Virginia Tech - MATH - 3214

Practice Exam 1: Math 3214; Spring, 20121.Let P = ( 1 1 1 ) , Q = ( 2 3 2 ) , R = ( 1 1 1 ).a)Find an equation for the plane passing through Q and orthogonal to Q P .b)Let L be the line through P in the direction of R and let ( x y z ) be thepoint

Virginia Tech - MATH - 3214

Math 3214: Practice Exam 2 and Take HomeProblem to be Turned in with 4-4-12 Exam1.Let (x, y ) = y sin x + x cos y and let C be the curve described parametrically by x = t, y = t2 , 0 t 1. With F (X ) = F (x, y ) = (x, y ), computethe line integral C F

Virginia Tech - MATH - 3214

Name:Math 3214 Project; Due: 04/30/12.Basic Setting:We consider the elliptical regionR R2 ; R = cfw_x, y4x2 + y 2 4 .The surface is the portion of the graph of the functionz = (x, y ) = 1 y2x244lying above R in R3 . The curve C is the boundary

Virginia Tech - MATH - 3214

Virginia Tech - MATH - 3214

Virginia Tech - MATH - 3214

NameQuiz 4, Math 3214, Spring 2012Due in 418 McBryde, Friday, April 27, 2012. Use this page ascover sheet and staple, please. This quiz is worth 32 points.Use spherical coordinates to compute the integral1.Ax 2 + y 2 + z 2 dx dy dzwhere A is the h

Virginia Tech - MATH - 3214

Virginia Tech - MATH - 3214

NameClassroom IDQuiz 2: Math 3214; Due: Monday, Feb. 13, 2012Note: The symbolis attached.indicates the transpose of the vector to which it1. Let C be the curve in R 2 given by y = x3 , 0 x 1/2.Compute the arc length integralC2.f (x, y ) ds,f (x

Virginia Tech - MATH - 3214

Virginia Tech - MATH - 3214

Clemson - ME - 303

ANNOUNCED qUtZNAME:#t - ME 303 -Spring 2oL2I otttTtoNDATE:This is an open book quiz. You may use a calculator. A grade of zero will be given if the honorspledge is not signed,1. Consider a tank having a volume of 0.5 m3 that is initially evacuated

Clemson - ME - 303

ANNOUNCED QUIZ #2- ME 3oS -Spring 2at2So LuTt DNNAME:DATE:This is an open book quiz. You may use a calculator. A grade of zero will be given if the honorspledge is not signed.1.ln icemaker makes ice by transferring heat from liquid sater at OoC t

Clemson - ME - 303

ANNOUNCED QUIZ #3iYAME:SOL TTIDN- ME 303 -Spring 2012DATE:This is an open book quiz. You may use a calculator.pledge is not signed.l.A grade of zero will be given if the honorsj-llustrated below is for a Carnot cycle that uses a fixed qualtity

Clemson - ME - 303

ANNOUNCED QUIZ #4-ME 303SoLL)Ttovl-Spring201-2This is an open book quiz. You may use a calculator. A grade of zero will be given if the honorspledge is not signed.1. Coasider a horizontal piston-cylinder assenbly containlng 0.5 kg of propane whic

Clemson - ME - 303

ANNOUNCED QUIZ #6-ME 303-Spring 2012SOTUTI ON'&o/zb"t< q,riz. You may use a calculator. A grade of zero will be given if the honorsThtr t"pledge i"not signed.s "p"ata1x 6tto cycle that has a pressure of 95 lbf/1nz ard a teElperature of 1000oR

Clemson - ME - 303

ANNOUNCED QUIZ #7Solcfw_Avcfw_E:* ME 303Spring 2012-t-uTt oN'/4 ,H)ILDAIIE:This is an open book quiz. You may use a calculator.pledge is not signed.A grade of zero will be given if the honors1. Consider a vapor conpression heat pump. The worki

Clemson - ME - 303

- ME 303 -ANNOUNCED QUIZ #SSNAME:oLUrtSpring 2012oThis is a closed book quiz. You may not use a calculator. A grade of zero will be given if the honorspledge is not signed.1. The van der Haals equation of state i-s:P:w:P1/- b 7r=*-+,(lg-cfw

Clemson - ME - 303

ANNOUNCED QUIZ #9- ME 303 -Spring 2012SoLuTl0NNAME:This is a closed book quiz. You may not use a calculator, A grade of zero will be given if the honorrpledge is nnt signed.grain at 2A'C contalning 407" noisture by nass enters a dryer operating at

Clemson - ME - 303

ANNOUNCED QUIZ #!O- ME303-Spring 2012soLoTtoNNAME:This is ,r$ open book quiz. You may use a calculator. A grade of zero will be given if the honorspledge is not signed.1. A vesselIl,initial-y contains 1 kmol of llz and 4 knol of N2. An equlllbr

Clemson - ME - 303

FINAL EXAM EQUATION SHEETConservation of EnergyE = Q WdE=QWdtdEC.V.= QC.V. WC.V. +dt(1)(2)mi ( h i +iVi2+ gzi ) 2me ( h e +eVe2+ gze )2(3)Entropy Balance2QTS =1b+(4)(5)jQj+Tj(6)jQj+TjS =dS=dtdSC.V.=dtjQj+

Clemson - ME - 303

EXAM #1Sections 001 and 002 - ThermodynamicsProf. J. R. Salor-Spring 2012Sot UTtoNNAME:This is- ME 303 -a closed book exam. Zero creditwill be earned for this exam if the honors pledge is not signed.1. (10 poi-nts) A heat pump maintains a house

Clemson - ME - 303

EXAM #2 - ME 303 - ThemrodynarnicsProf. j. R. SaylorSNAME:otDTt-Spring 2012oNThis is a closed book quiz. You may use a calculator. A grade of zero will be given if the honors pledge is notsigned.at B MPa and 480"C leaves the steam generator of a

Clemson - ME - 303

EXAM#3- ME 303 - Thermodynamics - SpringProf. J. R Saylorcfw_ 0 LUTNAME:This isa closed20120/Vbook exam. You may useacalculator. A grade of zerowillbe givenif the honors pledge is notsigned.1. Thedifference between the two specific heats

Clemson - ME - 303

Clemson - ME - 303

Homework Assignment ScheduleME 303 Thermodynamics Prof. J. R. Saylor Spring 2012Assignment # Assignment12/31,64 3/70,125 4/45,102,11325/5,18,31,5835/64,65,75,77 6/446/14,24,43,5756/82,86,97,14966/139,152 8/2,13,3478/49,52 9/11,20,2189/28

Clemson - ME - 303

Clemson - ME - 303

Clemson - ME - 303

Clemson - ME - 303

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation o

Clemson - ME - 303

Clemson - ME - 303

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation o

Clemson - ME - 303

Clemson - ME - 303

Clemson - ME - 303

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation o

Clemson - ME - 303

Clemson - ME - 303

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation o

Clemson - ME - 303

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation o

Clemson - ME - 303

Clemson - ME - 303

Clemson - ME - 303

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation o

Clemson - ME - 303

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation o

Clemson - ME - 303

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation o

Clemson - ME - 303

Clemson - ME - 303

ME 303 Problem Solving FormatAdhere to the following guidelines when solving homework, quiz or exam problems. Theseguidelines may be updated as the course progresses. If they are, you will be notied by e-mailthat a new version of the guidelines has bee

Clemson - MTHSC - 434

Clemson - MTHSC - 434

Clemson - MTHSC - 434

Clemson - MTHSC - 434

MTHSC 434, Section 1, Homework Assignment 1Dierential Equations and Linear IndependenceDue: 9:05am, Wednesday, Jan. 19, 2011Point value: 20The purpose of this homework assignment is to help you:1. recall strategies to compute solutions to dierential

Clemson - MTHSC - 434

MTHSC 434-001 Homework 1 Solution1. (a) The characteristic equation is 2 4 + 5 = 0, and the roots are 1 = 2 + i,2 = 2 i. Thus the general solution isy (t) = e2t (c1 cos(t) + c2 sin(t) .Note that y (t) = e2t (2c1 + c2 ) cos(t) + (2c2 c1 ) sin(t).Thus

Clemson - MTHSC - 434

MTHSC 434, Section 1, Homework Assignment 2Integration by parts and more ODEsDue: 9:05am, Friday, Jan. 28, 2011Point value: 20The purpose of this homework assignment is to help you:1. recall techniques for integration by parts;2. resolve solutions t

Clemson - MTHSC - 434

MTHSC 434, Section 1, Homework Assignment 2 Solution1. (a)x2 y1 (x) + 2xy1 (x) 6y1 (x) = x2 (2) + 2x(2x) 6x2= 0.(b) The dierential equation must be in standard form in order to use the reductionof order technique given in the text. After dividing by

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 3Inner Products and OrthogonalityDue: Feb. 4, 2011Total Point Value: 20 pointsThe purpose of this homework assignment is to help you1. generalize the concept of inner products;2. write arbitrary vectors in te

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 3 Solution1. (a) We need to compute the inner products of each distinct pair of vectors to determine orthogonality.(v1 , v2 ) = 1(0) + 2(1) + (2)(1)=0(v1 , v3 ) = 1(4) + 2(1) + (2)(1)=0(v2 , v3 ) = (4)(0) + 1

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 4Fourier Series expansionsDue: Feb. 11, 2011Total Point Value: 20 pointsThe purpose of this homework assignment is to help you1. recall properties of periodic and even/odd functions;2. compute coecients assoc

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 4 Solution2= 1. Note also that21. (a) The fundamental period isf (x + p) = cos (2 (x + p)= cos (2x + 2p)which equals f (x) = cos (2x) when p = 1.2L(b) The fundamental period is=.4/L2(c) The fundament

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 5More on Fourier series expansionsDue: Feb. 18, 2011Total Point Value: 20 pointsThe purpose of this homework assignment is to help you1. compute half-range Fourier series expansions;2. notice minimization pro

Clemson - MTHSC - 434

Homework 5 Solution1. We need to compute the regular Fourier series, the half-range Fouriercosine series, and the half-range Fourier sine series for the given piecewise dened function.(a) For the regular Fourier series, we assume the period length of t

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 6 Solution1. Note that p = 1 in this case. The coecient for the complex Fourier series is21f (x)einx dx2(1) 012(1)einx dx=2112=einx 12ini=e2in ein2ncn =Note thate2in = cos (2n ) i sin (2n )=1

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 7More Sturm-Liouiville ProblemsDue: March 4, 2011Total Point Value: 20 pointsThe purpose of this homework assignment is to help you1. nd solutions to more general Sturm-Liouville problems;2. write a linear or

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 7 Solution1. The characteristic equation associated with this problem isr2 + = 0,which has rootsr = .Once again, we consider three cases: = 0, < 0 and > 0.(a) = 0:The general solution is y (x) = c1 x + c2 .

Clemson - MTHSC - 434

MTHSC434, Section 1: Homework Assignment 8The Heat EquationDue: March 11, 2011Total Point Value: 20 pointsThe purpose of this homework assignment is to help you1. classify partial dierential equations;2. write an initial boundary value problem that