- - t D -!> TO. z. $1 V\c..t. - - To. e- 0 ~ "'2'('\" ~~1( ---->-... .;. s-c ().)e.. t..o.y\ w ('\ ~-e._. To :::. \ ~ ~ = T() c~> f.::.

Size: px
Start display at page:

Download "- - t D -!> TO. z. $1 V\c..t. - - To. e- 0 ~ "'2'('\" ~~1( ---->-... .;. s-c ().)e.. t..o.y\ w ('\ ~-e._. To :::. \ ~ ~ = T() c~> f.::."

Transcription

1 j_, \i~ \_t>~ Tc ~ 1-a... i-e_ -ztl ~\G\.Y\S? ' e.j. Ti> ::::. l.sec:. 9 "f"'lft 0. t L 'A -zrr \f''4el..4(' c... Tc Tb=- ;1o 11.. c_ => J () 't '2Tlv-~~ec. - - To $,'b \j'-o t-o,}rt.\m - 'Z. Tr - - CQ. \.l ~l.s L..-l) - '2.\1 z. $1 V\c..t. To 'ro~/;ec e- 0 ~ "'2'('\" ~~1( ---->-... t D -!> TO ~ ~ ~. ~To l f\.r u """be'(- C)f c.~ c\e~/jec... = - 70 To :::. \ ~ ~ = T() c~> f.::. lo t+s.;. s-c ().)e.. t..o.y\ w ('\ ~-e._ )0 i< L \:) -::- A~ ( w 0 -b) W\i V\_ Wot.:. 0 Mrl '2..lT f I) t-.::: e -= f ~tq_ 1Je"'c.'1 J~ rteat-5!$ z,4 Pa I (p

2 % Table of frequency and Period clc,clear all format rat % Fractions frequency = [ ] ; period= 1./[frequency]; % c = rdivide(a,b) and c = a./b perform right-array division %by dividing each element of a by the corresponding element of b. %If inputs a and b are not the same s i ze, %one of them must be a scalar value. % % One Way to do it - display and align A=[frequency;period] '; % Make 2X6 Array disp( ' frequency-hz period-seconds' ) disp (A) % Better way Make a table varnames={ 'Frequency', 'Period' } T=table(frequency',period', 'VariableNames',{ 'Frequency', 'Period' }) frequency-hz period-seconds 1 1 / 10 1 / / / / varnames = lx2 cell array { 'Frequency' } {'Period'} T 6x2 table Frequency Period le+os le-05 Published with MATLAB R20 I Ba

3 18 CHAPTER 2 SINUSOIDS 2-4 I.. ' rcn~ '~. - I t - I t - I 0 I t (a) (b) (c) / Figure 2-8 Illustration of time-shifting: (a) the triangular signal s(t); (b) shifted to the right by 2 s, x1 (t) = s(t - 2); (c) shifted to the left by 1 s, x2(t) = s(t + 1). j EXERCISE 2.2 Derive the equations for the shifted signal x2(t) = s(t + 1). We will have many occasions to consider time-shifted signals. Whenever a signal can be expressed in the form x 1 (t) = s(t - t 1 ), we say that x 1 (t) is a time-shifted version of s(t). If t 1 is a positive number, then the shift is to the right, and we say that the signal s(t) has been delayed in time. When t 1 is a negative number, then the shift is to the left, and we say that the signal s(t) was advanced in time. In summary, time shifting is essentially a redefinition of the time origin of the signal. In general, any function of the forms (t - t 1 ) has its time origin moved to the location t = t 1 For a sinusoid, the time shift is defined ~ith respect to a zero-phase cosine that has a positive peak at t = 0. Since a sinusoid has many positive peaks, we must pick one to define the time shift, so we pick the positive peak of the sinusoid that is closest tot = 0. In the plot of Fig. 2-6, the time where this positive peak occurs is t 1 = s.'since the peak in this case occurs at a positive time (to the right oft = 0), we say that the time shift is a delay of the zero-phase cosine signal. Now we can relate the time delay to phase. Let x 0 (t) = A cos(wot) denote a cosine signal with zero phase. A delay of x 0 (t) can be converted to a phase <p by making the following comparison: vjf;l\ C-~ \ xo(t - t i ) =A cos (wo(t - t1)) =A cos(wot + <p). c; l ~ f'd.:r> => cos(w 0 t - wot1) = cos(wot + <p) e o..'f'i J-. f 'fi '-S~ince the second equation must hold for all t, we conclude that <p = -w 0 t 1 Notice that -\\'JV'-. \o ~ '&' the ph~j.s _!!egative when the time sb!!t t 1 is positive (a del'!y ~ We can also express the Q ~~ ~ v\ 1:. phase in terms of the period (To = 1 /Jo) wliere we get the more intuitive formula S ~ ~ -'::>c'0 v S"'~ ( t ) ~ 1 -r(l '1 '\11'-Q._. -S t f\ <p = -w 0 t 1 = - 2rr _..!... (2.7a) ~ ~ '\"'~ 11 1~1 which states that the phase is 2rr times the fraction of a period given by the ratio of the "W time shift to the period. If we need to get the time shift from the phase, we solve for t 1 DEMO Sine Drill <p <p <pto t, = - - = --- = -- Wo 2rrfo 2rr (2.7b) Since the pos1t1ve peak nearest to t = 0 must always lie within the interval [ -~ To, ~ T 0 ], the phase calculated in (2.7a) will always satisfy - rr < <p ::: rr. However,

4 J:>-e /t:a-t..tt.~ q ~ ~n. ;e.'-'v\cls ( Sc } ~ c..-\ 't 7-. '--/l 'f'g<.d / ~ Yl.-' -= I"' t U>~ ::.. Pe..r-10~ -=. '1 C ycj ~ ).f.6.m.tf.._ <=. qc ~ UQ\'\Cl1 S <D _J -::= +--dr.lom-1 t-~ ~-c. ~'fv"+ 1.e. +t:,ml -z._tr T CZ-.~~MPl--\: z.rr <'tt.~ j ~ f ~ / uo\ ; ;,~, ~'t 1n +-C.. S\q\-t fuf' A CA-a.-( 2-rr+ - {!) ~A ~&::t-t-t,j] l~-v\l. f-~j ~ 0 T= t.s.ee- ~ Sl-.14- f;-,t,t,jo..{ ~ ~ 77 lc T ~ ~ I:. ~He_ e.-1,..eq: i 27T:. <1jLJ J,, 11/2.-- ~ r:::. )4>ec ~A~ Grr(~ -Vf)l 1il Yz_ I ' '

5 +=- 6)141\ \) o Sc~ ' ~ ~ (._,,... 2-rr ~~ \. C1 2, 1 p ~ t {) \o ~l 271 Cfltot -b 1 1t rr) - 0 i 2.. ~ (),,~7_ c z ( l 7 Y/;(_ s ) =- oyts tf.vt ~

6 ;oms 0 ' G.C'S ~LV1 l 0 z-3 SINUSOIDAL SIGNALS Yr-t... Y-r'2-15 ~GJ 'll-- $& I' so we define the phase to be cp = cp' - TC /2 in (2.2). For simplicity and to prevent confusion, we often avoid using the sine function. t. ( c) w 0 is called the radian frequency. Since the argument of the cosine function must be in radians, which is dimensionless, the quantity wot must likewise be dimensionless. Thus, w 0 must have units of rad/sift has units of seconds. Similarly, Jo= w 0 /2n is called the cyclic frequency, and Jo must have units of s- 1, or hertz. ssions netric ntities.tu ting tmple,.ty 1 book on for s 96l, Sinusoids EXAMPLE 2-1 Plotting Sinusoids Figure 2-6 shows a plot of the signal x(t) = 20cos(2n(40)t - 0.4n) (2.3) In terms of our definitions, the signal parameters are A = 20, wo = 2n ( 40) rad/s, Jo = 40 Hz, and cp = -0.4n rad. The signal size depends on the amplitude parameter A; its maximum and minimum values are +20 and -20, respectively. In Fig. 2-6 the maxima occur at and the minima at t =..., -0.02, 0.005, 0.03,......, , , ,... The time interval between successive maxima in Fig. 2-6 is s, which is equal to 1 / J 0. To understand why the signal has these properties, we will need to do more analysis. naking lowing (2.2) 1endent es how +1 and gument unction 1e, e.g.,. use the Relation of Frequency to Period IO x(t) 0-10 The sinusoid plotted in Fig. 2-6 is a periodic signal. The period of the sinusoid, denoted by T 0, is the time duration of one cycle of the sinusoid. In general, the frequency of the sinusoid determines its period, and the relationship can be found by applying the definition of periodicity x(t + T 0 ) = x(t) as follows: Vd-.,n \[ e,ef' '1,t}.,LJ> _,_~... ~~...,,.G "--... ~~.L.-~-'--'-'-'-~~ ~10 i'\? Ti,me t (s) 5..-vi> Ju~V\'f Jo 2.Tf' F Q, ~ ::-XU <<Jl_ ~l~!),,\ Figure 2-6 Sinusoidal signal with parameters A= 20, wo = 2rr(40), fo = 40 Hz, and <p = -0.4rr rad. Pvuo~'c... t:- :::-_.; nt.s to /l1~~t Tb -~ '/(i:> )t:q_ f<u\..e_ ~ Fo""

7 % Plot of cosine and shifted cosine % 20*cosine(2*pi* *pi) vs 20*cosine(2*pi*40) % TO= 1/40 = 25ms. Consider a time axis from to seconds taxis= -. 04:. 001:.04; xl=cos (2*pi*40*taxis) ; x2=cos(2*pi*40*taxis -0.4*pi); subplot(2,1,1); plot(taxis,xl) subplot(2,1,2); plot(taxis,x2) grid on Published with MATLAB R20 I Ba

8 LA l3eg~ ~(N ~ F=-1 ~ L> r<..c,...t od L5-0.5 X:O Y: ,,_.'-----'-~~-'-~-"-"--'--~----'~~-'--"-"-~-'--~~..,......J O.D '------"'..L...l..~~---L-~~...l...""'-L ~~----'-~~'...l..._~~.l..._~----J Time in Seconds - DSPf PG 15

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I $T1P#(

More information

Chapter II TRIANGULAR NUMBERS

Chapter II TRIANGULAR NUMBERS Chapter II TRIANGULAR NUMBERS Part of this work contained in this chapter has resulted in the following publications: Gopalan, M.A. and Jayakuar, P. "Note on triangular nubers in arithetic progression",

More information

K E L LY T H O M P S O N

K E L LY T H O M P S O N K E L LY T H O M P S O N S E A O LO G Y C R E ATO R, F O U N D E R, A N D PA R T N E R K e l l y T h o m p s o n i s t h e c r e a t o r, f o u n d e r, a n d p a r t n e r o f S e a o l o g y, a n e x

More information

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No xhibit 2-9/3/15 Invie Filing Pge 1841 f Pge 366 Dket. 44498 F u v 7? u ' 1 L ffi s xs L. s 91 S'.e q ; t w W yn S. s t = p '1 F? 5! 4 ` p V -', {} f6 3 j v > ; gl. li -. " F LL tfi = g us J 3 y 4 @" V)

More information

i;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s

i;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s 5 C /? >9 T > ; '. ; J ' ' J. \ ;\' \.> ). L; c\ u ( (J ) \ 1 ) : C ) (... >\ > 9 e!) T C). '1!\ /_ \ '\ ' > 9 C > 9.' \( T Z > 9 > 5 P + 9 9 ) :> : + (. \ z : ) z cf C : u 9 ( :!z! Z c (! $ f 1 :.1 f.

More information

Prof. Shayla Sawyer CP08 solution

Prof. Shayla Sawyer CP08 solution What does the time constant represent in an exponential function? How do you define a sinusoid? What is impedance? How is a capacitor affected by an input signal that changes over time? How is an inductor

More information

SOLUTION SET. Chapter 9 REQUIREMENTS FOR OBTAINING POPULATION INVERSIONS "LASER FUNDAMENTALS" Second Edition. By William T.

SOLUTION SET. Chapter 9 REQUIREMENTS FOR OBTAINING POPULATION INVERSIONS LASER FUNDAMENTALS Second Edition. By William T. SOLUTION SET Chapter 9 REQUIREMENTS FOR OBTAINING POPULATION INVERSIONS "LASER FUNDAMENTALS" Second Edition By William T. Silfvast C.11 q 1. Using the equations (9.8), (9.9), and (9.10) that were developed

More information

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone. OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

9 Mixed Exercise. vector equation is. 4 a

9 Mixed Exercise. vector equation is. 4 a 9 Mixed Exercise a AB r i j k j k c OA AB 7 i j 7 k A7,, and B,,8 8 AB 6 A vector equation is 7 r x 7 y z (i j k) j k a x y z a a 7, Pearson Education Ltd 7. Copying permitted for purchasing institution

More information

Laplace Transform Analysis of Signals and Systems

Laplace Transform Analysis of Signals and Systems Laplace Transform Analysis of Signals and Systems Transfer Functions Transfer functions of CT systems can be found from analysis of Differential Equations Block Diagrams Circuit Diagrams 5/10/04 M. J.

More information

SOUTHWESTERN ELECTRIC POWER COMPANY SCHEDULE H-6.1b NUCLEAR UNIT OUTAGE DATA. For the Test Year Ended March 31, 2009

SOUTHWESTERN ELECTRIC POWER COMPANY SCHEDULE H-6.1b NUCLEAR UNIT OUTAGE DATA. For the Test Year Ended March 31, 2009 Schedule H-6.lb SOUTHWSTRN LCTRIC POWR COMPANY SCHDUL H-6.1b NUCLAR UNIT OUTAG DATA For the Test Year nded March 31, 29 This schedule is not applicable to SVvPCO. 5 Schedule H-6.1 c SOUTHWSTRN LCTRIC POWR

More information

SOLUTION SET. Chapter 8 LASER OSCILLATION ABOVE THRESHOLD "LASER FUNDAMENTALS" Second Edition

SOLUTION SET. Chapter 8 LASER OSCILLATION ABOVE THRESHOLD LASER FUNDAMENTALS Second Edition SOLUTION SET Chapter 8 LASER OSCILLATION ABOVE THRESHOLD "LASER FUNDAMENTALS" Second Edition By William T. Silfvast - 1. An argon ion laser (as shown in Figure 10-S(b)) operating at 488.0 nm with a gainregion

More information

~,. :'lr. H ~ j. l' ", ...,~l. 0 '" ~ bl '!; 1'1. :<! f'~.., I,," r: t,... r':l G. t r,. 1'1 [<, ."" f'" 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'..

~,. :'lr. H ~ j. l' , ...,~l. 0 ' ~ bl '!; 1'1. :<! f'~.., I,, r: t,... r':l G. t r,. 1'1 [<, . f' 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'.. ,, 'l t (.) :;,/.I I n ri' ' r l ' rt ( n :' (I : d! n t, :?rj I),.. fl.),. f!..,,., til, ID f-i... j I. 't' r' t II!:t () (l r El,, (fl lj J4 ([) f., () :. -,,.,.I :i l:'!, :I J.A.. t,.. p, - ' I I I

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

S U E K E AY S S H A R O N T IM B E R W IN D M A R T Z -PA U L L IN. Carlisle Franklin Springboro. Clearcreek TWP. Middletown. Turtlecreek TWP.

S U E K E AY S S H A R O N T IM B E R W IN D M A R T Z -PA U L L IN. Carlisle Franklin Springboro. Clearcreek TWP. Middletown. Turtlecreek TWP. F R A N K L IN M A D IS O N S U E R O B E R T LE IC H T Y A LY C E C H A M B E R L A IN T W IN C R E E K M A R T Z -PA U L L IN C O R A O W E N M E A D O W L A R K W R E N N LA N T IS R E D R O B IN F

More information

Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.

Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4. te SelfGi ZltAn Dbnyei Intdtin ; ) Q) 4 t? ) t _ 4 73 y S _ E _ p p 4 t t 4) 1_ ::_ J 1 `i () L VI O I4 " " 1 D 4 L e Q) 1 k) QJ 7 j ZS _Le t 1 ej!2 i1 L 77 7 G (4) 4 6 t (1 ;7 bb F) t f; n (i M Q) 7S

More information

Nrer/ \f l xeaoe Rx RxyrZH IABXAP.qAATTAJI xvbbqaat KOMnAHT1. rvfiqgrrox 3Axl4 Pn br H esep fiyraap: qa/oq YnaaH6aarap xor

Nrer/ \f l xeaoe Rx RxyrZH IABXAP.qAATTAJI xvbbqaat KOMnAHT1. rvfiqgrrox 3Axl4 Pn br H esep fiyraap: qa/oq YnaaH6aarap xor 4 e/ f l ee R RyZH BXP.J vbb KOMnH1 vfig 3l4 Pn b H vlun @*,/capn/t eep fiyaap: a/ YnaaH6aaap eneaneee 6ana tyail CaHafiu cafigun 2015 Hu 35 nyaap l'p 6ana4caH "Xe4ee a aylzh abap gaan" XKailH gypeu"uzn

More information

r(j) -::::.- --X U.;,..;...-h_D_Vl_5_ :;;2.. Name: ~s'~o--=-i Class; Date: ID: A

r(j) -::::.- --X U.;,..;...-h_D_Vl_5_ :;;2.. Name: ~s'~o--=-i Class; Date: ID: A Name: ~s'~o--=-i Class; Date: U.;,..;...-h_D_Vl_5 _ MAC 2233 Chapter 4 Review for the test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the derivative

More information

8. Introduction and Chapter Objectives

8. Introduction and Chapter Objectives Real Analog - Circuits Chapter 8: Second Order Circuits 8. Introduction and Chapter Objectives Second order systems are, by definition, systems whose input-output relationship is a second order differential

More information

Solutions to ECE 2026 Problem Set #1. 2.5e j0.46

Solutions to ECE 2026 Problem Set #1. 2.5e j0.46 Solutions to ECE 2026 Problem Set #1 PROBLEM 1.1.* Convert the following to polar form: (a) z 3 + 4j 3 2 + 4 2 e jtan 1 ( 4/3) 5e j0.295 3 4j 5e (b) z ---------------- ------------------------ j0.295 3

More information

c. What is the average rate of change of f on the interval [, ]? Answer: d. What is a local minimum value of f? Answer: 5 e. On what interval(s) is f

c. What is the average rate of change of f on the interval [, ]? Answer: d. What is a local minimum value of f? Answer: 5 e. On what interval(s) is f Essential Skills Chapter f ( x + h) f ( x ). Simplifying the difference quotient Section. h f ( x + h) f ( x ) Example: For f ( x) = 4x 4 x, find and simplify completely. h Answer: 4 8x 4 h. Finding the

More information

2.' -4-5 I fo. - /30 + ;3, x + G: ~ / ~ ) ~ ov. Fd'r evt.'i') cutckf' ()y\e.._o OYLt dtt:vl. t'"'i ~ _) y =.5_21/2-+. 8"'- 2.

2.' -4-5 I fo. - /30 + ;3, x + G: ~ / ~ ) ~ ov. Fd'r evt.'i') cutckf' ()y\e.._o OYLt dtt:vl. t''i ~ _) y =.5_21/2-+. 8'- 2. Statistics 100 Sample FINAL Instructions: I. WORK ALL PROBLEMS. Please, give details and explanations and SHOW ALL YOUR WORK so that partial credits can be given. 2. You may use four pages of notes, tables

More information

R e p u b lic o f th e P h ilip p in e s. R e g io n V II, C e n tra l V isa y a s. C ity o f T a g b ila ran

R e p u b lic o f th e P h ilip p in e s. R e g io n V II, C e n tra l V isa y a s. C ity o f T a g b ila ran R e p u b l f th e P h lp p e D e p rt e t f E d u t R e V, e tr l V y D V N F B H L ty f T b l r Ju ly, D V N M E M R A N D U M N. 0,. L T F E N R H G H H L F F E R N G F R 6 M P L E M E N T A T N T :,

More information

Keep this exam closed until you are told to begin.

Keep this exam closed until you are told to begin. Name: (please print) Signature: ECE 2300 -- Exam #1 October 11, 2014 Keep this exam closed until you are told to begin. 1. This exam is closed book, closed notes. You may use one 8.5 x 11 crib sheet, or

More information

ECE 4213/5213 Test 1. SHOW ALL OF YOUR WORK for maximum partial credit! GOOD LUCK!

ECE 4213/5213 Test 1. SHOW ALL OF YOUR WORK for maximum partial credit! GOOD LUCK! ECE 4213/5213 Test 1 Fall 2018 Dr. Havlicek Monday, October 15, 2018 4:30 PM - 5:45 PM Name: S_O_L_U_'T_I Q_t\l Student Num: Directions: This test is open book. You may also use a calculator, a clean copy

More information

::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2...

::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2... Math 3298 Exam 1 NAME: SCORE: l. Given three points A(I, l, 1), B(l,;2, 3), C(2, - l, 2). (a) Find vectors AD, AC, nc. (b) Find AB+ DC, AB - AC, and 2AD. -->,,. /:rf!:,-t- f1c =-

More information

Problem Value

Problem Value GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM DATE: 30-Apr-04 COURSE: ECE-2025 NAME: GT #: LAST, FIRST Recitation Section: Circle the date & time when your Recitation

More information

l [ L&U DOK. SENTER Denne rapport tilhører Returneres etter bruk Dokument: Arkiv: Arkivstykke/Ref: ARKAS OO.S Merknad: CP0205V Plassering:

l [ L&U DOK. SENTER Denne rapport tilhører Returneres etter bruk Dokument: Arkiv: Arkivstykke/Ref: ARKAS OO.S Merknad: CP0205V Plassering: I Denne rapport thører L&U DOK. SENTER Returneres etter bruk UTLÅN FRA FJERNARKIVET. UTLÅN ID: 02-0752 MASKINVN 4, FORUS - ADRESSE ST-MA LANETAKER ER ANSVARLIG FOR RETUR AV DETTE DOKUMENTET. VENNLIGST

More information

Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v

Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v ll f x, h v nd d pr v n t fr tf l t th f nt r n r

More information

LABORATORY 1 DISCRETE-TIME SIGNALS

LABORATORY 1 DISCRETE-TIME SIGNALS LABORATORY DISCRETE-TIME SIGNALS.. Introduction A discrete-time signal is represented as a sequence of numbers, called samples. A sample value of a typical discrete-time signal or sequence is denoted as:

More information

. ~ ~~::::~m Review Sheet #1

. ~ ~~::::~m Review Sheet #1 . ~ ~~::::~m Review Sheet #1 Math lla 1. 2. Which ofthe following represents a function(s)? (1) Y... v \ J 1\ -.. - -\ V i e5 3. The solution set for 2-7 + 12 = 0 is :---:---:- --:...:-._",,, :- --;- --:---;-..!,..;-,...

More information

o V fc rt* rh '.L i.p -Z :. -* & , -. \, _ * / r s* / / ' J / X - -

o V fc rt* rh '.L i.p -Z :. -* & , -. \, _ * / r s* / / ' J / X - - -. ' ' " / ' * * ' w, ~ n I: ».r< A < ' : l? S p f - f ( r ^ < - i r r. : '. M.s H m **.' * U -i\ i 3 -. y$. S 3. -r^ o V fc rt* rh '.L i.p -Z :. -* & --------- c it a- ; '.(Jy 1/ } / ^ I f! _ * ----*>C\

More information

STEEL PIPE NIPPLE BLACK AND GALVANIZED

STEEL PIPE NIPPLE BLACK AND GALVANIZED Price Sheet Effective August 09, 2018 Supersedes CWN-218 A Member of The Phoenix Forge Group CapProducts LTD. Phone: 519-482-5000 Fax: 519-482-7728 Toll Free: 800-265-5586 www.capproducts.com www.capitolcamco.com

More information

C(s) R(s) 1 C(s) C(s) C(s) = s - T. Ts + 1 = 1 s - 1. s + (1 T) Taking the inverse Laplace transform of Equation (5 2), we obtain

C(s) R(s) 1 C(s) C(s) C(s) = s - T. Ts + 1 = 1 s - 1. s + (1 T) Taking the inverse Laplace transform of Equation (5 2), we obtain analyses of the step response, ramp response, and impulse response of the second-order systems are presented. Section 5 4 discusses the transient-response analysis of higherorder systems. Section 5 5 gives

More information

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING ECE 26 Summer 14 Quiz #1 June 11, 14 NAME: (FIRST) (LAST) GT username: (e.g., gtxyz123) Circle your recitation section (otherwise

More information

Sub: Submission of the copy of Investor presentation under regulation 30 of SEBI (Listing Obligations & Disclosure Reguirements) Regulations

Sub: Submission of the copy of Investor presentation under regulation 30 of SEBI (Listing Obligations & Disclosure Reguirements) Regulations matrimny.cm vember 1, 218 tinal Stck xchange f India Ltd xchan laza, 5th Flr Plt : C/1, Sand Krla Cmplex, Sa Mmbai - 4 51 Crpte Relatinship Department SS Ltd., Phirze Jeejheebhy Twers Dalal Street, Mmbai

More information

n

n p l p bl t n t t f Fl r d, D p rt nt f N t r l R r, D v n f nt r r R r, B r f l. n.24 80 T ll h, Fl. : Fl r d D p rt nt f N t r l R r, B r f l, 86. http://hdl.handle.net/2027/mdp.39015007497111 r t v n

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

Problem Value

Problem Value GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM DATE: 30-Apr-04 COURSE: ECE-2025 NAME: GT #: LAST, FIRST Recitation Section: Circle the date & time when your Recitation

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

to", \~~!' LSI'r-=- 5 b H 2-l

to, \~~!' LSI'r-=- 5 b H 2-l Math 10 Name_\< Ei_' _ WORKSHEET 2.2 - Surface Area Part 1 - Find SA of different objects Usepage 3 of your data booklet to find the formulae for SAof objects! 1. Find the SA of the square pyramid below.

More information

Integrated II: Unit 2 Study Guide 2. Find the value of s. (s - 2) 2 = 200. ~ :-!:[Uost. ~-~::~~n. '!JJori. s: ~ &:Ll()J~

Integrated II: Unit 2 Study Guide 2. Find the value of s. (s - 2) 2 = 200. ~ :-!:[Uost. ~-~::~~n. '!JJori. s: ~ &:Ll()J~ Name: 1. Find the value of r., (r + 4) 2 = 48 4_ {1 1:. r l f 11i),_ == :r (t~ : t %J3 (t:; KL\J5 ~ ~ v~~f3] ntegrated : Unit 2 Study Guide 2. Find the value of s. (s 2) 2 = 200 ~ :!:[Uost ~~::~~n '!JJori

More information

4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n tr t d n R th

4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n tr t d n R th n r t d n 20 2 :24 T P bl D n, l d t z d http:.h th tr t. r pd l 4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n

More information

I N A C O M P L E X W O R L D

I N A C O M P L E X W O R L D IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e

More information

Vr Vr

Vr Vr F rt l Pr nt t r : xt rn l ppl t n : Pr nt rv nd PD RDT V t : t t : p bl ( ll R lt: 00.00 L n : n L t pd t : 0 6 20 8 :06: 6 pt (p bl Vr.2 8.0 20 8.0. 6 TH N PD PPL T N N RL http : h b. x v t h. p V l

More information

Сборник 2 fhxn "HeHo, Dolty!" HAL LEONARD D/X/ELAND COMBO PAK 2 Music and Lyric by JERRY HERMÁN Arranged by PAUL SEVERSON CLARNET jy f t / / 6f /* t ü.. r 3 p i

More information

1. Given ) inl. 61T 3^nr 13. f(x) : (2-3x)-r, lr'. i. find the binomial expansion of(x), in ascending powers ofx, up to and including the term

1. Given ) inl. 61T 3^nr 13. f(x) : (2-3x)-r, lr'. i. find the binomial expansion of(x), in ascending powers ofx, up to and including the term 61T 3^nr 13 1. Given ) f(x) : (2-3x)-r, lr'. i find the binomial expansion of(x), in ascending powers ofx, up to and including the term inl. Give each coeflicient as a simplified fraction. 2. (a) Use integration

More information

'NOTAS"CRITICAS PARA UNA TEDRIA DE M BUROCRACIA ESTATAL * Oscar Oszlak

'NOTASCRITICAS PARA UNA TEDRIA DE M BUROCRACIA ESTATAL * Oscar Oszlak OVí "^Ox^ OqAÍ"^ Dcument SD-11 \ 'NOTAS"CRTCAS PARA UNA TEDRA DE M BUROCRACA ESTATAL * Oscr Oszlk * El presente dcument que se reprduce pr us exclusv de ls prtcpntes de curss de Prrms de Cpctcón, se h

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 4 Digital Signal Processing Pro. Mark Fowler ote Set # Using the DFT or Spectral Analysis o Signals Reading Assignment: Sect. 7.4 o Proakis & Manolakis Ch. 6 o Porat s Book /9 Goal o Practical Spectral

More information

Section 8.1 Vector and Parametric Equations of a Line in

Section 8.1 Vector and Parametric Equations of a Line in Section 8.1 Vector and Parametric Equations of a Line in R 2 In this section, we begin with a discussion about how to find the vector and parametric equations of a line in R 2. To find the vector and parametric

More information

I.~ I ./ TT. Figure P6.1: Loops of Problem 6.1.

I.~ I ./ TT. Figure P6.1: Loops of Problem 6.1. CHAPTER 6 249 Chapter 6 Sections 6-1 to 6-6: Faraday's Law and its Applications Problem 6.1 The switch in the bottom loop of Fig. 6-17 (p6.1) is closed at t = 0 and then opened at a later time tl. What

More information

ECE 4213/5213 Test 2

ECE 4213/5213 Test 2 ECE 4213/5213 Test 2 Fall 2018 Dr. Havlicek Wednesday, November 14, 2018 4:30 PM - 5:45 PM Name: SOLU1 \ 0 N Student Num: Directions: This test is open book. You may also use a calculator, a clean copy

More information

Tausend Und Eine Nacht

Tausend Und Eine Nacht Connecticut College Digital Commons @ Connecticut College Historic Sheet Music Collection Greer Music Library 87 Tausend Und Eine Nacht Johann Strauss Follow this and additional works at: https:digitalcommonsconncolledusheetmusic

More information

LINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09

LINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09 LINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09 ENGR. M. MANSOOR ASHRAF INTRODUCTION Thus far our analysis has been restricted for the most part to dc circuits: those circuits excited by constant or time-invariant

More information

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r n r t d n 20 22 0: T P bl D n, l d t z d http:.h th tr t. r pd l 0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n.

More information

wo(..lr.i L"'J b]. tr+ +&..) i'> 't\uow).,...,. (o.. J \,} --ti \(' m'\...\,,.q.)).

wo(..lr.i L'J b]. tr+ +&..) i'> 't\uow).,...,. (o.. J \,} --ti \(' m'\...\,,.q.)). Applying Theorems in Calculus 11ter111ediate Value Theorem, Ettreme Value Theorem, Rolle 's Theorem, and l\ea11 Value Theorem Before we begin. let's remember what each of these theorems says about a function.

More information

Math 345: Applied Mathematics

Math 345: Applied Mathematics Math 345: Applied Mathematics Introduction to Fourier Series, I Tones, Harmonics, and Fourier s Theorem Marcus Pendergrass Hampden-Sydney College Fall 2012 1 Sounds as waveforms I ve got a bad feeling

More information

n r t d n :4 T P bl D n, l d t z d th tr t. r pd l

n r t d n :4 T P bl D n, l d t z d   th tr t. r pd l n r t d n 20 20 :4 T P bl D n, l d t z d http:.h th tr t. r pd l 2 0 x pt n f t v t, f f d, b th n nd th P r n h h, th r h v n t b n p d f r nt r. Th t v v d pr n, h v r, p n th pl v t r, d b p t r b R

More information

We enclose herewith a copy of your notice of October 20, 1990 for your reference purposes.

We enclose herewith a copy of your notice of October 20, 1990 for your reference purposes. W-E AND ISuC ATTORNEYS AT lhw 10 QUEEN STIlEET P. 0. BOX NO. 201 NEWTOWN. CONNEWICUT 06470 OEOROE N. WNCELEE HENRY J. ISAAC BUWrpOff 203 9992218 FAX NO. 903-4P6-3011 October 30, 1990.. The Master Collectors

More information

5 s. 00 S aaaog. 3s a o. gg pq ficfi^pq. So c o. H «o3 g gpq ^fi^ s 03 co -*«10 eo 5^ - 3 d s3.s. as fe«jo. Table of General Ordinances.

5 s. 00 S aaaog. 3s a o. gg pq ficfi^pq. So c o. H «o3 g gpq ^fi^ s 03 co -*«10 eo 5^ - 3 d s3.s. as fe«jo. Table of General Ordinances. 5 s Tble f Generl rinnes. q=! j-j 3 -ri j -s 3s m s3 0,0 0) fife s fert " 7- CN i-l r-l - p D fife s- 3 Ph' h ^q 3 3 (j; fe QtL. S &&X* «««i s PI 0) g #r

More information

-74- Chapter 6 Simulation Results. 6.1 Simulation Results by Applying UGV theories for USV

-74- Chapter 6 Simulation Results. 6.1 Simulation Results by Applying UGV theories for USV Chapter 6 Simulation Results 6.1 Simulation Results by Applying UGV theories for USV The path planning with two obstacles by utilizing algorithms which are developed and tested for UGV is given below.

More information

Software Process Models there are many process model s in th e li t e ra t u re, s om e a r e prescriptions and some are descriptions you need to mode

Software Process Models there are many process model s in th e li t e ra t u re, s om e a r e prescriptions and some are descriptions you need to mode Unit 2 : Software Process O b j ec t i ve This unit introduces software systems engineering through a discussion of software processes and their principal characteristics. In order to achieve the desireable

More information

Nagoya Institute of Technology

Nagoya Institute of Technology 09.03.19 1 2 OFDM SC-FDE (single carrier-fde)ofdm PAPR 3 OFDM SC-FDE (single carrier-fde)ofdm PAPR 4 5 Mobility 2G GSM PDC PHS 3G WCDMA cdma2000 WLAN IEEE802.11b 4G 20112013 WLAN IEEE802.11g, n BWA 10kbps

More information

Introduction to DSP Time Domain Representation of Signals and Systems

Introduction to DSP Time Domain Representation of Signals and Systems Introduction to DSP Time Domain Representation of Signals and Systems Dr. Waleed Al-Hanafy waleed alhanafy@yahoo.com Faculty of Electronic Engineering, Menoufia Univ., Egypt Digital Signal Processing (ECE407)

More information

EE 313 Linear Systems and Signals The University of Texas at Austin. Solution Set for Homework #1 on Sinusoidal Signals

EE 313 Linear Systems and Signals The University of Texas at Austin. Solution Set for Homework #1 on Sinusoidal Signals Solution Set for Homework #1 on Sinusoidal Signals By Mr. Houshang Salimian and Prof. Brian L. Evans September 7, 2018 1. Prologue: This problem helps you to identify the points of interest in a sinusoidal

More information

4.1 Distance and Length

4.1 Distance and Length Chapter Vector Geometry In this chapter we will look more closely at certain geometric aspects of vectors in R n. We will first develop an intuitive understanding of some basic concepts by looking at vectors

More information

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd n r t d n 20 20 0 : 0 T P bl D n, l d t z d http:.h th tr t. r pd l 4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n,

More information

University Libraries Carnegie Mellon University Pittsburgh PA ON COMPLETIONS OF UNIFORM LIMIT SPACES. Oswald Wyler.

University Libraries Carnegie Mellon University Pittsburgh PA ON COMPLETIONS OF UNIFORM LIMIT SPACES. Oswald Wyler. ON COMPLETIONS OF UNIFORM LIMIT SPACES by Oswald Wyler Report 67-3 February, 1967 University Libraries Carnegie Mellon University Pittsburgh PA 15213-3890 ON COMPLETIONS OP UNIFORM LIMIT SPACES by Oswald

More information

Read each question and its parts carefully before starting. Show all your work. Give units with your answers (where appropriate).

Read each question and its parts carefully before starting. Show all your work. Give units with your answers (where appropriate). ECSE 10, Fall 013 NAME: Quiz #1 September 17, 013 ID: Read each question and its parts carefully before starting. Show all your work. Give units with your answers (where appropriate). 1. Consider the circuit

More information

Stat 710: Mathematical Statistics Lecture 40

Stat 710: Mathematical Statistics Lecture 40 Stat 710: Mathematical Statistics Lecture 40 Jun Shao Department of Statistics University of Wisconsin Madison, WI 53706, USA Jun Shao (UW-Madison) Stat 710, Lecture 40 May 6, 2009 1 / 11 Lecture 40: Simultaneous

More information

22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f

22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f n r t d n 20 2 : 6 T P bl D n, l d t z d http:.h th tr t. r pd l 22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r

More information

Vector Geometry. Chapter 5

Vector Geometry. Chapter 5 Chapter 5 Vector Geometry In this chapter we will look more closely at certain geometric aspects of vectors in R n. We will first develop an intuitive understanding of some basic concepts by looking at

More information

EE5138R: Problem Set 5 Assigned: 16/02/15 Due: 06/03/15

EE5138R: Problem Set 5 Assigned: 16/02/15 Due: 06/03/15 EE538R: Problem Set 5 Assigned: 6/0/5 Due: 06/03/5. BV Problem 4. The feasible set is the convex hull of (0, ), (0, ), (/5, /5), (, 0) and (, 0). (a) x = (/5, /5) (b) Unbounded below (c) X opt = {(0, x

More information

Colby College Catalogue

Colby College Catalogue Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1866 Colby College Catalogue 1866-1867 Colby College Follow this and additional works at: http://digitalcommons.colby.edu/catalogs

More information

Lecture10: Plasma Physics 1. APPH E6101x Columbia University

Lecture10: Plasma Physics 1. APPH E6101x Columbia University Lecture10: Plasma Physics 1 APPH E6101x Columbia University Last Lecture - Conservation principles in magnetized plasma frozen-in and conservation of particles/flux tubes) - Alfvén waves without plasma

More information

I if +5sssi$ E sr. Egglg[[l[aggegr glieiffi*gi I I a. gl$[fli$ilg1li3fi[ Ell F rss. F$EArgi. SEgh*rqr. H uf$:xdx. FsfileE

I if +5sssi$ E sr. Egglg[[l[aggegr glieiffi*gi I I a. gl$[fli$ilg1li3fi[ Ell F rss. F$EArgi. SEgh*rqr. H uf$:xdx. FsfileE (tl Sh*q +sss$!! ll ss s ;s$ll s ; B 3 $ Sest -9[*; s$t 1,1 - e^ -" H u$xdx fd $A sfle *9,9* '. s. \^ >X!l P s H 2.ue ^ O - HS 1- -l ( l[[l[e lff* l$[fl$l1l3f[ U, -.1 $tse;es s TD T' ' t B $*l$ \l - 1

More information

Problem Value Score No/Wrong Rec 3

Problem Value Score No/Wrong Rec 3 GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING QUIZ #1 ATE: 4-Feb-11 COURSE: ECE-2025 NAME: GT username: LAST, FIRST (ex: gtbuzz8) 3 points 3 points 3 points Recitation Section:

More information

Mathematics Extension 1

Mathematics Extension 1 BAULKHAM HILLS HIGH SCHOOL TRIAL 04 YEAR TASK 4 Mathematics Etension General Instructions Reading time 5 minutes Working time 0 minutes Write using black or blue pen Board-approved calculators may be used

More information

APPENDIX F WATER USE SUMMARY

APPENDIX F WATER USE SUMMARY APPENDX F WATER USE SUMMARY From Past Projects Town of Norman Wells Water Storage Facltes Exstng Storage Requrements and Tank Volume Requred Fre Flow 492.5 m 3 See Feb 27/9 letter MACA to Norman Wells

More information

VECTORS AND THE GEOMETRY OF SPACE

VECTORS AND THE GEOMETRY OF SPACE VECTORS AND THE GEOMETRY OF SPACE VECTORS AND THE GEOMETRY OF SPACE A line in the xy-plane is determined when a point on the line and the direction of the line (its slope or angle of inclination) are given.

More information

ECE145A/218A Course Notes

ECE145A/218A Course Notes ECE145A/218A Course Notes Last note set: Introduction to transmission lines 1. Transmission lines are a linear system - superposition can be used 2. Wave equation permits forward and reverse wave propagation

More information

1 Introduction & Objective

1 Introduction & Objective Signal Processing First Lab 13: Numerical Evaluation of Fourier Series Pre-Lab and Warm-Up: You should read at least the Pre-Lab and Warm-up sections of this lab assignment and go over all exercises in

More information

ON THE DIVERGENCE OF FOURIER SERIES

ON THE DIVERGENCE OF FOURIER SERIES ON THE DIVERGENCE OF FOURIER SERIES RICHARD P. GOSSELIN1 1. By a well known theorem of Kolmogoroff there is a function whose Fourier series diverges almost everywhere. Actually, Kolmogoroff's proof was

More information

'5E _ -- -=:... --!... L og...

'5E _ -- -=:... --!... L og... F U T U R E O F E M B E D D I N G A N D F A N - O U T T E C H N O L O G I E S R a o T u m m a l a, P h. D ; V e n k y S u n d a r a m, P h. D ; P u l u g u r t h a M. R a j, P h. D ; V a n e s s a S m

More information

46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th

46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th n r t d n 20 0 : T P bl D n, l d t z d http:.h th tr t. r pd l 46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l

More information

q-..1 c.. 6' .-t i.] ]J rl trn (dl q-..1 Orr --l o(n ._t lr< +J(n tj o CB OQ ._t --l (-) lre "_1 otr o Ctq c,) ..1 .lj '--1 .IJ C] O.u tr_..

q-..1 c.. 6' .-t i.] ]J rl trn (dl q-..1 Orr --l o(n ._t lr< +J(n tj o CB OQ ._t --l (-) lre _1 otr o Ctq c,) ..1 .lj '--1 .IJ C] O.u tr_.. l_-- 5. r.{ q-{.r{ ul 1 rl l P -r ' v -r1-1.r ( q-r ( @- ql N -.r.p.p 0.) (^5] @ Z l l i Z r,l -; ^ CJ (\, -l ọ..,] q r 1] ( -. r._1 p q-r ) (\. _l (._1 \C ' q-l.. q) i.] r - 0r) >.4.-.rr J p r q-r r 0

More information

J2 e-*= (27T)- 1 / 2 f V* 1 '»' 1 *»

J2 e-*= (27T)- 1 / 2 f V* 1 '»' 1 *» THE NORMAL APPROXIMATION TO THE POISSON DISTRIBUTION AND A PROOF OF A CONJECTURE OF RAMANUJAN 1 TSENG TUNG CHENG 1. Summary. The Poisson distribution with parameter X is given by (1.1) F(x) = 23 p r where

More information

t Hei I Y taxi L Y D L A teethed to get the matrix I T A Nettled Use theformula same Theorem 1) Identity transformation:

t Hei I Y taxi L Y D L A teethed to get the matrix I T A Nettled Use theformula same Theorem 1) Identity transformation: ) Identity transformation: Use theformula Theorem to get the matrix I T A Nettled taxi t Hei I Y 2) stretch by factor of.5 horizontally, and.75 vertically: T L A teethed L Y D same 3) reflect across the

More information

ECE430 Name 5 () ( '-'1-+/~ Or"- f w.s. Section: (Circle One) 10 MWF 12:30 TuTh (Sauer) (Liu) TOTAL: USEFUL INFORMATION

ECE430 Name 5 () ( '-'1-+/~ Or- f w.s. Section: (Circle One) 10 MWF 12:30 TuTh (Sauer) (Liu) TOTAL: USEFUL INFORMATION " ~~~~~,",,_~"",,"cr,~ - r " ECE430 Name 5 () ( '-'1-+/~ Or"- f ws Exam #2 (print Name) Spring 2005 Section: (Circle One) 10 MWF 12:30 TuTh (Sauer) (Liu) Problem 1 Problem 2 Problem 3 Problem 4 TOTAL:

More information

APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 4200 Physics of Fluids Rotating Fluid Flow October 6, 2011 1.!! Hydrostatics of a Rotating Water Bucket (again) 2.! Bath Tub Vortex 3.! Ch. 5: Problem Solving 1 Key Definitions & Concepts Ω U Cylindrical

More information

Lecture 7:Time Response Pole-Zero Maps Influence of Poles and Zeros Higher Order Systems and Pole Dominance Criterion

Lecture 7:Time Response Pole-Zero Maps Influence of Poles and Zeros Higher Order Systems and Pole Dominance Criterion Cleveland State University MCE441: Intr. Linear Control Lecture 7:Time Influence of Poles and Zeros Higher Order and Pole Criterion Prof. Richter 1 / 26 First-Order Specs: Step : Pole Real inputs contain

More information

THE USE OF A CALCULATOR, CELL PHONE, OR ANY OTHER ELEC- TRONIC DEVICE IS NOT PERMITTED DURING THIS EXAMINATION.

THE USE OF A CALCULATOR, CELL PHONE, OR ANY OTHER ELEC- TRONIC DEVICE IS NOT PERMITTED DURING THIS EXAMINATION. MATH 220 NAME So\,t\\OV\ '. FINAL EXAM 18, 2007\ FORMA STUDENT NUMBER INSTRUCTOR SECTION NUMBER This examination will be machine processed by the University Testing Service. Use only a number 2 pencil

More information

CoHrrNOz 7. CeHllN2OaBr [,-) ,/,'JZ-4)..,,.[J. (o*:)s - n"etu tl't - decer.-(, .",.L<., r(y H,c=cHr*r,r, O(

CoHrrNOz 7. CeHllN2OaBr [,-) ,/,'JZ-4)..,,.[J. (o*:)s - netu tl't - decer.-(, .,.L<., r(y H,c=cHr*r,r, O( CE}24 Dr. Spence 1. Calculate the degree of unsaturation for each of the following compounds: Coo 6l CorrNOz 7 Ca+OClz Ll Cros 1 CellN2Oa [,-) C2a2aN3OP F 1,1 l./ ow many degrees of unsaturation are present

More information

,., [~== -I ] ~y_/5 =- 21 Y -/ Y. t. \,X ::: 3J ~ - 3. Test: Linear equations and Linear inequalities. At!$fJJ' ~ dt~ - 5 = -7C +4 + re -t~ -+>< 1- )_

,., [~== -I ] ~y_/5 =- 21 Y -/ Y. t. \,X ::: 3J ~ - 3. Test: Linear equations and Linear inequalities. At!$fJJ' ~ dt~ - 5 = -7C +4 + re -t~ -+>< 1- )_ CST 11 Math - September 16 th, 2016 Test: Linear equations and Linear inequalities NAME: At!$fJJ' ~ Section: MCU504: -- - 86 1100 1. Solve the equations below: (4 marks) 2 5 a) 3("3 x -"3) = - x + 4 /{J1:x

More information

New Mexico Tech Hyd 510

New Mexico Tech Hyd 510 Vectors vector - has magnitude and direction (e.g. velocity, specific discharge, hydraulic gradient) scalar - has magnitude only (e.g. porosity, specific yield, storage coefficient) unit vector - a unit

More information