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Ohio State - ECON - 200
OLD EXAMSIf the diagrams don't show up on your screen, go to Print Preview or View Print Layout. You can also try printing that page.1EXAM # 11. Bob decided to go on a year-long cruise he won after graduation instead of working, although he got an off
Ohio State - ECON - 200
ANSWER KEYSExam # 11. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. b a e d b d a c b b b a c a c d d b c d a b d c aExam # 21. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 2
Ohio State - ECON 200 - 200
2010 Pearson Addison- 2010 Pearson Addison-The Firm and Its Economic ProblemA firm is an institution that hires factors of production and organizes them to produce and sell goods and services. The Firm's Goal A firm's goal is to maximize profit. If th
Ohio State - ECON 200 - 200
2010 Pearson Addison- 2010 Pearson Addison-A Housing Market with a Rent CeilingA price ceiling or price cap is a regulation that makes it illegal to charge a price higher than a specified level. When a price ceiling is applied to a housing market it i
Ohio State - BUS-M&L - 650
BUS M&L 650 EXAM 1 5:30 p. m. Class Summer Quarter 2007 Exam answers will be posted on course carmen.osu site at 7 pm. 1. Data mining enabled Harrah's to identify its most profitable customer segmenta. global high rollers b. off duty employees c. betters
Ohio State - BUS-M&L - 650
BUS M&L 650 Second Midterm-Sample Exam 1. Brand loyalty is highest for customers who buy _. a. convenience products b. shopping products c. specialty products d. unsought products 2. Price is generally lowest for _. a. convenience products b. shopping pro
Ohio State - BUS-M&L - 650
BUS M&L 650 Sample Exam 3 1. Corporate, contractual, and administered are the categories for _. a. full service wholesalers b. limited line wholesalers c. vertical marketing systems d. channel conflict resolution processes 2. Exclusive distribution is mos
Ohio State - BUS-M&L - 650
M&L 650 Practice Exam 1 AnswersQuestion 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Answer c b b b b c c d a a a b b b d c a b c d a d c b b a d b e a a
Ohio State - BUS-M&L - 650
M&L 650 Sample Exam Answer Key Question Answer1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 c a b c d b d c c a a b b a c c b d d c c c b d a c c c d d c d c c c c
Ohio State - BUS-M&L - 650
M&L 650 Sample Exam Answer Key Question Answer1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 c b b b a d c b c e c c a c b d d c b b d
Ohio State - BUS-FIN - 620
Business Finance 620 Practice Exam 1_ 1. Which of the following statements provides the most plausible explanation for a company whose statement of cash flows exhibits an increase in the ending cash balance, at the same time cash flows from both operatio
Ohio State - BUS-FIN - 620
Business Finance 620 Practice Exam 2_ 1. If the market yield on comparable debt is 5.405%, how much should an investor expect to pay for an A-rated corporate bond with a 6.145% annual coupon, nine years to maturity and a $1,000 par value? A. $1,000 B. $9
Ohio State - BUS-FIN - 620
Business Finance 620 Practice Final Exam_ 1. Your firm has a portrait of the company founder that originally cost $250, has an undepreciated book value of zero, and is worth an estimated $175,000 because the artist is famous. Last week, the Ann Arbor Mus
Ohio State - BUS-FIN - 620
SMALL BUSINESS CASE Economic Break-Even RevenueA number of students have asked for additional information on economic break-even revenue, so I've prepared the following explanation based on the small business case we used in class. I hope you find this u
Ohio State - BUS-FIN - 620
Business Finance 620Exam 1 Practice Questions1Chapter 1+2 ReviewWhich of the following statements about the corporate form of organization is correct? g A. When a corporation fails, shareholders cannot lose more than the amount of their personal wealt
Ohio State - BUS-FIN - 620
Business Finance 620Exam 2 Practice Questions30Chapter 11 ReviewHow much should you be willing to pay for a share of stock with a dividend yield of 5.5%, a 13.7% required y q return, and an expected price one year from today of $40? A. B. C. D. $33.42
Ohio State - BUS-FIN - 620
Business Finance 620Final Exam Practice Questions53Chapter 13 ReviewWhat is BMT's WACC? BMT Products reports the following information: 1.57 million shares of common stock outstanding with a price of $26.50 69,000 shares of preferred stock outstandi
Colorado - MATH - 4430
Discontinuous RHSThe method of Laplace transforms gives us a way of dealing with the nonhomogeneous equationy + p(x)y + q (x)y = g (x)when g (x) is piecewise continuous, which for our purposes we will take to mean a function that iscontinuous except f
Colorado - MATH - 4430
Eulers MethodWe have seen that few rst order IVPs can be solved explicitly, but that in many cases we canverify that a unique solution does exist. In practice, it will suce to have an accurate approximationto that solution. Here we will examine one of
Colorado - MATH - 4430
Exact EquationsIn solving rst-order linear equations and separable equations, we made use of exact derivatives.We now look at the most general setting in which we can use this idea to solve rst-order ODEs.We want to know when a rst-order dierential equ
Colorado - MATH - 4430
Existence/UniquenessRecall the theorem:Theorem Given the IVPy = f (x, y ),y (x0 ) = y0 ,suppose f and f /y are continuous in the rectangle R given byx0 x x0 + a|y y0 | b.Compute the valuesM=max |f (x, y )|, = min a,(x,y ) in RbM.Then the P
Colorado - MATH - 4430
1st-Order LinearHomogeneous CaseOn of the simplest dierential equations we can consider is a rst-order linear nonhomogeneousdierential equation, i.e. one of the formy + f (x)y = 0.A theme we will keep returning to is the idea of an exact derivative.
Colorado - MATH - 4430
Improved Eulers MethodEulers method was a good rst start at approximating solutions to dierential equations that wecannot solve. The error (i.e. the dierence between y (x) and y (x) at a particular x-value) is atmost a xed constant times the step size
Colorado - MATH - 4430
Differential EquationsTerminologyDefinition Let y = f (x). An ordinary dierential equation is a relation between y and one ormore of its derivatives.ExampleThe following are all ordinary dierential equations:(1)dy+ 5xy = 0dx(2)d2 y= x + y2dx2
Colorado - MATH - 4430
Picard IteratesFrom our study of exact equations, it becomes apparent that very few dierential equations (henceIVPs) can be solved explicitly. Soon, we will study methods for numerically approximating solutionsto an IVP, and in any practical applicatio
Colorado - MATH - 4430
Runge-Kutta MethodThe Runge-Kutta method, discovered by German mathematicians Carl Runge and Martin Kutta,is a powerful fourth order method (i.e. the error is at most a xed constant times the fourth powerof the step size, h), thus a great improvement o
Colorado - MATH - 4430
Separable EquationsWe have found a strategy for solving rst-order linear equations, and would now like to consider aparticular class of rst-order nonlinear equations. We will again make use of exact derivatives.Definition A dierential equation that can
Colorado - MATH - 4430
Algebraic Properties of Solutions2nd-Order Linear HomogeneousWe will begin our study of second-order dierential equations with the linear homogeneous case,that is we will consider dierential equations of the formy + p(x)y + q (x)y = 0.Since this equa
Colorado - MATH - 4430
Linear Eqs With Constant CoefficientsWe continue to look at the dierential equationay + by + cy = 0but now consider the case where the roots of the characteristic equation are complex. We rst buildsome tools to help us toward this goal.Complex-valued
Colorado - MATH - 4430
Linear Eqs With Constant CoefficientsWe still want to consider 2nd order linear equations of the formy + p(x)y + q (x)y = 0but now we will restrict our attention to the case where p(x) and q (x) are constant functions. Wewont lose anything by allowing
Colorado - MATH - 4430
Impulsive FunctionsOften in applications, we want to solve the dierential equationy + p(x)y + q (x)y = g (x)but all we know about g (x) is(1) g (x) = 0 except on a small interval x0 x x1(2) the integral of g (x) over this small interval has some know
Colorado - MATH - 4430
Judicious Guessing(or Undetermined Coefficients)Recall that Variation of Parameters gave us a way to produce a particular solution to the nonhomogeneous equation, given that we could solve the homogeneous equation. Here we will look at afew shortcuts t
Colorado - MATH - 4430
The Laplace TransformWe begin by dening a certain linear operator called the Laplace transform, which we will use toturn the problem of solving a second order dierential equation into the much simpler problem ofsolving an algebraic equation.Definition
Colorado - MATH - 4430
Laplace Transform PropertiesBy building up some basic properties of the Laplace transform, we can expand the list of functionswe know the transform of, thus increasing the number of IVPs we can solve by this method.Property 1: If F (s) = L [f (x)], the
Colorado - MATH - 4430
The Nonhomogeneous EquationLinear Operators and KernelsWe have seen that given a second-order linear homogeneous equationy + p(x)y + q (x)y = 0we can always dene a linear operatorL[y ] = y + p(x)y + q (x)y.In this terminology, the function y (x) is
Colorado - MATH - 4430
Reduction of Order and Double RootsWe have found the general solution to the equationay + by + cy = 0in the case where the characteristic equation has distinct real roots, or complex roots. It remainsto consider the case when we have a double root, th
Colorado - MATH - 4430
Variation of ParametersRecall that our last theorem states that the nonhomogeneous equationy + p(x)y + q (x)y = g (x)has the general solutiony (x) = (x) + c1 y1 (x) + c2 y2 (x)where (x) is a particular solution to the nonhomogeneous equation and c1 y
Colorado - MATH - 4430
The Laplace TransformWe again consider the nonhomogeneous IVPy (x0 ) = y 0 .y = Ay + gIn class, following Braun pp. 368-369, we showed that the Laplace transform applied to both sidesof this equation gave the new matrix equation(sI A)Y (s) = y 0 + G
Colorado - MATH - 4430
Results from Linear AlgebraWe rst state the basic existence/uniqueness theorem for 1st-order linear systems and examine someof the consequences.Theorem (Existence/Uniqueness) The 1st-order linear homogeneous IVPy = Ay ,y (x0 ) = y 0always has a uniq
Colorado - MATH - 4430
Linear SystemsWe will now generalize some of the results from second order equations by considering(1) higher order dierential equations(2) systems of rst order dierential equations.It will turn out that the rst case can be reduced to the second, so w
Colorado - MATH - 4430
Repeated EigenvaluesRecallWe are now in the position that we can nd (at least) as many linearly-independent solutions tothe homogeneous equationy = Ayas there are distinct eigenvalues of A (real or complex). This is because for each real eigenvalue
Colorado - MATH - 4430
Variation of ParametersWe now consider the nonhomogeneous IVPy (x0 ) = y 0 .y = Ay + gIn class, following Braun pp. 360-361, we showed that the method of variation of parameters couldbe used to nd the following solution to this IVP:xy (x) = eA(xx0
Colorado - MATH - 4430
Complex EigenvaluesBackground on Complex Eigenvectors/EigenvaluesRecall that given a matrix A, we said that a nonzero vector v was an eigenvector of A with eigenvalue ifAv = vwhere is a scalar. Nothing about this denition required that be a real numb
Colorado - MATH - 4430
The Eigenvector/Eigenvalue MethodWe rst recall the following from linear algebra:Definition Let A be an n n matrix. A vector v such thatAv = vfor some scalar is called an eigenvector (EV) of A with eigenvalue (ev) .Before we discuss how these objects
Colorado - MATH - 4430
Fundamental Matrix SolutionsNow that we can solve the homogeneous equationy = Aywe will develop some machinery that will become useful as we move toward techniques for solvingthe nonhomogeneous equation.Recall that the general solution to the homogen
Colorado - PHYS - 3220
Physics 3220Homework 4 Solutions1. Visualizing a possible harmonic oscillator ground state. (5 points)In PHYS 2170 and occasionally in class, we write the Schrdinger equation toemphasize the curvature of the wave functions. You can use the curvature t
Colorado - PHYS - 3220
Physics 3220Homework 6 SolutionsDue Oct. 7, 20111. Figure out the p-space representation of x_operator. (5 points)In the position-space representation of quantum mechanics, we use a spatial and timedependent wave function and a group of operators for
Colorado - PHYS - 3220
In[5]:=ListPlot0, 0 , 1, 3 , 3, 6 , 3, 9 , 3, 11 , 1, 12 ,6, 14 , 3, 17 , 3, 18 , 3, 19 , 6, 21 , AxesLabeld, En2015En10512345d6
Colorado - PHYS - 3220
b)r(u0Sa Ctth:,c~)r.,.t'"--(-:~J[)v, ~.lG:-t't1&11 [r":(, if>A ,L ,\.lVW'ViOL).E.t; b"f'cfw_: iA-c,Jtlt- fl,\ \ s ;,'.Dcfw_.-(I/l),!)'1 lll.l; ) :;- ('3 I "3 J; I'Ii /1\.~~Oly"t+~\~Q;nI(]3)-:>"'Cf<:U\rt Sof'.tf Nt
Colorado - PHYS - 3220
In[9]:=2f _ :Sin 412Cos Cos Sin 2Cos In[10]:=44Sin 2g _ :Cos 2In[13]:=Plot4Sin 2Sin 2, , 0, 100,14Sin 2Cos 4Cos 0.5200.51.0Out[13]=1.52.02.53.0406080100
Colorado - PHYS - 3220
Lecture Notes on Quantum Mechanics - Part IIYunbo ZhangInstituter of Theoretical Physics, Shanxi UniversityAbstractIn this chapter we solve the stationary Schrdinger equation for various types of one dimensionalopotentials, including square potentia
Colorado - PHYS - 3220
11/10/2010Lecture 17: Angular MomentumReading: E&R Chapter 18.4, 18.5Outline:Classical DescriptionCommutation and QuantizationThe Spherical Harmonics1Classical Angular Momentum Consider a body of mass undergoing circular motion: Since velocity i
Baton Rouge CC - CHEM - 101
Chemistry 101 ReportSeparation of a MixtureFeb 25th, 2012Purpose:This lab was the separation of the components of a mixture. The three objectives in this lab were:1. Learn the different separation techniques which include; sublimation, extraction,de
Simon Fraser - BUSINESS - 424
The Measurement Approachto Decision UsefulnessScott Chapter 6 | ShillerPresented by: TeresaChiuDominic FungKay KuangDanielle LeeJing LiuAgendaIntroduction to MeasurementApproach and Behavioural FinanceTeresaProspect TheoryKayStock Market Bu
Simon Fraser - BUSINESS - 424
OLD PERFORMANCE SYSTEM (result control)Managers spent more time explaining why changes in costs were caused by problemswith our accting system than they did fixing the problems. Bob NenniGoal in Kansas City Works: differentiation orientedCash incentiv