu he rin grden 10 or more from your house o keep wer wy from your foundion.
4 3 soil & sizing For home grdens, he size of he grden is no erribly imporn. If you hve pleny of room, ry o size he grden o hold n inch of rin from he re h drins o i. Th migh be somehing like n 8' by 10' grden o cch he rin from downspou he corner of ypicl house. If you don hve h much spce, design he grden o fi your lndscpe. Mos rin grdens re bou 4" o 8 deep. Try o pick deph h will le he wer sok ino he soil wihin 24 hours. To do his, dig hole in he grden re (8" wide nd 8" deep), fill i wih wer, nd mesure how fs he wer soks ino he soil. This my ke number of hours. For exmple, if he wer level goes down 1" in 4 hours, he soil will percole bou 6" in 24 hours, so you would mke your grden 6" deep. If he grden only holds wer for dy, mosquioes cn breed in i.
5 4 preprion Ouline he shpe of he grden, remove he exising sod, nd dig o cree grden he size nd deph you wn. If you hve cly or compced soils, over-dig he grden bou 12", brek up lrge clods nd mix generous mouns of compos ino he soil o cree spces for roo penerion. Grde he grden so h wer will spred ou over lrge, fl re. Afer he grden bed is prepred, fill i wih wer o mke sure i will infilre he soil wihin 24 hours, nd h i drins in he direcion you wn when i overflows. If mos of he plns you choose do no like very we or sured condiions, cu noch in he downhill side of he grden berm so h wer does no fill up he grden for he firs yer. This helps he plns ge esblished. Mure plns cn olere more wer hn seedlings. Afer he firs growing seson, you cn fill in he noch nd le he grden hold more wer. 5 C h I T l P g C l W w p T p o
6 5 plns Consider plning nive wildflowers, grsses, nd shrubs. Mny hve very deep roos h do good job of breking up cly soils nd incresing infilrion ech yer. If vilble, plugs re n economicl pln selecion. Plugs re young plns in coniners bou 2" in dimeer by 5" deep. They esblish fser hn seeds, nd re less expensive hn lrge poed plns. Pick 6 or 8 pln species o ry firs. Group he sme plns ogeher in clumps of les 3 o cree mounds of color. Pln grsses beween he clumps of wildflowers. This helps prop up he flowers when hey ge ll. Choose pln locions in he grden bsed on how much wer hey will olere. Plce plns h like weer condiions in he lowes pr of he grden. Pu plns h like drier condiions round he edges. When picking plns, lso consider how ll nd wide he plns will ge when hey mure. Spce hem ccordingly. Plce ller plns in he cener of he grden. The pln lis righ conins species h re common in mny prs of he U.S. We like he nive species becuse hey hrive in our locl condiions nd hve deep roo sysems, nd mny olere boh spring rins nd summer droughs. Bu you ren limied o his lis. If you like culived vrieies, choose plns h like verge-o-mois condiions. plns for your re* Nme Sun Wer Color Heigh (in fee) Bloom Monh Plm Sedge M-W Yellow Blue Flg Iris M-W Blue Viole Mrsh Milkweed M-W Pink Whie 2-3 My-Jun Swichgrss D-W Yellow 4-6 Jul-Aug Joe Pye Weed Obedien Pln Purple Coneflower Lile Blue Sem M Purple 3-4 Jul-Aug M D-M Pink Whie Pink Purple Nine Brk D-M Pink Whie 3-4 Jun-Sep 2-8 Jul-Aug D-M Brown My-Jun River Birch M-W Brown Green Moisure: D - Dry, M - Medium, W - We * For full lising of nive plns in your re conc your locl nursery.
7 6 cre Wer your plns regulrly unil hey re esblished. Mulch he grden wih shredded hrdwood mulch. Weed he grden regulrly. Where wer eners he grden, rrnge rocks in decorive fshion o c s splsh block, help brek up he wer flow, nd preven big sorms from wshing ou he grden inle. Ech spring, prune ded vegeion, prune plns h ge oo lrge, weed he grden, nd ouch up he mulch. Then weed nd cre for he grden s you would ny oher grden. If wsh-off from drivewy or rod begins o cover he plns where he wer eners he grden, clen snd nd sedimen from he grden. Wch he plns, nd don be frid o move hem wihin he grden if hey need more or less wer. Phoo: Mid-Americ Regionl Council (MARC)
4.8 Improper Integrals
4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls
More informatione t dt e t dt = lim e t dt T (1 e T ) = 1
Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie
More informationAverage & instantaneous velocity and acceleration Motion with constant acceleration
Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission
More information0 for t < 0 1 for t > 0
8.0 Sep nd del funcions Auhor: Jeremy Orloff The uni Sep Funcion We define he uni sep funcion by u() = 0 for < 0 for > 0 I is clled he uni sep funcion becuse i kes uni sep = 0. I is someimes clled he Heviside
More informationMotion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.
Moion Accelerion Pr : Consn Accelerion Accelerion Accelerion Accelerion is he re of chnge of velociy. = v - vo = Δv Δ ccelerion = = v - vo chnge of velociy elpsed ime Accelerion is vecor, lhough in one-dimensionl
More informationPHYSICS 1210 Exam 1 University of Wyoming 14 February points
PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry 2013 150 poins This es is open-noe nd closed-book. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher
More informationSeptember 20 Homework Solutions
College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum
More informationMTH 146 Class 11 Notes
8.- Are of Surfce of Revoluion MTH 6 Clss Noes Suppose we wish o revolve curve C round n is nd find he surfce re of he resuling solid. Suppose f( ) is nonnegive funcion wih coninuous firs derivive on he
More informationThe solution is often represented as a vector: 2xI + 4X2 + 2X3 + 4X4 + 2X5 = 4 2xI + 4X2 + 3X3 + 3X4 + 3X5 = 4. 3xI + 6X2 + 6X3 + 3X4 + 6X5 = 6.
[~ o o :- o o ill] i 1. Mrices, Vecors, nd Guss-Jordn Eliminion 1 x y = = - z= The soluion is ofen represened s vecor: n his exmple, he process of eliminion works very smoohly. We cn elimine ll enries
More informationMagnetostatics Bar Magnet. Magnetostatics Oersted s Experiment
Mgneosics Br Mgne As fr bck s 4500 yers go, he Chinese discovered h cerin ypes of iron ore could rc ech oher nd cerin mels. Iron filings "mp" of br mgne s field Crefully suspended slivers of his mel were
More information2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.
Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl
More information22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 9: The High Beta Tokamak
.65, MHD Theory of Fusion Sysems Prof. Freidberg Lecure 9: The High e Tokmk Summry of he Properies of n Ohmic Tokmk. Advnges:. good euilibrium (smll shif) b. good sbiliy ( ) c. good confinemen ( τ nr )
More informationMATH 124 AND 125 FINAL EXAM REVIEW PACKET (Revised spring 2008)
MATH 14 AND 15 FINAL EXAM REVIEW PACKET (Revised spring 8) The following quesions cn be used s review for Mh 14/ 15 These quesions re no cul smples of quesions h will pper on he finl em, bu hey will provide
More informationPosition, Velocity, and Acceleration
rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME-9493 1 Car ME-9454 1 Fan Accessory ME-9491 1 Moion Sensor II CI-6742A 1 Track Barrier Purpose The purpose
More informationSome Inequalities variations on a common theme Lecture I, UL 2007
Some Inequliies vriions on common heme Lecure I, UL 2007 Finbrr Hollnd, Deprmen of Mhemics, Universiy College Cork, fhollnd@uccie; July 2, 2007 Three Problems Problem Assume i, b i, c i, i =, 2, 3 re rel
More informationMinimum Squared Error
Minimum Squred Error LDF: Minimum Squred-Error Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > for ll smples y i solve sysem of liner inequliies MSE procedure y i = i for ll smples
More informationMinimum Squared Error
Minimum Squred Error LDF: Minimum Squred-Error Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > 0 for ll smples y i solve sysem of liner inequliies MSE procedure y i i for ll smples
More information( ) ( ) ( ) ( ) ( ) ( y )
8. Lengh of Plne Curve The mos fmous heorem in ll of mhemics is he Pyhgoren Theorem. I s formulion s he disnce formul is used o find he lenghs of line segmens in he coordine plne. In his secion you ll
More information1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor.
In Eercise 1, use sndrd recngulr Cresin coordine sysem. Le ime be represened long he horizonl is. Assume ll ccelerions nd decelerions re consn. 1. Consider PSA iniilly res in he beginning of he lef-hnd
More informationProperties of Logarithms. Solving Exponential and Logarithmic Equations. Properties of Logarithms. Properties of Logarithms. ( x)
Properies of Logrihms Solving Eponenil nd Logrihmic Equions Properies of Logrihms Produc Rule ( ) log mn = log m + log n ( ) log = log + log Properies of Logrihms Quoien Rule log m = logm logn n log7 =
More informationA Kalman filtering simulation
A Klmn filering simulion The performnce of Klmn filering hs been esed on he bsis of wo differen dynmicl models, ssuming eiher moion wih consn elociy or wih consn ccelerion. The former is epeced o beer
More informationA new model for limit order book dynamics
Anewmodelforlimiorderbookdynmics JeffreyR.Russell UniversiyofChicgo,GrdueSchoolofBusiness TejinKim UniversiyofChicgo,DeprmenofSisics Absrc:Thispperproposesnewmodelforlimiorderbookdynmics.Thelimiorderbookconsiss
More informationA 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m
PHYS : Soluions o Chper 3 Home Work. SSM REASONING The displcemen is ecor drwn from he iniil posiion o he finl posiion. The mgniude of he displcemen is he shores disnce beween he posiions. Noe h i is onl
More informationGRADE 4. Division WORKSHEETS
GRADE Division WORKSHEETS Division division is shring nd grouping Division cn men shring or grouping. There re cndies shred mong kids. How mny re in ech shre? = 3 There re 6 pples nd go into ech bsket.
More informationINTEGRALS. Exercise 1. Let f : [a, b] R be bounded, and let P and Q be partitions of [a, b]. Prove that if P Q then U(P ) U(Q) and L(P ) L(Q).
INTEGRALS JOHN QUIGG Eercise. Le f : [, b] R be bounded, nd le P nd Q be priions of [, b]. Prove h if P Q hen U(P ) U(Q) nd L(P ) L(Q). Soluion: Le P = {,..., n }. Since Q is obined from P by dding finiely
More information(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.
Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)
More informationMathematics 805 Final Examination Answers
. 5 poins Se he Weiersrss M-es. Mhemics 85 Finl Eminion Answers Answer: Suppose h A R, nd f n : A R. Suppose furher h f n M n for ll A, nd h Mn converges. Then f n converges uniformly on A.. 5 poins Se
More informationK The slowest step in a mechanism has this
CM 6 Generl Chemisry II Nme SLUTINS Exm, Spring 009 Dr. Seel. (0 pins) Selec he nswer frm he clumn n he righ h bes mches ech descripin frm he clumn n he lef. Ech nswer cn be used, ms, nly nce. E G This
More information1. Find a basis for the row space of each of the following matrices. Your basis should consist of rows of the original matrix.
Mh 7 Exm - Prcice Prolem Solions. Find sis for he row spce of ech of he following mrices. Yor sis shold consis of rows of he originl mrix. 4 () 7 7 8 () Since we wn sis for he row spce consising of rows
More informationChapter 2: Evaluative Feedback
Chper 2: Evluive Feedbck Evluing cions vs. insrucing by giving correc cions Pure evluive feedbck depends olly on he cion ken. Pure insrucive feedbck depends no ll on he cion ken. Supervised lerning is
More informationVersion 001 test-1 swinney (57010) 1. is constant at m/s.
Version 001 es-1 swinne (57010) 1 This prin-ou should hve 20 quesions. Muliple-choice quesions m coninue on he nex column or pge find ll choices before nswering. CubeUniVec1x76 001 10.0 poins Acubeis1.4fee
More information3. Renewal Limit Theorems
Virul Lborories > 14. Renewl Processes > 1 2 3 3. Renewl Limi Theorems In he inroducion o renewl processes, we noed h he rrivl ime process nd he couning process re inverses, in sens The rrivl ime process
More informationExample. Have precipitation and streamflow data, need to estimate losses
Excess Rinfll Excess rinfll Rinfll tht is neither retined on the lnd surfce nor infiltrted into the soil Grph of excess rinfll versus time is clled excess rinfll hyetogrph Direct runoff = observed stremflow
More informationPhysics 2A HW #3 Solutions
Chper 3 Focus on Conceps: 3, 4, 6, 9 Problems: 9, 9, 3, 41, 66, 7, 75, 77 Phsics A HW #3 Soluions Focus On Conceps 3-3 (c) The ccelerion due o grvi is he sme for boh blls, despie he fc h he hve differen
More informationEXERCISE - 01 CHECK YOUR GRASP
UNIT # 09 PARABOLA, ELLIPSE & HYPERBOLA PARABOLA EXERCISE - 0 CHECK YOUR GRASP. Hin : Disnce beween direcri nd focus is 5. Given (, be one end of focl chord hen oher end be, lengh of focl chord 6. Focus
More informationChapter 7: Solving Trig Equations
Haberman MTH Secion I: The Trigonomeric Funcions Chaper 7: Solving Trig Equaions Le s sar by solving a couple of equaions ha involve he sine funcion EXAMPLE a: Solve he equaion sin( ) The inverse funcions
More informationNotes 04 largely plagiarized by %khc
Noes 04 largely plagiarized by %khc Convoluion Recap Some ricks: x() () =x() x() (, 0 )=x(, 0 ) R ț x() u() = x( )d x() () =ẋ() This hen ells us ha an inegraor has impulse response h() =u(), and ha a differeniaor
More informationProblem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are:
(x + y ) = y + (x + y ) = x + Problem Set 9 Discussion: Nov., Nov. 8, Nov. (on probbility nd binomil coefficients) The nme fter the problem is the designted writer of the solution of tht problem. (No one
More informationSection 7.4 Modeling Changing Amplitude and Midline
488 Chaper 7 Secion 7.4 Modeling Changing Ampliude and Midline While sinusoidal funcions can model a variey of behaviors, i is ofen necessary o combine sinusoidal funcions wih linear and exponenial curves
More informationWeek 8 Lecture 3: Problems 49, 50 Fourier analysis Courseware pp (don t look at French very confusing look in the Courseware instead)
Week 8 Lecure 3: Problems 49, 5 Fourier lysis Coursewre pp 6-7 (do look Frech very cofusig look i he Coursewre ised) Fourier lysis ivolves ddig wves d heir hrmoics, so i would hve urlly followed fer he
More informationConstant Acceleration
Objecive Consan Acceleraion To deermine he acceleraion of objecs moving along a sraigh line wih consan acceleraion. Inroducion The posiion y of a paricle moving along a sraigh line wih a consan acceleraion
More informationChapter Direct Method of Interpolation
Chper 5. Direc Mehod of Inerpolion Afer reding his chper, you should be ble o:. pply he direc mehod of inerpolion,. sole problems using he direc mehod of inerpolion, nd. use he direc mehod inerpolns o
More informationBiol. 356 Lab 8. Mortality, Recruitment, and Migration Rates
Biol. 356 Lab 8. Moraliy, Recruimen, and Migraion Raes (modified from Cox, 00, General Ecology Lab Manual, McGraw Hill) Las week we esimaed populaion size hrough several mehods. One assumpion of all hese
More informationMixed Upland Lowland Aspen, Spruce/Fir High Density Mixed Northern Maple, Beech,
Rge Commes: Pge 1 of 4 1 4319 - Mixe Upl Fores 11.5 113 Mixe s wih vrible species. 4 6117 - Lowl 8.8 1 5 4134 - Aspe, Spruce/Fir 1.4 15 Cu i 1993 o Ol Hericks Birch II. Mos of he s is i comp 166 s 3. 6
More informationdt = C exp (3 ln t 4 ). t 4 W = C exp ( ln(4 t) 3) = C(4 t) 3.
Mah Rahman Exam Review Soluions () Consider he IVP: ( 4)y 3y + 4y = ; y(3) = 0, y (3) =. (a) Please deermine he longes inerval for which he IVP is guaraneed o have a unique soluion. Soluion: The disconinuiies
More informationPhysics 101 Lecture 4 Motion in 2D and 3D
Phsics 11 Lecure 4 Moion in D nd 3D Dr. Ali ÖVGÜN EMU Phsics Deprmen www.ogun.com Vecor nd is componens The componens re he legs of he righ ringle whose hpoenuse is A A A A A n ( θ ) A Acos( θ) A A A nd
More information6. Gas dynamics. Ideal gases Speed of infinitesimal disturbances in still gas
6. Gs dynmics Dr. Gergely Krisóf De. of Fluid echnics, BE Februry, 009. Seed of infiniesiml disurbnces in sill gs dv d, dv d, Coninuiy: ( dv)( ) dv omenum r r heorem: ( ( dv) ) d 3443 4 q m dv d dv llievi
More informationMotion in a Straight Line
Moion in Srigh Line. Preei reched he mero sion nd found h he esclor ws no working. She wlked up he sionry esclor in ime. On oher dys, if she remins sionry on he moing esclor, hen he esclor kes her up in
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signals & Sysems Prof. Mark Fowler Noe Se #1 C-T Sysems: Convoluion Represenaion Reading Assignmen: Secion 2.6 of Kamen and Heck 1/11 Course Flow Diagram The arrows here show concepual flow beween
More informationREAL ANALYSIS I HOMEWORK 3. Chapter 1
REAL ANALYSIS I HOMEWORK 3 CİHAN BAHRAN The quesions re from Sein nd Shkrchi s e. Chper 1 18. Prove he following sserion: Every mesurble funcion is he limi.e. of sequence of coninuous funcions. We firs
More informationIntroduction to LoggerPro
Inroducion o LoggerPro Sr/Sop collecion Define zero Se d collecion prmeers Auoscle D Browser Open file Sensor seup window To sr d collecion, click he green Collec buon on he ool br. There is dely of second
More information5.1-The Initial-Value Problems For Ordinary Differential Equations
5.-The Iniil-Vlue Problems For Ordinry Differenil Equions Consider solving iniil-vlue problems for ordinry differenil equions: (*) y f, y, b, y. If we know he generl soluion y of he ordinry differenil
More information( ) a system of differential equations with continuous parametrization ( T = R + These look like, respectively:
XIII. DIFFERENCE AND DIFFERENTIAL EQUATIONS Ofen funcions, or a sysem of funcion, are paramerized in erms of some variable, usually denoed as and inerpreed as ime. The variable is wrien as a funcion of
More informationMath 334 Fall 2011 Homework 11 Solutions
Dec. 2, 2 Mah 334 Fall 2 Homework Soluions Basic Problem. Transform he following iniial value problem ino an iniial value problem for a sysem: u + p()u + q() u g(), u() u, u () v. () Soluion. Le v u. Then
More informationf t f a f x dx By Lin McMullin f x dx= f b f a. 2
Accumulion: Thoughs On () By Lin McMullin f f f d = + The gols of he AP* Clculus progrm include he semen, Sudens should undersnd he definie inegrl s he ne ccumulion of chnge. 1 The Topicl Ouline includes
More informationImproper Integrals, and Differential Equations
Improper Integrls, nd Differentil Equtions October 22, 204 5.3 Improper Integrls Previously, we discussed how integrls correspond to res. More specificlly, we sid tht for function f(x), the region creted
More informationCSE 5365 Computer Graphics. Take Home Test #1
CSE 5365 Comper Graphics Take Home Tes #1 Fall/1996 Tae-Hoon Kim roblem #1) A bi-cbic parameric srface is defined by Hermie geomery in he direcion of parameer. In he direcion, he geomery ecor is defined
More informationAn integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples.
Improper Inegrls To his poin we hve only considered inegrls f(x) wih he is of inegrion nd b finie nd he inegrnd f(x) bounded (nd in fc coninuous excep possibly for finiely mny jump disconinuiies) An inegrl
More information() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration
Secion 1.4 Moion in Spce: Velociy nd Acceleion We e going o dive lile deepe ino somehing we ve ledy inoduced, nmely () nd (). Discuss wih you neighbo he elionships beween posiion, velociy nd cceleion you
More informationSection 4.8. D v(t j 1 ) t. (4.8.1) j=1
Difference Equtions to Differentil Equtions Section.8 Distnce, Position, nd the Length of Curves Although we motivted the definition of the definite integrl with the notion of re, there re mny pplictions
More information3 Motion with constant acceleration: Linear and projectile motion
3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr
More informationChapter 0. What is the Lebesgue integral about?
Chpter 0. Wht is the Lebesgue integrl bout? The pln is to hve tutoril sheet ech week, most often on Fridy, (to be done during the clss) where you will try to get used to the ides introduced in the previous
More information= ( ) ) or a system of differential equations with continuous parametrization (T = R
XIII. DIFFERENCE AND DIFFERENTIAL EQUATIONS Ofen funcions, or a sysem of funcion, are paramerized in erms of some variable, usually denoed as and inerpreed as ime. The variable is wrien as a funcion of
More informationScientific notation is a way of expressing really big numbers or really small numbers.
Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific
More informationFishing limits and the Logistic Equation. 1
Fishing limis and he Logisic Equaion. 1 1. The Logisic Equaion. The logisic equaion is an equaion governing populaion growh for populaions in an environmen wih a limied amoun of resources (for insance,
More informationContraction Mapping Principle Approach to Differential Equations
epl Journl of Science echnology 0 (009) 49-53 Conrcion pping Principle pproch o Differenil Equions Bishnu P. Dhungn Deprmen of hemics, hendr Rn Cmpus ribhuvn Universiy, Khmu epl bsrc Using n eension of
More information1. Kinematics I: Position and Velocity
1. Kinemaics I: Posiion and Velociy Inroducion The purpose of his eperimen is o undersand and describe moion. We describe he moion of an objec by specifying is posiion, velociy, and acceleraion. In his
More informationLecture 2e Orthogonal Complement (pages )
Lecture 2e Orthogonl Complement (pges -) We hve now seen tht n orthonorml sis is nice wy to descrie suspce, ut knowing tht we wnt n orthonorml sis doesn t mke one fll into our lp. In theory, the process
More informationMath 2142 Exam 1 Review Problems. x 2 + f (0) 3! for the 3rd Taylor polynomial at x = 0. To calculate the various quantities:
Mah 4 Eam Review Problems Problem. Calculae he 3rd Taylor polynomial for arcsin a =. Soluion. Le f() = arcsin. For his problem, we use he formula f() + f () + f ()! + f () 3! for he 3rd Taylor polynomial
More informationSolutions to Assignment 1
MA 2326 Differenial Equaions Insrucor: Peronela Radu Friday, February 8, 203 Soluions o Assignmen. Find he general soluions of he following ODEs: (a) 2 x = an x Soluion: I is a separable equaion as we
More informationCSE-4303/CSE-5365 Computer Graphics Fall 1996 Take home Test
Comper Graphics roblem #1) A bi-cbic parameric srface is defined by Hermie geomery in he direcion of parameer. In he direcion, he geomery ecor is defined by a poin @0, a poin @0.5, a angen ecor @1 and
More informationMath 2214 Solution Test 1A Spring 2016
Mah 14 Soluion Tes 1A Spring 016 sec Problem 1: Wha is he larges -inerval for which ( 4) = has a guaraneed + unique soluion for iniial value (-1) = 3 according o he Exisence Uniqueness Theorem? Soluion
More informationPolygons, Pingos, and Thermokarst! Oh my!
Polygons, Pingos, nd Thermokrst! Oh my! Overview: Ares underlin with permfrost exhibit common fetures due to freezing nd thwing in such res. Ice wedge polygons, pingos, nd thermokrst re some of the most
More informationNEWTON S SECOND LAW OF MOTION
Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during
More informationToday: Falling. v, a
Today: Falling. v, a Did you ge my es email? If no, make sure i s no in your junk box, and add sbs0016@mix.wvu.edu o your address book! Also please email me o le me know. I will be emailing ou pracice
More informationRecitation 3: More Applications of the Derivative
Mth 1c TA: Pdric Brtlett Recittion 3: More Applictions of the Derivtive Week 3 Cltech 2012 1 Rndom Question Question 1 A grph consists of the following: A set V of vertices. A set E of edges where ech
More informationENGR 1990 Engineering Mathematics The Integral of a Function as a Function
ENGR 1990 Engineering Mhemics The Inegrl of Funcion s Funcion Previously, we lerned how o esime he inegrl of funcion f( ) over some inervl y dding he res of finie se of rpezoids h represen he re under
More informationCHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA
Hrris: Quntittive Chemicl Anlysis, Eight Edition CHAPTER 08: MONOPROTIC ACIDBASE EQUILIBRIA CHAPTER 08: Opener A CHAPTER 08: Opener B CHAPTER 08: Opener C CHAPTER 08: Opener D CHAPTER 08: Opener E Chpter
More informationf(x) dx with An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples dx x x 2
Impope Inegls To his poin we hve only consideed inegls f() wih he is of inegion nd b finie nd he inegnd f() bounded (nd in fc coninuous ecep possibly fo finiely mny jump disconinuiies) An inegl hving eihe
More information3.6 Derivatives as Rates of Change
3.6 Derivaives as Raes of Change Problem 1 John is walking along a sraigh pah. His posiion a he ime >0 is given by s = f(). He sars a =0from his house (f(0) = 0) and he graph of f is given below. (a) Describe
More informationWeek 1 Lecture 2 Problems 2, 5. What if something oscillates with no obvious spring? What is ω? (problem set problem)
Week 1 Lecure Problems, 5 Wha if somehing oscillaes wih no obvious spring? Wha is ω? (problem se problem) Sar wih Try and ge o SHM form E. Full beer can in lake, oscillaing F = m & = ge rearrange: F =
More informationRESPONSE UNDER A GENERAL PERIODIC FORCE. When the external force F(t) is periodic with periodτ = 2π
RESPONSE UNDER A GENERAL PERIODIC FORCE When he exernl force F() is periodic wih periodτ / ω,i cn be expnded in Fourier series F( ) o α ω α b ω () where τ F( ) ω d, τ,,,... () nd b τ F( ) ω d, τ,,... (3)
More informationPhysic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =
Mi i fd l Phsic 3 Lecure 4 Min poins of od s lecure: Emple: ddiion of elociies Trjecories of objecs in dimensions: dimensions: g 9.8m/s downwrds ( ) g o g g Emple: A foobll pler runs he pern gien in he
More information1 jordan.mcd Eigenvalue-eigenvector approach to solving first order ODEs. -- Jordan normal (canonical) form. Instructor: Nam Sun Wang
jordnmcd Eigenvlue-eigenvecor pproch o solving firs order ODEs -- ordn norml (cnonicl) form Insrucor: Nm Sun Wng Consider he following se of coupled firs order ODEs d d x x 5 x x d d x d d x x x 5 x x
More informationMATH STUDENT BOOK. 10th Grade Unit 5
MATH STUDENT BOOK 10th Grde Unit 5 Unit 5 Similr Polygons MATH 1005 Similr Polygons INTRODUCTION 3 1. PRINCIPLES OF ALGEBRA 5 RATIOS AND PROPORTIONS 5 PROPERTIES OF PROPORTIONS 11 SELF TEST 1 16 2. SIMILARITY
More informationRiemann Sums and Riemann Integrals
Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 203 Outline Riemnn Sums Riemnn Integrls Properties Abstrct
More informationCS667 Lecture 6: Monte Carlo Integration 02/10/05
CS667 Lecture 6: Monte Crlo Integrtion 02/10/05 Venkt Krishnrj Lecturer: Steve Mrschner 1 Ide The min ide of Monte Crlo Integrtion is tht we cn estimte the vlue of n integrl by looking t lrge number of
More informationMath 61CM - Solutions to homework 9
Mth 61CM - Solutions to homework 9 Cédric De Groote November 30 th, 2018 Problem 1: Recll tht the left limit of function f t point c is defined s follows: lim f(x) = l x c if for ny > 0 there exists δ
More informationPhys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole
Phys 221 Fall 2014 Chaper 2 Moion in One Dimension 2014, 2005 A. Dzyubenko 2004 Brooks/Cole 1 Kinemaics Kinemaics, a par of classical mechanics: Describes moion in erms of space and ime Ignores he agen
More informationSolution for Assignment 1 : Intro to Probability and Statistics, PAC learning
Solution for Assignment 1 : Intro to Probbility nd Sttistics, PAC lerning 10-701/15-781: Mchine Lerning (Fll 004) Due: Sept. 30th 004, Thursdy, Strt of clss Question 1. Bsic Probbility ( 18 pts) 1.1 (
More informationTwo Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
More informationMath 10B: Mock Mid II. April 13, 2016
Name: Soluions Mah 10B: Mock Mid II April 13, 016 1. ( poins) Sae, wih jusificaion, wheher he following saemens are rue or false. (a) If a 3 3 marix A saisfies A 3 A = 0, hen i canno be inverible. True.
More informationMath 23 Spring Differential Equations. Final Exam Due Date: Tuesday, June 6, 5pm
Mah Spring 6 Differenial Equaions Final Exam Due Dae: Tuesday, June 6, 5pm Your name (please prin): Insrucions: This is an open book, open noes exam. You are free o use a calculaor or compuer o check your
More informationLecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.
Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More informationPhysics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011
Physics 9 Fll 0 Homework - s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you
More informationForms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics:
SPH4U: Inroducion o ork ork & Energy ork & Energy Discussion Definiion Do Produc ork of consn force ork/kineic energy heore ork of uliple consn forces Coens One of he os iporn conceps in physics Alernive
More informationPARABOLA. moves such that PM. = e (constant > 0) (eccentricity) then locus of P is called a conic. or conic section.
wwwskshieducioncom PARABOLA Le S be given fixed poin (focus) nd le l be given fixed line (Direcrix) Le SP nd PM be he disnce of vrible poin P o he focus nd direcrix respecively nd P SP moves such h PM
More informationRiemann Sums and Riemann Integrals
Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 2013 Outline 1 Riemnn Sums 2 Riemnn Integrls 3 Properties
More informationThink of the Relationship Between Time and Space Again
Repor nd Opinion, 1(3),009 hp://wwwsciencepubne sciencepub@gmilcom Think of he Relionship Beween Time nd Spce Agin Yng F-cheng Compny of Ruid Cenre in Xinjing 15 Hongxing Sree, Klmyi, Xingjing 834000,
More information