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Course: MATH 2061, Spring 2011
School: 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
End of Chapter 1 Questions and Answers 1. Is real estate a discipline? Look up the word &quot;discipline&quot; in the dictionary and see how well real estate fits. Can you name a discipline? Why is it hard to name a pure discipline within business? Answer: Accordin
Texas State - FIN - 4380
End of Chapter 2 Discussion Questions and Answers 1. Define a submarket. How does an office submarket differ from a residential submarket? Answer: The market in which the property of interest (the `subject' property) competes is called a submarket. Submar
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 (&quot;metropolitan statistical area&quot;) 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 &quot;factor of production&quot;? 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 &quot;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
End of Chapter 7 Questions and Answers 1. Steve and Ruth Marcus have listed their home with Miami Vice Realty. The Marcus's built the home themselves and included an array of features that make the home particularly attractive. An agent from Miami Vice ha
Texas State - FIN - 4380
End of Chapter 8 Questions and Answers 1. What are the elements of a valid contract? i. Offer ii. Acceptance iii. Consideration iv. Written evidence of an agreement 2. What type of deed would you like to have if you are the buyer? Answer: A General Warran
Texas State - FIN - 4380
End of Chapter 9 Questions and Answers 1. Explain alternative names for win-lose negotiation. What are the presumptions inherent in this approach? Answer: Win-lose negotiation can also be called &quot;military negotiation&quot; or &quot;power negotiation&quot; This approach
Texas State - FIN - 4380
End of Chapter 10 Questions and Answers 1. What is the purpose of zoning? Answer: To prevent negative externalities from affecting property value for different uses and by balancing land uses to maximize overall property values. 2. Does zoning positively
Texas State - FIN - 4380
End of Chapter 11 Questions and Answers 1. What is the difference between nominal returns and real returns? Answer: Nominal returns include inflation while real returns have inflation netted out. For example, a nominal return of 12% during a year of 3% in
Texas State - FIN - 4380
End of Chapter 12 Questions and Answers 1. Distinguish between cost, price and value concepts. Answer: Cost and price are factual in nature while value is theoretical. Cost is either an estimate based on a bid or actual cost of a parcel of land, building
Texas State - FIN - 4380
End of Chapter 13 Questions and Answers 1. Define market value. Answer: The maximum price at which buyer will buy and the minimum acceptable price to the seller, both fully informed, acting without duress and with reasonable financing, can be called the m
Texas State - FIN - 4380
End of Chapter 14 Questions and Answers 1. Can a property have a break even point above 1.0? What would this imply? Answer: No, it would imply greater than 100% occupancy. 2. What is the difference between the Net Operating Income and the Before-tax Cash
Texas State - FIN - 4380
End of Chapter 15 Questions and Answers 1. What is the traditional income approach to value? Answer: The traditional technique for commercial property is the income approach to value, which uses the simple formula: NOI Value = R R is the &quot;capitalization r
Texas State - FIN - 4380
End of Chapter 16 Questions and Answers 1. What is the difference between the leverage ratio (LR) and the loan-to-value ratio (LTV)? How much greater property value can be purchased with a 75% LTV than with a 50% LTV? What is the LR associated with each o
Texas State - FIN - 4380
End of Chapter 17 Questions and Answers 1. Where does mortgage money come from? Answer: Mortgage money competes with other capital market investments. While some mortgage money comes from financial institutions through savings and checking account deposit
Texas State - FIN - 4380
Extra Mortgage Problems and Answers For Chapter 18 1. What is the monthly mortgage payment for a \$150,000 FRM at 9.25% for 15 years, 20 years, 25 years, 30 years, and 50 years? Mortgage Payments for 9.25% for \$150,000 for: 15 years \$1,543.79 20 years \$1,3
Texas State - FIN - 4380
End of Chapter 19 Questions and Answers 1. What is the difference between the primary mortgage market and the secondary market? Answer: The primary mortgage market is where loans are originated while the secondary mortgage market is where existing loans a
Texas State - FIN - 4380
End of Chapter 20 Questions and Answers 1. How is the commercial mortgage underwriting process different from the residential mortgage underwriting process? Answer: There is much more emphasis on the property and income generation of the property versus e
Texas State - FIN - 4380
End of Chapter 21 Questions and Answers 1. What are the restrictions on REIT annual gross revenue sources and taxable income distributions necessary for a REIT to maintain its exemption from corporate income tax? Answer: 75% or more of the REITs total ass
Texas State - FIN - 4380
End of Chapter 22 Questions and Answers 1. What does NAR stand for? What is the difference between a broker, agent and REALTOR? Answer: NAR stands for the National Association of REALTORS, a trade association made up primarily of licensed real estate agen
Texas State - FIN - 4380
End of Chapter 23 Questions and Answers 1. What types of skills are required for a commercial broker or leasing agent? Answer: Good analytical, communication, presentation, and negotiation skills. They need to understand the business of their clients and
Texas State - FIN - 4380
End of Chapter 24 Questions and Answers 1. Suggested Assignment: To become better at thinking about how everything affects real estate, watch the local news one evening and take notes on the stories. Other than the stories about weather, fires, car crashe
Texas State - FIN - 4380
End of Retail Property Chapter Questions and Answers 1. What is a simple method to project future retail sales growth? Can you suggest some refinements to this simple model? Answer: The easiest way to forecast sales is by extending past trends. That is if
Texas State - FIN - 4380
Chapter 1 Introduction to the Real Estate Industry&quot;Real Estate Principles for the New Economy&quot; By Norman G. Miller and David M. GeltnerOutline of Topics What is Real Estate? What skills and personality traits arerequired? What career paths are possibl
Texas State - FIN - 4380
Chapter 2 What drives Real Estate Markets?&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics Real Estate economic and market terms How Real Estate markets differ from otherasset markets How capital markets
Texas State - FIN - 4380
Chapter 3 Central Cities and Regional Market Analysis&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics Why do cities exist? Why do cities of different sizes exist? What is a metropolitan statistical area? W
Texas State - FIN - 4380
Chapter 4 Urban Land Values, Transportation Costs Impact and the Urban Form&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics How transportation costs and productivity affect land values in a city Why and ho
Texas State - FIN - 4380
Chapter 5 Residential Market Analysis&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics Demand drivers for home ownership Drivers of long and short term owner occupied housing market The decision to buy or r
Texas State - FIN - 4380
Chapter 6Office &amp; Industrial PropertyOffice Property Defining office space qualityMajor Topics The demand drivers for office space Translating employment growth to office space demand The trends that shape the amount of space required per worker The s
Texas State - FIN - 4380
Chapter 7 Real Estate Property Rights, Fixtures and Ownership&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics What is real property? Legal methods of Property description Holding title to the real property
Texas State - FIN - 4380
Chapter 8 Contracts and Transferring Real Estate Interests&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics Documents used to transfer title to real estate Concept of &quot;good title&quot; to real estate Insuring th
Texas State - FIN - 4380
Chapter 9Negotiation, Ethics and Risk Management in the Contracting Process&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics Principles of successful negotiation styles How ethical perspectives influence n
Texas State - FIN - 4380
Chapter 10 Land Use Controls and Property Taxes&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics Origin, purpose and types of local land use controls Uses and process of determining property taxation Impact
Texas State - FIN - 4380
Chapter 11 Introduction to Investment Concepts&quot;Real Estate Principles for the New Economy&quot;: Norman G. Miller and David M. GeltnerMajor Topics Investor Objectives Sources of real estate returns Introduction to Cash Flow Analysis What we mean by direct a
Texas State - FIN - 4380
Chapter 18Real Estate Finance Tools: PresentValue and Mortgage MathematicsReal Estate Principles for the NewEconomy: Norman G. Miller andDavid M. GeltnerMajor TopicsTime value of money calculationsPresent value of a single sum or annuity paymentF
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 &quot;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) &lt; 1. (Note that it is already positive since et &gt; 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