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Course: MATH 2061, Spring 2011School: University of Sydney
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UNIVERSITY THE OF SYDNEY MATH2061 VECTOR CALCULUS Summer School Assignment 2010 INSTRUCTIONS This assignment is worth 10% of your assessment for this half of the MATH2061 course. The assignment is due at 4pm on Friday February 4 (to be collected at the end of the tutorial.) There is one question worth a total of 10 marks. Write your fully worked solutions IN PEN on A4 paper and staple into them a manilla...
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UNIVERSITY THE OF SYDNEY
MATH2061 VECTOR CALCULUS
Summer School
Assignment
2010
INSTRUCTIONS This assignment is worth 10% of your assessment for this half of the MATH2061 course. The assignment is due at 4pm on Friday February 4 (to be collected at the end of the tutorial.) There is one question worth a total of 10 marks. Write your fully worked solutions IN PEN on A4 paper and staple into them a manilla folder. You must also sign and attach the included Assignment Cover Sheet.
QUESTIONS 1. Calculate the work done by the force field F = 3xyi + 5y 2 j - 3yzk (i) along the path from (1, 0, 0) to (0, 1, 0) (ii) along the path from (1, 0, 0) to (1, 1, 0), then to (0, 1, 0) (iii) along the upper semicircle y = x2 - 1 in the xy-plane (so z=0)
(Question 1 is worth 10 marks) 1
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University of Sydney - MATH - 2061
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2011Quiz 1a - Solutions1. The set S = t 1 | t R is a subspace of R2 . 0 Which one of the following statements is not true? a) If b) If c) If d) Ifx y x y x y x y S then S then S then S
University of Sydney - MATH - 2061
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2011Quiz 1b - Solutions 0 2 0 1. Find the eigenvalues of the matrix 1 1 0. 0 -1 1 a) -1, 1, -2 b) 1, 1, 2 c) 1, 1, -2 d) -1, 1, 2 Solution d)2. The set S = t 1 | t R is a subspace of R2
University of Sydney - MATH - 2061
January 2010 MATH2061 Linear Algebra Summer School Sample Quiz 1 Each question will be marked out of 2 to give a total out of 10 4 2 0 8 1. Suppose A = 0 0 -3, and b = 9. 0 0 2 2 How many solutions does Ax = b have? (a) one unique solution (b) infinitely
University of Sydney - MATH - 2061
MATH2061 Linear Algebra Summer School 2010 Practice Questions for Quiz 2 The Quiz will be marked out of 10 1. Find a basis for the vector space V = ax2 + bx + c P2 | 2a + b = 5c . -1 2 1 V = Span 0 , 1 , 4 . 0 0 0 Find a basis for V What is the dimension
University of Sydney - MATH - 2061
The University of Sydney School of Mathematics and StatisticsSolutions to Vector Calculus - Quiz AMATH2061/2067: Semester 1, 20111. Let F = 2x i + y j. Find the fluxCF n ds, where C is the unit circle,centre (0, 0), taken once anti-clockwise, and n
University of Sydney - MATH - 2061
The University of Sydney School of Mathematics and StatisticsSolutions to Vector Calculus - Quiz BMATH2061/2067: 1. Find a potential function of the gradient field F = (y 2 - (sin x)ez ) i + 2xy j + (cos x)ez k. (a) xy 2 + (cos x)ez (c) 2xy - (sin x)ez
University of Sydney - MATH - 2061
The University of Sydney School of Mathematics and StatisticsPractice questions for the vector calculus quizMATH2061/2067: Vector Calculus Semester 1, 2011These are practice questions only. The actual test will have 15 multiple choice questions and the
University of Sydney - MATH - 2061
Math2061 Vector Calculus Quiz Version B Solutions 1. (a) 2 marks for correct sketch r(t)=7i +6j + t(-3i -5j), (2 marks) Also correct is x =7 -3t,y =6 -5t, 0 = t = 1 (1 mark) (b) 2 marks for correct sketch x = t,y = t3
University of Sydney - MATH - 2061
Math2061 Vector Calculus Quiz Version BSolutions1. (a) 2 marks for correct sketch r(t) = 7i + 6j + t(-3i - 5j), (2 marks) Also correct is x = 7 - 3t, y = 6 - 5t, 0 t 1 (1 mark) (b) 2 marks for correct sketch x = t, y = t3 (1 mark) -2 t 1 (c) 2 marks for
University of Sydney - MATH - 2061
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2010Tutorial 1 - Solutions 3 0 4 5 1 1 2 -2. a) Calculate the matrix product -1 3 5 4 b) Find the unique solution of the linear system of equations which corresponds to the augmented matr
University of Sydney - MATH - 2061
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Summer School Math2061 2010Tutorial 2 (week 2) - Solutions1. For each of the sets of vectors X R3 below, explicitly describe all of the vectors in the subspace Span(X) of R3 . 1 1 a) X = cfw_0. 1 , 0 d) X =
University of Sydney - MATH - 2061
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Summer School Math2061 2010Tutorial 3 (week 3) - Solutions1. a) Let X =1 0 0 0,b) Let Y = cfw_p1 (x), p2 (x), p3 (x), where p1 (x) = 1, p2 (x) = 2x - 1 and p3 (x) = (2x - 1)2 . Show that Y is a linearly
University of Sydney - MATH - 2061
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2010Tutorial 4 - Solutions1. You are given the following data points: x -1 0 1 2 y 4 1 -2 1 Construct a Lagrange basis cfw_p0 , p1 , p2 , p3 of P3 using the x values from the data set. H
University of Sydney - MATH - 2061
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2010Tutorial 5 - Solutions1. Find a geometric interpretation for the following linear transformations. a) T : R2 - R2 ; T a - a+b . b b b) T : R2 - R2 ; Ta b- 1 3 a- b 2 2 1 3 a+ b 2 2
University of Sydney - MATH - 2061
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2010Tutorial 6 - Solutions1. Suppose that A and P are defined as follows: A=1 1 - 1 4 4 1 0 0 0 1 0andP =1 1 4 4 1 1 1 - 2 2 1 1 1 1.Define a sequence of numbers cfw_ un | n 0 by u
University of Sydney - MATH - 2061
The University of SydneySummer School MATH2061: Linear Mathematics Assignment This assignment consists of five questions. Full marks will only be awarded where working is shown. One question is due in each of your first five tutorials. Attach an assignme
Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
End of Chapter 3 Questions and Answers 1. What is the difference between an MSA and a CMSA? Answer: An MSA ("metropolitan statistical area") is a basic metropolitan area. Each MSA consists of one (or a very few) designated central cities whose population
Texas State - FIN - 4380
End of Chapter 4 Questions and Answers 1. What is meant by a "factor of production"? Name four categories or types of productive factors. How does land differ from the other factors? Answer: All the necessary inputs required for production are called "fac
Texas State - FIN - 4380
End of Chapter 5 Questions and Answers 1. Explain how the U.S. taxation laws encourage homeownership. Answer: The higher a person's income tax rate the more likely they are to become a homeowner, as the after tax costs are reduced in proportion to their t
Texas State - FIN - 4380
End of Chapter 6 Questions and Answers 1. What were the primary reasons for over building in the late 1980's and early 1990's? Answer: Over supply in the mid 1980's to mid 1990's was induced by the additional factors of tax law changes and deregulation of
Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
Chapter 9Negotiation, Ethics and Risk Management in the Contracting Process"Real Estate Principles for the New Economy": Norman G. Miller and David M. GeltnerMajor Topics Principles of successful negotiation styles How ethical perspectives influence n
Texas State - FIN - 4380
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Texas State - FIN - 4380
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Texas State - FIN - 4380
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University of Colorado Denver - APPM - 4520
APPM 4/5520 Problem Set One (Due Wednesday, August 31st) 1. Let X be a random variable with the binomial distribution with parameters n and p, (ie: X bin(n, p). Find the distribution of Y = n - X. (Name it!) 2. Let X unif (0, 1). Find the distribution of
University of Colorado Denver - APPM - 4520
APPM 4/5520 Solutions to Problem Set One 1. The binomial random variable X counts the number of successes in n trials where p is the probability of success on any single trial. So, Y = n - X represents the number of failures in n trials. If we rename "fai
University of Colorado Denver - APPM - 4520
APPM 4/5520 Problem Set Two (Due Wednesday, September 7th) 1. Suppose that X1 , X2 exp(rate = ). Find the distribution of 2. Let X1 and X2 have the joint pdf fX1 ,X2 (x1 , x2 ) = 2e-x1 -x2 I(0,x2 ) (x1 )I(0,) (x2 ). (a) Find the marginal pdfs for X1 and X
University of Colorado Denver - APPM - 4520
APPM 4/5520 Solutions to Problem Set Two 1. Let y1 = g1 (x1 , x2 ) = x1 /(x1 + x2 ) Then-1 x1 = g1 (y1 , y2 ) = y1 y2and lety2 = g2 (x1 , x2 ) = x1 + x2 .and-1 x2 = g2 (y1 , y2 ) = y2 - y1 y2 = y2 (1 - y1 ).X1 , X2 exp(rate = )iidfX1 ,X2 (x1 , x2
University of Colorado Denver - APPM - 4520
APPM 4/5520 Problem Set Three (Due Wednesday, September 14th) 1. Let X geom0 (p). (a) Compute the moment generating function of X. Be sure to give and explain restrictions, if any, on the domain of the mgf. (b) Let Y geom1 (p). How does Y relate to X? Use
University of Colorado Denver - APPM - 4520
APPM 4/5520 Solutions to Problem Set Three 1. (a) f (x) = p(1 - p)x Icfw_0,1,2,. (x) MX (t) = E[etX ] = = p x=0 tx x=0 e p(1 - p)xxet (1 - p)This geometric sum converges if et (1 - p) < 1. (Note that it is already positive since et > 0 and since 0 p
University of Colorado Denver - APPM - 4520
APPM 4/5520 Problem Set Four (Due Wednesday, October 5th) 1. Let X1 , X2 , . . . , Xn be a random sample from any distribution with mean and variance 2 . From class, we know that = X is an unbiased estimator of . ^ Suppose that we want to estimate the var
University of Colorado Denver - APPM - 4520
APPM 4/5520 Solutions to Problem Set Four 1. (a)2 E[S2 ] =1 E[ n-1(Xi - X)2 ]Option One: Square (Xi - X) and take the sum through: (Xi - X)2 = = = = = = So Xi2 - 2X (Xi2 - 2X + X ) Xi + nX1 n 2 2Xi2 - 2X n Xi + nX22Xi2 - 2X nX + nX Xi2 - 2nX + n