k of the incident wave) will be greater t is too small to satisfy the required kinematics boundary condition, (19)

Size: px
Start display at page:

Download "k of the incident wave) will be greater t is too small to satisfy the required kinematics boundary condition, (19)"

Transcription

1 TOTAL INTRNAL RFLTION Kmacs pops Sc h vcos a coplaa, l s cosd h cd pla cocds wh h X pla; hc 0. y y y osd h cas whch h lgh s cd fom h mdum of hgh dx of faco >. Fo cd agls ga ha h ccal agl s 1 ( /, h hooal compo of (.. h compo x of h cd wav wll b ga ha h magud of h asmd lgh s vco = (/ '. Ths s show h fgu blow; oc s oo small o sasfy h qud macs bouday codo, x x (19 Thus, h s o al vco o sasfy h codo (19 wh >. as = as > c Slow mdum c ' fas mdum ' X ' < Sll s law o bg fulflld Fg. 0 Toal al flco. Fo > h lgh of h al-vaabl wavvco (asmd wav us ou o b oo small o sasfy h bouday codo x x. Tha s, dos o xs a al-vaabl wav-vco abl o sasfy h mac codos (Sll s law a h bouday. Th mplcao s ha h cd wav s fully flcd (h s o popagag asmd wav pag h dco.

2 Th s a way o g aoud hs lmao. W allow h Idd, v hough h magud of s fxd ad qual o, Noc, x ( x ( ' could b ga ha pu complx umb, ' f o b a complx vco. ( wh gav; ha s, f w a Accodgly, l s cosd a asmd wav of complx vco, (, 0, complx vco (0 whos modulus squa x x x ( 0 x ( j x s qud o sasfy, (0 ' Th complx wav-vco (, 0, j s h abl o sasfy h Sll s law fo cd agls >, Noc also x o, (1 x x x ' (1

3 as = as > c Slow mdum fas mdum < c ( x, 0, omplx vco Fg. 1 Noc o h gh-sd dagam ha h vasc wav popagas alog h fac wh wav-vco compo x, ( x > (/. x X Nx, fo a gv cd agl >, l s fgu ou h cospodg valu of. Th macs codo x x x mpls, x x S S. x x S ( Usg hs valu (1, gvs, x x S S S (3 Usg s 1 ( /

4 S Sc fo > (3 I summay, Icdwav Rflcd wav Tasm d wav - o (4 - (4 o - o, wh ( x, 0, j (4 o x x x j γ - ω ω x o j ( x x - ω o - Fo h pacula cas a hads, w a h posv sg (ohws w would hav a wav cayg f gy. γ x x - ω o (fo < 0 - o - o < c ' x ( x, 0, j ' X o γ x x - ω Fg. Th facd wav popagas oly paalll o h sufac (wh wav-vco x ad s auad xpoally (dcay faco alog h vcal dco h mdum of low dx of faco.

5 So, dos xs lcomagc fld h mdum of low dx of faco, bu s auad xpoally byod h fac. No gy flow (o popagag gy cosss vcally h fac. Dyamcs pops How o copoa h complx vco Fs, Sll s law sas s / Noc, Hc, o has, s s s s o h Fsl quaos? s. I ms of h ccal agl (5 s 1 fo > (5 s a complx agl wh >. [ Noc, fo a complx agl / j o obas 1 s ( / j 1 1 ( j 1 >1 ] L s valua also h cos of h complx agl. O o had, w hav ' os os, o h oh had, whch gvs os Usg h xpsso fo gv (3, os S whch gvs, os S S Sc 1 1 fo > (6

6 Noc fom (4 ad (6 ha h complx agl sasfs, s cos 1 (7 Th xpsso fo cos, obad abov fo h cas wh > a sd ow h Fsl s quaos: Fo T o s- polaao o o os os os os Amplud flco coffc o o os os os Amplud asmsso coffc Noc ha fo a complx os, as gv (6, h magud of s qual o1, as xpcd a oal al flco cas. 1 (8 Fo TM o p- polaao o os os o os os Amplud flco coffc o o os os os Amplud asmsso coffc Noc also ha (6 mpls, 1 (6 Noc ha boh cass, T ad TM polaao, h complx os gv (4 suls complx amplud flco coffcs. I mpls ha, ud oal al flco codos, h s (7 a chag h phas of h flcd wav. Fsl s hombus. Ths phas chags ca b uld o cov o yp of polaao o aoh. Fo xampl a Fsl s hombus, laly polad lgh wh qual T ad TM polaao ampluds s covd by wo succssv al flcos (ach volvg a lav phas chag of 45 o o cculaly polad lgh.

7

Phys Nov. 3, 2017 Today s Topics. Continue Chapter 2: Electromagnetic Theory, Photons, and Light Reading for Next Time

Phys Nov. 3, 2017 Today s Topics. Continue Chapter 2: Electromagnetic Theory, Photons, and Light Reading for Next Time Phys 31. No. 3, 17 Today s Topcs Cou Chap : lcomagc Thoy, Phoos, ad Lgh Radg fo Nx Tm 1 By Wdsday: Radg hs Wk Fsh Fowls Ch. (.3.11 Polazao Thoy, Jos Macs, Fsl uaos ad Bws s Agl Homwok hs Wk Chap Homwok

More information

Part I- Wave Reflection and Transmission at Normal Incident. Part II- Wave Reflection and Transmission at Oblique Incident

Part I- Wave Reflection and Transmission at Normal Incident. Part II- Wave Reflection and Transmission at Oblique Incident Apl 6, 3 Uboudd Mda Gudd Mda Chap 7 Chap 8 3 mls 3 o 3 M F bad Lgh wavs md by h su Pa I- Wav Rlo ad Tasmsso a Nomal Id Pa II- Wav Rlo ad Tasmsso a Oblqu Id Pa III- Gal Rlao Bw ad Wavguds ad Cavy Rsoao

More information

Anouncements. Conjugate Gradients. Steepest Descent. Outline. Steepest Descent. Steepest Descent

Anouncements. Conjugate Gradients. Steepest Descent. Outline. Steepest Descent. Steepest Descent oucms Couga Gas Mchal Kazha (6.657) Ifomao abou h Sma (6.757) hav b pos ol: hp://www.cs.hu.u/~msha Tch Spcs: o M o Tusay afoo. o Two paps scuss ach w. o Vos fo w s caa paps u by Thusay vg. Oul Rvw of Sps

More information

The far field calculation: Approximate and exact solutions. Persa Kyritsi November 10th, 2005 B2-109

The far field calculation: Approximate and exact solutions. Persa Kyritsi November 10th, 2005 B2-109 Th fa fl calculao: Appoa a ac oluo Pa K Novb 0h 005 B-09 Oul Novb 0h 005 Pa K Iouco Appoa oluo flco fo h gou ac oluo Cocluo Pla wav fo Ic fl: pla wav k ( ) jk H ( ) λ λ ( ) Polaao fo η 0 0 Hooal polaao

More information

Lecture Y4: Computational Optics I

Lecture Y4: Computational Optics I Phooc ad opolcoc chologs DPMS: Advacd Maals Udsadg lgh ma acos s cucal fo w applcaos Lcu Y4: Compuaoal Opcs I lfos Ldoks Room Π, 65 746 ldok@cc.uo.g hp://cmsl.maals.uo.g/ldoks Rflco ad faco Toal al flco

More information

Existence of Nonoscillatory Solutions for a Class of N-order Neutral Differential Systems

Existence of Nonoscillatory Solutions for a Class of N-order Neutral Differential Systems Vo 3 No Mod Appd Scc Exsc of Nooscaoy Souos fo a Cass of N-od Nua Dffa Sysms Zhb Ch & Apg Zhag Dpam of Ifomao Egg Hua Uvsy of Tchoogy Hua 4 Cha E-ma: chzhbb@63com Th sach s facd by Hua Povc aua sccs fud

More information

Chapter 3 Plane EM Waves and Lasers in Distinct Media

Chapter 3 Plane EM Waves and Lasers in Distinct Media hap Pla Wavs a ass sc a - Nomal Icc a a Pla oucg oua a a Ic pla wav: flcv wav: Toal fl: oucg boua a s Sag wav: Zo ull of a - amum of a -λ Zo ull of a - amum of a -λ g. -pola pla wav f amplu6mvm popagas

More information

Boyce/DiPrima 9 th ed, Ch 7.6: Complex Eigenvalues

Boyce/DiPrima 9 th ed, Ch 7.6: Complex Eigenvalues BocDPm 9 h d Ch 7.6: Compl Egvlus Elm Dffl Equos d Boud Vlu Poblms 9 h do b Wllm E. Boc d Rchd C. DPm 9 b Joh Wl & Sos Ic. W cosd g homogous ssm of fs od l quos wh cos l coffcs d hus h ssm c b w s ' A

More information

Lecture 12: Introduction to nonlinear optics II.

Lecture 12: Introduction to nonlinear optics II. Lcur : Iroduco o olar opcs II r Kužl ropagao of srog opc sgals propr olar ffcs Scod ordr ffcs! Thr-wav mxg has machg codo! Scod harmoc grao! Sum frqucy grao! aramrc grao Thrd ordr ffcs! Four-wav mxg! Opcal

More information

MECE 3320 Measurements & Instrumentation. Static and Dynamic Characteristics of Signals

MECE 3320 Measurements & Instrumentation. Static and Dynamic Characteristics of Signals MECE 330 MECE 330 Masurms & Isrumao Sac ad Damc Characrscs of Sgals Dr. Isaac Chouapall Dparm of Mchacal Egrg Uvrs of Txas Pa Amrca MECE 330 Sgal Cocps A sgal s h phscal formao abou a masurd varabl bg

More information

By Joonghoe Dho. The irradiance at P is given by

By Joonghoe Dho. The irradiance at P is given by CH. 9 c CH. 9 c By Joogo Do 9 Gal Coao 9. Gal Coao L co wo po ouc, S & S, mg moocomac wav o am qucy. L paao a b muc ga a. Loca am qucy. L paao a b muc ga a. Loca po obvao P a oug away om ouc o a a P wavo

More information

11/8/2002 CS 258 HW 2

11/8/2002 CS 258 HW 2 /8/ CS 58 HW. G o a a qc of aa h < fo a I o goa o co a C cc c F ch ha F fo a I A If cc - c a co h aoa coo o ho o choo h o qc? I o g o -coa o o-coa? W ca choo h o qc o h a a h aa a. Tha f o o a h o h a:.

More information

Bethe-Salpeter Equation Green s Function and the Bethe-Salpeter Equation for Effective Interaction in the Ladder Approximation

Bethe-Salpeter Equation Green s Function and the Bethe-Salpeter Equation for Effective Interaction in the Ladder Approximation Bh-Salp Equaon n s Funcon and h Bh-Salp Equaon fo Effcv Inacon n h Ladd Appoxmaon Csa A. Z. Vasconcllos Insuo d Físca-UFRS - upo: Físca d Hadons Sngl-Pacl Popagao. Dagam xpanson of popagao. W consd as

More information

EMA5001 Lecture 3 Steady State & Nonsteady State Diffusion - Fick s 2 nd Law & Solutions

EMA5001 Lecture 3 Steady State & Nonsteady State Diffusion - Fick s 2 nd Law & Solutions EMA5 Lecue 3 Seady Sae & Noseady Sae ffuso - Fck s d Law & Soluos EMA 5 Physcal Popees of Maeals Zhe heg (6) 3 Noseady Sae ff Fck s d Law Seady-Sae ffuso Seady Sae Seady Sae = Equlbum? No! Smlay: Sae fuco

More information

9.6 Spherical Wave Solutions of the Scalar. Chapter 9: Radiating Systems, Multipole Fields and Radiation

9.6 Spherical Wave Solutions of the Scalar. Chapter 9: Radiating Systems, Multipole Fields and Radiation Cha 9: Raag Syss, Muo Fs a Raao A Ovvw of Chas o EM Wavs :(ov hs ous sou wav quao bouay Ch. 7 o a wav sa o wo s- sas saa by h - y a Ch. 8 o oug was - Ch. 9 J, ~ ougog g wav o sb, as a aa - Ch. J, ~ ougog

More information

Chapter 5 Transmission Lines

Chapter 5 Transmission Lines hap 5 asmsso s 5- haacscs of asmsso s asmsso l: has o coucos cay cu o suppo a M av hch s M o quas-m mo. Fo h M mo a H M H M a a M. h cu a h M av hav ff chaacscs. A M av popaas o ff lcc ma h paal flco a

More information

Chap 2: Reliability and Availability Models

Chap 2: Reliability and Availability Models Chap : lably ad valably Modls lably = prob{s s fully fucog [,]} Suppos from [,] m prod, w masur ou of N compos, of whch N : # of compos oprag corrcly a m N f : # of compos whch hav fald a m rlably of h

More information

NLO Basics. Bulk Second Harmonic Generation Examples. QuartzQ ZnO bulk and nanowires Organic nanowires

NLO Basics. Bulk Second Harmonic Generation Examples. QuartzQ ZnO bulk and nanowires Organic nanowires NLO Bascs Bul Scod Hamoc Gao xampls QuaQ ZO bul ad aows Ogac aows Ahamoc Poals U U- P χ χ χ Io P lco pah P Wav quao : quaos Maxwlls D J H B : chags f No 4 H B J D B μ ρ ρ s. : chags f No H H B J μ μ ρ

More information

Control Systems (Lecture note #6)

Control Systems (Lecture note #6) 6.5 Corol Sysms (Lcur o #6 Las Tm: Lar algbra rw Lar algbrac quaos soluos Paramrzao of all soluos Smlary rasformao: compao form Egalus ad gcors dagoal form bg pcur: o brach of h cours Vcor spacs marcs

More information

Geometrical optics. Textbook: Born and Wolf (chapters 3-5) Overview:

Geometrical optics. Textbook: Born and Wolf (chapters 3-5) Overview: Gomal ops Txbook: Bo a Wol aps -5 Ovvw: Elomag pla wavs om maxwll's quaos. T Ekoal quao a s vao ops a o wavlg. Rao ll's law lo Toal al lo T psm Dspso T ls Imagg as a pojv asomao. Opal ssms a ABCD max.

More information

Chapter 5 Transmission Lines

Chapter 5 Transmission Lines ap 5 ao 5- aacc of ao ao l: a o cou ca cu o uppo a M av c M o qua-m o. Fo M o a H M H a M a µ M. cu a M av av ff caacc. A M av popaa o ff lcc a paal flco a paal ao ll occu. A ob follo ul. ll la: p a β

More information

ECE 107: Electromagnetism

ECE 107: Electromagnetism ECE 07: Elcomagnsm S 8: Plan wavs Insuco: Pof. Valy Lomakn Dpamn of Elccal and Compu Engnng Unvsy of Calfona, San Dgo, CA 92093 Wav quaon Souc-f losslss Maxwll s quaons Apply cul = jωμ ε = = jωε μ = 2

More information

Parametric Down Conversion. Quantum optics seminar Winter 2008 Assaf Shaham

Parametric Down Conversion. Quantum optics seminar Winter 2008 Assaf Shaham Paam Dow Covso Quaum ops sma 7774 W 8 ssaf Shaham ox Iouo Thoy of lass Sum Fquy Gao Quaum Hamloa fo PDC pplaos No la ops Cao of w fqus h sysm. Usually h w fqus hav small amplu lav o h pu fqus. Hamo Dff

More information

ANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 2

ANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 2 Joh Rley Novembe ANSWERS O ODD NUMBERED EXERCISES IN CHAPER Seo Eese -: asvy (a) Se y ad y z follows fom asvy ha z Ehe z o z We suppose he lae ad seek a oado he z Se y follows by asvy ha z y Bu hs oads

More information

Convergence tests for the cluster DFT calculations

Convergence tests for the cluster DFT calculations Covgc ss o h clus DF clculos. Covgc wh spc o bss s. s clculos o bss s covgc hv b po usg h PBE ucol o 7 os gg h-b. A s o h Guss bss ss wh csg s usss hs b us clug h -G -G** - ++G(p). A l sc o. Å h c bw h

More information

Lecture 7 Diffusion. Our fluid equations that we developed before are: v t v mn t

Lecture 7 Diffusion. Our fluid equations that we developed before are: v t v mn t Cla ot fo EE6318/Phy 6383 Spg 001 Th doumt fo tutoal u oly ad may ot b opd o dtbutd outd of EE6318/Phy 6383 tu 7 Dffuo Ou flud quato that w dvlopd bfo a: f ( )+ v v m + v v M m v f P+ q E+ v B 13 1 4 34

More information

An Analysis of a Double-layer Electromagnetic Shield for a Universal Contactless Battery Charging Platform

An Analysis of a Double-layer Electromagnetic Shield for a Universal Contactless Battery Charging Platform A Aalyss of a Doubl-lay Elcomagc Shld fo a Uvsal Coaclss Bay Chagg Plafom Absac A pad doubl-lay plaa sucu s mployd o shld h lcomagc EM fld a h boom of a uvsal chagg plafom. Th doubl-lay cosss of a lay

More information

Two-Dimensional Quantum Harmonic Oscillator

Two-Dimensional Quantum Harmonic Oscillator D Qa Haroc Oscllaor Two-Dsoal Qa Haroc Oscllaor 6 Qa Mchacs Prof. Y. F. Ch D Qa Haroc Oscllaor D Qa Haroc Oscllaor ch5 Schrödgr cosrcd h cohr sa of h D H.O. o dscrb a classcal arcl wh a wav ack whos cr

More information

8. Queueing systems. Contents. Simple teletraffic model. Pure queueing system

8. Queueing systems. Contents. Simple teletraffic model. Pure queueing system 8. Quug sysms Cos 8. Quug sysms Rfrshr: Sml lraffc modl Quug dscl M/M/ srvr wag lacs Alcao o ack lvl modllg of daa raffc M/M/ srvrs wag lacs lc8. S-38.45 Iroduco o Tlraffc Thory Srg 5 8. Quug sysms 8.

More information

Statics. Consider the free body diagram of link i, which is connected to link i-1 and link i+1 by joint i and joint i-1, respectively. = r r r.

Statics. Consider the free body diagram of link i, which is connected to link i-1 and link i+1 by joint i and joint i-1, respectively. = r r r. Statcs Th cotact btw a mapulato ad ts vomt sults tactv ocs ad momts at th mapulato/vomt tac. Statcs ams at aalyzg th latoshp btw th actuato dv tous ad th sultat oc ad momt appld at th mapulato dpot wh

More information

Characterizing Optical Thin Films (I)

Characterizing Optical Thin Films (I) Chaaczg Opcal Th Flms (I) Physcal vapo dposo s h mos commo chqu usd o dpos opcal h lms o a lag vay o applcaos. Ths qus h ably o g a sold maal o a vapo (gasous) om, o aspo o a suac oo whch h lm s o b dposd,

More information

Handout on. Crystal Symmetries and Energy Bands

Handout on. Crystal Symmetries and Energy Bands dou o Csl s d g Bds I hs lu ou wll l: Th loshp bw ss d g bds h bs of sp-ob ouplg Th loshp bw ss d g bds h ps of sp-ob ouplg C 7 pg 9 Fh Coll Uvs d g Bds gll hs oh Th sl pol ss ddo o h l slo s: Fo pl h

More information

Posterior analysis of the compound truncated Weibull under different loss functions for censored data.

Posterior analysis of the compound truncated Weibull under different loss functions for censored data. INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 oso yss of h oou u Wu u ff oss fuos fo so. Khw BOUDJRDA Ass CHADI Ho FAG. As I hs h Bys yss of gh u Wu suo s os u y II so. Bys sos osog ss hv v usg

More information

Lecture 23. Multilayer Structures

Lecture 23. Multilayer Structures Lcu Mullay Sucus In hs lcu yu wll lan: Mullay sucus Dlcc an-flcn (AR) cangs Dlcc hgh-flcn (HR) cangs Phnc Band-Gap Sucus C Fall 5 Fahan Rana Cnll Unvsy Tansmssn Ln Juncns and Dscnnus - I Tansmssn ln dscnnus

More information

Partial Fraction Expansion

Partial Fraction Expansion Paial Facion Expanion Whn ying o find h inv Laplac anfom o inv z anfom i i hlpfl o b abl o bak a complicad aio of wo polynomial ino fom ha a on h Laplac Tanfom o z anfom abl. W will illa h ing Laplac anfom.

More information

Bayesian Credibility for Excess of Loss Reinsurance Rating. By Mark Cockroft 1 Lane Clark & Peacock LLP

Bayesian Credibility for Excess of Loss Reinsurance Rating. By Mark Cockroft 1 Lane Clark & Peacock LLP By Cly o c o Lo Rc Rg By M Coco L Cl & Pcoc LLP GIRO coc 4 Ac Th pp c how o v cly wgh w po- pc-v o c o lo c. Th po co o Poo-Po ol ch wh po G o. Kywo c o lo c g By cly Poo Po G po Acowlg cl I wol l o h

More information

Fresnel Equations cont.

Fresnel Equations cont. Lecure 12 Chaper 4 Fresel quaos co. Toal eral refleco ad evaesce waves Opcal properes of meals Laer: Famlar aspecs of he eraco of lgh ad maer Fresel quaos r 2 Usg Sell s law, we ca re-wre: r s s r a a

More information

Chapter 8. Diffraction

Chapter 8. Diffraction Chap 8 Dffacon Pa I Phaso Addon Thom Wha s phaso? In mul-bam nfnc, ach ansmd bam can b xpssd as... 3 N ' ' ' ' ' 4 ' ' n [ n ] d S n q q ' ' ' 3 ' ' 5 '.., h -fld of ach bam s a complx numb n n ' ' A n

More information

Linear Perturbation Bounds of the Continuous-Time LMI-Based H Quadratic Stability Problem for Descriptor Systems

Linear Perturbation Bounds of the Continuous-Time LMI-Based H Quadratic Stability Problem for Descriptor Systems UGRN DE OF ENE ERNE ND NFORON EHNOOGE Volu No 4 ofa a ubao ouds of h ouous- -asd H uadac ably obl fo Dscpo yss dy ochv chcal Uvsy of ofa Faculy of uoacs Dpa of yss ad ool 756 ofa Eal ayochv@u-sofa.bg bsac

More information

The Variance-Covariance Matrix

The Variance-Covariance Matrix Th Varanc-Covaranc Marx Our bggs a so-ar has bn ng a lnar uncon o a s o daa by mnmzng h las squars drncs rom h o h daa wh mnsarch. Whn analyzng non-lnar daa you hav o us a program l Malab as many yps o

More information

(1) Cov(, ) E[( E( ))( E( ))]

(1) Cov(, ) E[( E( ))( E( ))] Impac of Auocorrelao o OLS Esmaes ECON 3033/Evas Cosder a smple bvarae me-seres model of he form: y 0 x The four key assumpos abou ε hs model are ) E(ε ) = E[ε x ]=0 ) Var(ε ) =Var(ε x ) = ) Cov(ε, ε )

More information

Technical Appendix for Inventory Management for an Assembly System with Product or Component Returns, DeCroix and Zipkin, Management Science 2005.

Technical Appendix for Inventory Management for an Assembly System with Product or Component Returns, DeCroix and Zipkin, Management Science 2005. Techc Appedx fo Iveoy geme fo Assemy Sysem wh Poduc o Compoe eus ecox d Zp geme Scece 2005 Lemm µ µ s c Poof If J d µ > µ he ˆ 0 µ µ µ µ µ µ µ µ Sm gumes essh he esu f µ ˆ > µ > µ > µ o K ˆ If J he so

More information

RAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels

RAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels AKE v wh Apv f Cs fo DS-CDMA Ss Muph Fg Chs JooHu Y Su M EEE JHog M EEE Shoo of E Egg Sou o Uvs Sh-og Gw-gu Sou 5-74 Ko E-: ohu@su As hs pp pv AKE v wh vs og s popos fo DS-CDMA ss uph fg hs h popos pv

More information

Direct current regimes in the linear electric circuits according to the relativistic circuit theory

Direct current regimes in the linear electric circuits according to the relativistic circuit theory ISSN: 63-316X (Ol OI: 1.9114/av.vol.ss1.66 Vol Iss 1 (18 Pblshd: 18-6-3 c c gms h la lcc ccs accodg o h lavsc cc ho ml Ivaov Paov 1 1 Tchcal Uvs of Vaa, pam of Thocal lccal gg ad Ismao, 91, 1 Sdsa S, Vaa,

More information

ENGG 1203 Tutorial. Difference Equations. Find the Pole(s) Finding Equations and Poles

ENGG 1203 Tutorial. Difference Equations. Find the Pole(s) Finding Equations and Poles ENGG 03 Tutoial Systms ad Cotol 9 Apil Laig Obctivs Z tasfom Complx pols Fdbac cotol systms Ac: MIT OCW 60, 6003 Diffc Equatios Cosid th systm pstd by th followig diffc quatio y[ ] x[ ] (5y[ ] 3y[ ]) wh

More information

CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane.

CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane. CBSE CBSE SET- SECTION. Gv tht d W d to fd 7 7 Hc, 7 7 7. Lt,. W ow tht.. Thus,. Cosd th vcto quto of th pl.. z. - + z = - + z = Thus th Cts quto of th pl s - + z = Lt d th dstc tw th pot,, - to th pl.

More information

Fourier Series: main points

Fourier Series: main points BIOEN 3 Lcur 6 Fourir rasforms Novmbr 9, Fourir Sris: mai pois Ifii sum of sis, cosis, or boh + a a cos( + b si( All frqucis ar igr mulipls of a fudamal frqucy, o F.S. ca rprs ay priodic fucio ha w ca

More information

ME 343 Control Systems

ME 343 Control Systems ME 343 Cl Sy cu 8 Ocb 8, 009 ME 343 Cl Sy Fall 009 343 R cu Cll Pla R E U Y C - H C D S Y C C R C H Wg h l ga a w a d acg h cld-l l a ga va ME 343 Cl Sy Fall 009 344 Chaacc Equa: R cu 0 Th f h chaacc qua

More information

9.4 Absorption and Dispersion

9.4 Absorption and Dispersion 9.4 Absoon and Dsson 9.4. loagn Wavs n Conduos un dnsy n a onduo ollowng Oh s law: J Th Maxwll s uaons n a onduo lna da should b: ρ B B B J To sly h suaon w agu ha h hag dsaas uly n a aoso od. Fo h onnuy

More information

Suppose we have observed values t 1, t 2, t n of a random variable T.

Suppose we have observed values t 1, t 2, t n of a random variable T. Sppose we have obseved vales, 2, of a adom vaable T. The dsbo of T s ow o belog o a cea ype (e.g., expoeal, omal, ec.) b he veco θ ( θ, θ2, θp ) of ow paamees assocaed wh s ow (whee p s he mbe of ow paamees).

More information

Introduction to Laplace Transforms October 25, 2017

Introduction to Laplace Transforms October 25, 2017 Iroduco o Lplc Trform Ocobr 5, 7 Iroduco o Lplc Trform Lrr ro Mchcl Egrg 5 Smr Egrg l Ocobr 5, 7 Oul Rvw l cl Wh Lplc rform fo of Lplc rform Gg rform b gro Fdg rform d vr rform from bl d horm pplco o dffrl

More information

Chapter 5. Long Waves

Chapter 5. Long Waves ape 5. Lo Waes Wae e s o compaed ae dep: < < L π Fom ea ae eo o s s ; amos ozoa moo z p s ; dosac pesse Dep-aeaed coseao o mass

More information

Department of Mathematics and Statistics Indian Institute of Technology Kanpur MSO202A/MSO202 Assignment 3 Solutions Introduction To Complex Analysis

Department of Mathematics and Statistics Indian Institute of Technology Kanpur MSO202A/MSO202 Assignment 3 Solutions Introduction To Complex Analysis Dpartmt of Mathmatcs ad Statstcs Ida Isttut of Tchology Kapur MSOA/MSO Assgmt 3 Solutos Itroducto To omplx Aalyss Th problms markd (T) d a xplct dscusso th tutoral class. Othr problms ar for hacd practc..

More information

Least squares and motion. Nuno Vasconcelos ECE Department, UCSD

Least squares and motion. Nuno Vasconcelos ECE Department, UCSD Las squars ad moo uo Vascoclos ECE Dparm UCSD Pla for oda oda w wll dscuss moo smao hs s rsg wo was moo s vr usful as a cu for rcogo sgmao comprsso c. s a gra ampl of las squars problm w wll also wrap

More information

Part B: Transform Methods. Professor E. Ambikairajah UNSW, Australia

Part B: Transform Methods. Professor E. Ambikairajah UNSW, Australia Par B: rasform Mhods Profssor E. Ambikairaah UNSW, Ausralia Chapr : Fourir Rprsaio of Sigal. Fourir Sris. Fourir rasform.3 Ivrs Fourir rasform.4 Propris.4. Frqucy Shif.4. im Shif.4.3 Scalig.4.4 Diffriaio

More information

Option Pricing in a Fractional Brownian Motion Environment

Option Pricing in a Fractional Brownian Motion Environment Opo Pcg a acoal owa Moo vom Cpa Ncula Acamy o coomc u ucha, omaa mal: cpc@yahoo.com h a: buay, Abac h pupo o h pap o oba a acoal lack-chol omula o h pc o a opo o vy [, ], a acoal lack-chol quao a a k-ual

More information

Get Funky this Christmas Season with the Crew from Chunky Custard

Get Funky this Christmas Season with the Crew from Chunky Custard Hol Gd Chcllo Adld o Hdly Fdy d Sudy Nhs Novb Dcb 2010 7p 11.30p G Fuky hs Chss Sso wh h Cw fo Chuky Cusd Fdy Nhs $99pp Sudy Nhs $115pp Tck pc cluds: Full Chss d buff, 4.5 hou bv pck, o sop. Ts & Codos

More information

(ΔM s ) > (Δ M D ) PARITY CONDITIONS IN INTERNATIONAL FINANCE AND CURRENCY FORECASTING INFLATION ARBITRAGE AND THE LAW OF ONE PRICE

(ΔM s ) > (Δ M D ) PARITY CONDITIONS IN INTERNATIONAL FINANCE AND CURRENCY FORECASTING INFLATION ARBITRAGE AND THE LAW OF ONE PRICE PARITY CONDITIONS IN INTERNATIONAL FINANCE AND CURRENCY FORECASTING Fv Pay Condons Rsul Fom Abag Acvs 1. Pucasng Pow Pay (PPP). T Fs Ec (FE) 3. T Innaonal Fs Ec (IFE) 4. Ins Ra Pay (IRP) 5. Unbasd Fowad

More information

Reliability Equivalence of Independent Non-identical Parallel and Series Systems.

Reliability Equivalence of Independent Non-identical Parallel and Series Systems. Lf Scc Jua 0;9(3) h://wwwfccc aby Euvac f Idd N-dca Paa ad S Sy Yuy Abdad 3 ; A I Shawy ad M I A-Ohay D f Mah acuy f Scc Uvy f Daa KSA D f Sac acuy f Scc Kg Abduazz Uvy PO Bx 8003 Jddah 589 Saud Aaba 3

More information

EffectofMagneticFieldonOscillatoryFlowPastParallelPlatesinaRotatingSystemwithHeatandMassTransfer

EffectofMagneticFieldonOscillatoryFlowPastParallelPlatesinaRotatingSystemwithHeatandMassTransfer Global Joual of Scc Fo Rsach: F Mahmacs a Dcso Sccs Volum 4 Issu 4 Vso. Ya 4 yp : Doubl Bl P Rw Iaoal Rsach Joual Publsh: Global Jouals Ic. (SA Ol ISSN: 49-466 & P ISSN: 975-5896 Effc of Magc Fl o Oscllaoy

More information

Dielectric Waveguide 1

Dielectric Waveguide 1 Dilctic Wavgui Total Ital Rflctio i c si c t si si t i i i c i Total Ital Rflctio i c i cos si Wh i t i si c si cos t j o cos t t o si i si bcoms pul imagia pul imagia i, al Total Ital Rflctio 3 i c i

More information

Bayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data

Bayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data Bys Eso of h s of h Wull-Wull gh-bs xu suos usg so S. A. Sh N Bouss I.S.S. Co Uvsy I.N.P.S. Algs Uvsy shsh@yhoo.o ou005@yhoo.o As I hs h s of h Wull-Wull lgh s xu suos s usg h Gs slg hqu u y I sog sh.

More information

Mathematical Statistics. Chapter VIII Sampling Distributions and the Central Limit Theorem

Mathematical Statistics. Chapter VIII Sampling Distributions and the Central Limit Theorem Mahmacal ascs 8 Chapr VIII amplg Dsrbos ad h Cral Lm Thorm Fcos of radom arabls ar sall of rs sascal applcao Cosdr a s of obsrabl radom arabls L For ampl sppos h arabls ar a radom sampl of s from a poplao

More information

Professor Wei Zhu. 1. Sampling from the Normal Population

Professor Wei Zhu. 1. Sampling from the Normal Population AMS570 Pofesso We Zhu. Samplg fom the Nomal Populato *Example: We wsh to estmate the dstbuto of heghts of adult US male. It s beleved that the heght of adult US male follows a omal dstbuto N(, ) Def. Smple

More information

Homework 1: Solutions

Homework 1: Solutions Howo : Solutos No-a Fals supposto tst but passs scal tst lthouh -f th ta as slowss [S /V] vs t th appaac of laty alty th path alo whch slowss s to b tat to obta tavl ts ps o th ol paat S o V as a cosquc

More information

Consider a system of 2 simultaneous first order linear equations

Consider a system of 2 simultaneous first order linear equations Soluon of sysms of frs ordr lnar quaons onsdr a sysm of smulanous frs ordr lnar quaons a b c d I has h alrna mar-vcor rprsnaon a b c d Or, n shorhand A, f A s alrady known from con W know ha h abov sysm

More information

Series of New Information Divergences, Properties and Corresponding Series of Metric Spaces

Series of New Information Divergences, Properties and Corresponding Series of Metric Spaces Srs of Nw Iforao Dvrgcs, Proprs ad Corrspodg Srs of Mrc Spacs K.C.Ja, Praphull Chhabra Profssor, Dpar of Mahacs, Malavya Naoal Isu of Tchology, Japur (Rajasha), Ida Ph.d Scholar, Dpar of Mahacs, Malavya

More information

A KAM theorem for generalized Hamiltonian systems without action-angle variables

A KAM theorem for generalized Hamiltonian systems without action-angle variables ho fo gald aloa sss whou ao-agl vaabls Yo u Jo u wa Jog : aual L UG Uvs Pogag oa Popl s publ of oa : Faul of ahas L UG Uvs Pogag oa Popl s publ of oa bsa povd a ho o s of vaa o gald aloa sss whou ao-agl

More information

The ray paths and travel times for multiple layers can be computed using ray-tracing, as demonstrated in Lab 3.

The ray paths and travel times for multiple layers can be computed using ray-tracing, as demonstrated in Lab 3. C. Trael me cures for mulple reflecors The ray pahs ad rael mes for mulple layers ca be compued usg ray-racg, as demosraed Lab. MATLAB scrp reflec_layers_.m performs smple ray racg. (m) ref(ms) ref(ms)

More information

Today s topic 2 = Setting up the Hydrogen Atom problem. Schematic of Hydrogen Atom

Today s topic 2 = Setting up the Hydrogen Atom problem. Schematic of Hydrogen Atom Today s topic Sttig up th Hydog Ato pobl Hydog ato pobl & Agula Motu Objctiv: to solv Schödig quatio. st Stp: to dfi th pottial fuctio Schatic of Hydog Ato Coulob s aw - Z 4ε 4ε fo H ato Nuclus Z What

More information

Integrated Optical Waveguides

Integrated Optical Waveguides Su Opls Faha Raa Cll Uvs Chap 8 Ia Opal Wavus 7 Dl Slab Wavus 7 Iu: A va f ff a pal wavus a us f a u lh a hp Th s bas pal wavu s a slab wavus shw blw Th suu s uf h - Lh s u s h b al al fl a h -la fas Cla

More information

School of Aerospace Engineering Origins of Quantum Theory. Measurements of emission of light (EM radiation) from (H) atoms found discrete lines

School of Aerospace Engineering Origins of Quantum Theory. Measurements of emission of light (EM radiation) from (H) atoms found discrete lines Ogs of Quatu Thoy Masuts of sso of lght (EM adato) fo (H) atos foud dsct ls 5 4 Abl to ft to followg ss psso ν R λ c λwavlgth, νfqucy, cspd lght RRydbg Costat (~09,7677.58c - ),,, +, +,..g.,,.6, 0.6, (Lya

More information

The Linear Regression Of Weighted Segments

The Linear Regression Of Weighted Segments The Lear Regresso Of Weghed Segmes George Dael Maeescu Absrac. We proposed a regresso model where he depede varable s made o up of pos bu segmes. Ths suao correspods o he markes hroughou he da are observed

More information

3.4 Properties of the Stress Tensor

3.4 Properties of the Stress Tensor cto.4.4 Proprts of th trss sor.4. trss rasformato Lt th compots of th Cauchy strss tsor a coordat systm wth bas vctors b. h compots a scod coordat systm wth bas vctors j,, ar gv by th tsor trasformato

More information

Key words: Fractional difference equation, oscillatory solutions,

Key words: Fractional difference equation, oscillatory solutions, OSCILLATION PROPERTIES OF SOLUTIONS OF FRACTIONAL DIFFERENCE EQUATIONS Musafa BAYRAM * ad Ayd SECER * Deparme of Compuer Egeerg, Isabul Gelsm Uversy Deparme of Mahemacal Egeerg, Yldz Techcal Uversy * Correspodg

More information

Dr. Junchao Xia Center of Biophysics and Computational Biology. Fall /21/2016 1/23

Dr. Junchao Xia Center of Biophysics and Computational Biology. Fall /21/2016 1/23 BIO53 Bosascs Lcur 04: Cral Lm Thorm ad Thr Dsrbuos Drvd from h Normal Dsrbuo Dr. Juchao a Cr of Bophyscs ad Compuaoal Bology Fall 06 906 3 Iroduco I hs lcur w wll alk abou ma cocps as lsd blow, pcd valu

More information

Let's revisit conditional probability, where the event M is expressed in terms of the random variable. P Ax x x = =

Let's revisit conditional probability, where the event M is expressed in terms of the random variable. P Ax x x = = L's rvs codol rol whr h v M s rssd rs o h rdo vrl. L { M } rrr v such h { M } Assu. { } { A M} { A { } } M < { } { } A u { } { } { A} { A} ( A) ( A) { A} A A { A } hs llows us o cosdr h cs wh M { } [ (

More information

Correlation in tree The (ferromagnetic) Ising model

Correlation in tree The (ferromagnetic) Ising model 5/3/00 :\ jh\slf\nots.oc\7 Chaptr 7 Blf propagato corrlato tr Corrlato tr Th (frromagtc) Isg mol Th Isg mol s a graphcal mol or par ws raom Markov fl cosstg of a urct graph wth varabls assocat wth th vrtcs.

More information

A Proportional Differentiation Model Based on Service Level

A Proportional Differentiation Model Based on Service Level ppl. ah. If. c. 6 o. pp. 453-46 ppld ahmacs & Ifomao ccs Iaoal Joual @ aual ccs ublshg Co. opooal Dffao odl d o vc Lvl K-o Cho Dpam of Idusal & aagm gg Hau Uvsy of og uds Yog 449-79 Koa Cospodg auho: mal:

More information

Hygienic Cable Glands

Hygienic Cable Glands ygc bl Gld followg h cll WA l h Mufcug h l oo c y Bocholog du hcl du: vodg buld-u cy. Gl bl ygc l food d d ckgg of ology y o o d u of ud ll ld hcucl wh hy ovd h f u o h cl o h o dh ooh fh No hd cod o d

More information

Note 6 Frequency Response

Note 6 Frequency Response No 6 Frqucy Rpo Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada. alyical Exprio

More information

EQUATION SHEETS FOR ELEC

EQUATION SHEETS FOR ELEC QUTON SHTS FO C 47 Fbuay 7 QUTON SHTS FO C 47 Fbuay 7 hs hυ h ω ( J ) h.4 ω υ ( µ ) ( ) h h k π υ ε ( / s ) G Os (Us > x < a ) Sll s aw s s s Shal z z Shal buay (, aus ) z y y z z z Shal ls ( s sua, s

More information

International Journal of Scientific & Engineering Research, Volume 7, Issue 5, May-2016 ISSN The Maximum Eccentricity Energy of a Graph

International Journal of Scientific & Engineering Research, Volume 7, Issue 5, May-2016 ISSN The Maximum Eccentricity Energy of a Graph Iaoa Joa of cfc & Egg Rsach Vom 7 Iss 5 ay6 IN 955 5 Th axmm Ecccy Egy of a Gaph Ahmd Na ad N D o Absac I Ths pap w odc h cocp of a maxmm cccy max oba som coffcs of h chaacsc poyoma of a cocd gaph G ad

More information

GNSS-Based Orbit Determination for Highly Elliptical Orbit Satellites

GNSS-Based Orbit Determination for Highly Elliptical Orbit Satellites -Bd D f Hghy p Q,*, ug, Ch Rz d Jy u Cg f u gg, g Uvy f u d u, Ch :6--987, -:.q@ud.uw.du. h f uvyg d p If y, Uvy f w uh W, u : h Hghy p H ufu f y/yhu f h dgd hv w ud pg h d hgh ud pg h f f h f. Du h g

More information

For the plane motion of a rigid body, an additional equation is needed to specify the state of rotation of the body.

For the plane motion of a rigid body, an additional equation is needed to specify the state of rotation of the body. The kecs of rgd bodes reas he relaoshps bewee he exeral forces acg o a body ad he correspodg raslaoal ad roaoal moos of he body. he kecs of he parcle, we foud ha wo force equaos of moo were requred o defe

More information

Homework: Introduction to Motion

Homework: Introduction to Motion Homwork: Inroducon o Moon Dsanc vs. Tm Graphs Nam Prod Drcons: Answr h foowng qusons n h spacs provdd. 1. Wha do you do o cra a horzona n on a dsancm graph? 2. How do you wak o cra a sragh n ha sops up?

More information

CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find

CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find BSE SMLE ER SOLUTONS LSS-X MTHS SET- BSE SETON Gv tht d W d to fd 7 7 Hc, 7 7 7 Lt, W ow tht Thus, osd th vcto quto of th pl z - + z = - + z = Thus th ts quto of th pl s - + z = Lt d th dstc tw th pot,,

More information

Lecture 3 summary. C4 Lecture 3 - Jim Libby 1

Lecture 3 summary. C4 Lecture 3 - Jim Libby 1 Lecue su Fes of efeece Ivce ude sfoos oo of H wve fuco: d-fucos Eple: e e - µ µ - Agul oeu s oo geeo Eule gles Geec slos cosevo lws d Noehe s heoe C4 Lecue - Lbb Fes of efeece Cosde fe of efeece O whch

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

A New Dynamic Random Fuzzy DEA Model to Predict Performance of Decision Making Units

A New Dynamic Random Fuzzy DEA Model to Predict Performance of Decision Making Units Jo o Ozo I Egg 6 75-9 A w D Ro Fzz DEA Mo o P Po o Do Mg U A gho * Mgho A Azoh S Sgh A Poo D o I Egg F o Egg P--oo U Th I Poo D o I Mg Ah T U Th I A Poo D o I Egg F o Egg P--oo U Th I R Oo 4; R 3 J 5;

More information

It is distinctly Kansas City Kansas City began as a trading post for early 18th century settlers traveling along the Missouri River.

It is distinctly Kansas City Kansas City began as a trading post for early 18th century settlers traveling along the Missouri River. mhw km gyo cho uo juy - my 2009 commuy v cy mk HYBRID RE-ENVISIONED Iv G Roof why h v cy mk? By uzg g oof ym h bu fo hvy uy u, h pojc g w mo. Th oof bcom pygou, g, occ f, pc o pcc T Ch, mo. I off omhg

More information

CONTENTS. Hugo Reitzel, the pickles enthusiast CERTIFICATIONS JARS POUCHES & CANS SALAD DRESSING MINI-TUBES

CONTENTS. Hugo Reitzel, the pickles enthusiast CERTIFICATIONS JARS POUCHES & CANS SALAD DRESSING MINI-TUBES v4. APRIL 2018. Hugo Rz, h pk hu Th of h uhd gu g ou Hugo Rz. I 1909, Ag, Sw vg, h uhd h ow op wh vo: o p up h wod of od! Ad fo ov o hudd ow, w hoo h hg b ug ou xp o o ov ou bu od o bo THE od p. W ufu

More information

Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables

Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables Improvd Epoal Emaor for Populao Varac Ug Two Aular Varabl Rajh gh Dparm of ac,baara Hdu Uvr(U.P., Ida (rgha@ahoo.com Pakaj Chauha ad rmala awa chool of ac, DAVV, Idor (M.P., Ida Flor maradach Dparm of

More information

Gauge Theories. Elementary Particle Physics Strong Interaction Fenomenology. Diego Bettoni Academic year

Gauge Theories. Elementary Particle Physics Strong Interaction Fenomenology. Diego Bettoni Academic year Gau Thors Elmary Parcl Physcs Sro Iraco Fomoloy o Bo cadmc yar - Gau Ivarac Gau Ivarac Whr do Laraas or Hamloas com from? How do w kow ha a cra raco should dscrb a acual hyscal sysm? Why s h lcromac raco

More information

Non-Equidistant Multi-Variable Optimum Model with Fractional Order Accumulation Based on Vector Continued Fractions Theory and its Application

Non-Equidistant Multi-Variable Optimum Model with Fractional Order Accumulation Based on Vector Continued Fractions Theory and its Application QIYUN IU NON-EQUIDISN MUI-VRIE OPIMUM MODE WIH FRCION ORDER... No-Equds Mu-V Ou Mod w Fco Od ccuuo sd o Vco Coud Fcos o d s co Qu IU * D YU. S oo o dcd Dsg d Mucu o Vc od Hu Us Cgs Hu 8 C. Cog o Mcc Egg

More information

Chapter 21: Connecting with a Network

Chapter 21: Connecting with a Network Pag 319 This chap discusss how o us h BASIC-256 wokig sams. Nwokig i BASIC-256 will allow fo a simpl "sock" cocio usig TCP (Tasmissio Cool Poocol). This chap is o ma o b a full ioducio o TCP/IP sock pogammig.

More information

Convolution of Generated Random Variable from. Exponential Distribution with Stabilizer Constant

Convolution of Generated Random Variable from. Exponential Distribution with Stabilizer Constant Appld Mamacal Scc Vol 9 5 o 9 78-789 HIKARI Ld wwwm-acom p://dxdoog/988/am5559 Covoluo of Gad Radom Vaabl fom Expoal Dbuo w Sablz Coa Dod Dvao Maa Lufaa Oaa ad Maa Aa Dpam of Mamac Facul of Mamac ad Naual

More information

Minimizing spherical aberrations Exploiting the existence of conjugate points in spherical lenses

Minimizing spherical aberrations Exploiting the existence of conjugate points in spherical lenses Mmzg sphecal abeatos Explotg the exstece of cojugate pots sphecal leses Let s ecall that whe usg asphecal leses, abeato fee magg occus oly fo a couple of, so called, cojugate pots ( ad the fgue below)

More information

4/12/2018. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105. Plan for Lecture 34: Review radiating systems

4/12/2018. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105. Plan for Lecture 34: Review radiating systems PHY 7 Eodynams 9-9:5 M MWF On 5 Pan o u : Rvw adang sysms Souon o Maxw s quaons wh sous Tm pod sous Examps //8 PHY 7 Spng 8 -- u //8 PHY 7 Spng 8 -- u Gna vw -- SI uns mosop o vauum om ( P M ): Couombs

More information

ELECTROMAGNETISM, NUCLEAR STRUCTURES & GRAVITATION

ELECTROMAGNETISM, NUCLEAR STRUCTURES & GRAVITATION . l & a s s Vo Flds o as l axwll a l sla () l Fld () l olasao () a Flx s () a Fld () a do () ad è s ( ). F wo Sala Flds s b dd l a s ( ) ad oool a s ( ) a oal o 4 qaos 3 aabls - w o Lal osas - oz abo Lal-Sd

More information