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1. NAME_____________________________ IT personnel use _____ to produce _____. A. IT components, IT services B. Computer-based information systems, IT architecture C. IT infrastructure, IT architecture D. IT infrastructure, IT platform 2. Amazon is using its IT infrastructure to deliver a variety of services for all of the following reasons except: A. because the company only uses 10 percent of its processing capacity at any one time B. to stablize profits and revenue C. to compete with Google D. to help start-up companies with their IT needs 3. Which of the following statements about information systems is not correct? A. Information systems are concentrated in the IS Department. B. Information systems tend to follow the structure of the organization. C. Information systems are based on the needs of employees. D. Any information system can be strategic. E. Managing information systems is difficult. 4. The Internet has had which of the following impacts on the way you purchase your textbooks? A. The Internet gives you fewer choices. B. The Internet increases your bargaining power. C. The Internet provides you with less information. D. The Internet decreases your bargaining power. E. The Internet increases your switching costs. 5. Which of the following is a traditional, major IS function? A. Managing systems development B. Partnering with the firms executives C. Managing outsourcing D. Educating non-IS managers about IT E. Incorporating the Internet and electronic commerce into the business 6. Which of the following is not an overall trend in software? A. Increased complexity B. Increased cost C. Increased number of errors D. Increased amount of mainframe software written by users E. Increasingly large percentage of information systems costs 7. Which of the following is not a characteristic of todays typical software? A. Efficient B. Full of errors C. Poorly designed D. Expensive E. An art as well as a science 8. Which of the following is not an advantage of open-source software? A. Produces high quality code B. Produces code that can be changed to meet the needs of the users C. Bugs are discovered quickly D. Support available only through online communities of core developers E. Produces reliable code
9. A(n) _____ is a network designed to serve the internal informational needs of a single organization. A. global network B. extranet C. Internet D. intranet E. World Wide Web 10. Applications offered by the Internet2 include which of the following? A. remote diagnosis B. digital libraries C. distance education D. virtual laboratories E. all of the above 11. The _____ is a global wide-area network that connects approximately one million organizational computer networks. A. global network B. extranet C. Internet D. intranet E. World Wide Web 12. The ______________________ holds that the timing of the user of specialized knowledge can create a differentiation advantage as long as the knowledge remains unique. A. stakeholders model B. shareholder value model C. customer relationship model D. stockholder share model E. unlimited resources model 13. The business diamond is useful for designing new organizations and diagnosing organizational troubles. Which component of the business diamond would include payroll, accounting, and inventory? A. Business Processes B. Values and Beliefs C. Tasks and Structures D. Business Levers E. Management Systems 14. General managers should take an active role in decisions about information systems. This is vital because of which one of the following reasons? A. IS cannot be trusted to make good decisions. B. IS staff has not been trained to make general business decisions. C. IS personnel do not have the companies best interests as their focus D. IS systems are designed to support business decisions. E. IS systems are normally incongruent with business goals. 15. It is very difficult to manage data for which of the following reasons? A. amount of data stays about the same over time B. data are scattered throughout organizations C. decreasing amount of external data needs to be considered D. data security is easy to maintain E. data are stored in the same format throughout organizations 16. You have moved to a different apartment, but your electricity bill continues to go to your old address. The Post Office in your town has a problem with its data management, which is: A. Data redundancy
B. Data inconsistency C. Data isolation D. Data security E. Data dependence 17. The data in a data warehouse have which of the following characteristics? A. are organized by subject B. are coded in different formats C. are updated in real time D. are typically retained for a defined, but limited, period of time E. are organized in a hierarchical structure 18. Electronic commerce provides opportunities to do all of the following except: A. For companies to expand their reach B. For companies to expand at relatively high cost C. For companies to put rich information on their Web sites D. For companies to increase market share E. For companies to adopt new business models 19. The advantages of B2C for consumers include all of the following except: A. You can buy from home 24 hours per day, 7 days per week. B. You have a wider variety of products to choose from. C. You typically cannot access additional information, so you do not have information overload. D. You can easily compare prices and features. E. You can find unique items. 20. In the _____ B2B application, the orders of many buyers are aggregated so that they total to a large volume, in order to merit more seller attention. A. buy-side B. sell-side C. auctions D. group purchasing E. electronic exchange 21. This asks the questions, "What tasks will be performed? How will the work be performed?, Who will do the work?, and Where will the work be performed"? A. Job design framework B. Job description analysis C. Custom system framework D. Work entry point E. Job analysis system 22. This technology has enabled changes in many jobs. For example financial analysts can download reports from a corporate web site in minutes. A. email system B. groupware C. Internet D. laptops E. collaboration 23. Technology has significantly changed the way work is done and how managers interact with employees. One technological solution helps to solve the problem of lack of direct supervision by permitting managers to monitor employees based on ________________________ compensation strategies. A. valued added work B. pay for performance C. team work
D. work performance E. piece work performance 24. Enterprise resource planning systems are very _____ software products, meaning that companies typically have to change their _____ to accommodate how the software functions. A. unstructured, business processes B. structured, reporting relationships C. structured, accounting processes D. unstructured, control inventory E. structured, business processes` 25. If you buy a science fiction book from Amazon.com, the companys software will automatically recommend similar books bought by other readers. This is an example of: A. cross-selling B. up-selling C. one-to-one marketing D. viral marketing E. permission marketing 26. Supply chain complexity and scale: A. Affect both very small companies and large, global organizations B. Were difficult to address before the Internet C. Result when firms product complex products and services D. Result when firms implement full-scale, supply chain management systems E. Result when companies implement extranets and EDI 27. Which era of information resources focused primarily on effectiveness such solving problems and creating opportunities? A. 1960s B. 1970s C. 1980s D. 1990s E. 2000+ 28.This is defined as the available data, technology, people, and processes within an organization? A. Information Management B. Information Technology C. Information Systems D. Information Resources E. Information Networks 29. Which one of the following would NOT be considered an information resource that is available to a firm? A. Information and knowledge B. Proprietary technology C. End users of IS D. Business processes E. Customer interaction 30. In this business structure a common view of a firm is as a hierarchy organized around a set of functions. Each group has a core competency that it concentrates upon. A. Technology B. Business reengineering approach C. Silo D. Process Control E. Business process
31. These are comprehensive software packages that incorporate all modules needed to run the operations of a business. They should include the following modules: Manufacturing, Accounting, Human resources and Sales. A. BRP systems B. Groupware system C. ERP systems D. TQM systems E. BBB systems 32. By 1998, approximately _____% of companies with annual revenues greater than $1 billion has installed ERP systems. A. 20 B. 25 C. 30 D. 35 E. 40 33. Decisions today are becoming _____ complex, due to _____ uncertainty in the decision environment. A. less, decreased B. more, decreased C. less, increased D. more, increased E. about the same, decreased 34. _____ provides users with a view of what is happening, where _____ addresses why it is happening. A. Multidimensional data analysis, structured query language B. Data mining, multidimensional data analysis C. Data mining, expert system D. Multidimensional data analysis, neural networks E. Multidimensional data analysis, data mining 35. Which of the following are not provided by digital dashboards? A. Drill down B. Transaction processing C. Status access D. Key performance indicators E. Exception reporting 36. The information systems planning process proceeds in which order? A. Organization mission organization strategic plan IS strategic plan new IT architecture B. Organization mission IS strategic plan organization strategic plan IS operational plan C. Organization strategic plan organization mission IS strategic plan new IT architecture D. IT architecture IS strategic plan organization strategic plan organization mission E. IS development projects IS operational plan new IT architecture organization mission 37. The _____ that changes are made in the systems development life cycle, the _____ expensive these changes become. A. sooner, less B. later, less C. more frequently, more D. more extensively, more E. sooner, more 38. Any systems acquisition effort is mainly driven by A. organizational change B. feasibility studies C. data needs
D. user information requirements E. corporate strategy 39. This counts the actual activities that go into making a specific product or delivering a specific service. A. Total Activity Costing B. Focused Based Costing C. Activity Based Costing D. Unit Based Costing E. Activity Induced Costing 40. This financial calculation provides a percentage rate that measures the relationship between the amount the business gets back from an investment and the amount invested. A. IRR B. ROI C. Payback D. NPV E. EVA 41. Managers want to analyze the costs of informal support of their IT infrastructure for two reasons: the costs and the ____________________________. A. time to fix a problem B. effect the support activity has on morale C. quantity of informal support activity D. the quality of the informal support activity E. relative need across the company 42. What is _____ is not necessarily _____. A. Illegal, unethical B. Ethical, illegal C. Unethical, illegal D. Unethical, legal E. Ethical, legal 43. Which of the following statements is correct? A. An individuals right to privacy is absolute. B. It is difficult to determine and enforce privacy regulations. C. An individuals right to privacy supersedes the needs of society. D. Advances in information technologies have not affected individual privacy. E. The Internet has increased individuals privacy. 44. Your companys computers have been taken over by an attacker and used to attack another organizations information systems. Your problem is which of the following? A. poor security policies and procedures B. lack of due diligence C. downstream liability D. poor service-level agreements E. users have a lack of information security awareness 45. Individuals are finding it convenient and productive to use wireless devices for which of the following reasons? A. To make use of time that was formerly wasted B. To become more efficient C. Work locations are more flexible D. To be able to allocate working time around personal and professional obligations E. All of the above 46. Of the following, which is the major problem with smart phones?
A. They are too slow. B. They are too expensive. C. They can be used to compromise security. D. Their screens are too small. E. Their browsers are not fully functional. 47. Which of the following statements about Wi-Fi is not correct? A. Wi-Fi provides simple Internet access. B. Laptop PC scan contain chips that can send and receive Wi-Fi signals. C. Many companies offer free Wi-Fi access in their stores. D. Wi-Fi requires encryption for secure transmissions. E. Wi-Fi is expensive to set up. 48. This is a piece of data that is stored on the users computer by a company that the user accesses using a web browser? A. Script B. Cookie C. Data-Link File D. DLL File E. Data file 49. This ethical theory states that managers are entrusted with a fiduciary responsibility to all those who hold a stake in or a claim on the firm. A. Stockholder theory B. Stakeholder theory C. Property theory D. Fiduciary theory E. Normative theory 50. What information does a person or an organization have a right or a privilege to obtain, under what conditions and with what safeguards is part of this ethical issue? A. Privacy B. Accuracy C. Accessibility D. Perfection E. Property

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American College of Gastroenterology - ACCOUNTING - ac550

PROJECT 2Note: Each part of the case is independent of each other. Upload into your Dropbox when you complete the assignment.Part AOn December 31, 2010 Felt Company's inventory burned. Sales and purchases for the year had been $1,400,000 and $980,000, r

Acadia - WOMENS STU - 190

Wang1Hercules,Achilles,Superman.Theseareindividualsidentifiedasheroes.Aside fromthesuperhumanstrength,extraordinarypowers,anddevilishgoodlooks,these heroesallhaveonethingincommon:theyarefictional.Heroes,inthetruestsenseof theword,donotexistinreallifethey

Penn State - CHEM - 466

Ch 6 Entropy and The Boltzmann Law

UNC Wilmington - MATH - 6203

2 Basic Options79boundary to appear while in the region (D0 /r, ) it is possible for a free boundary to appear. If D0 /r < , then in the entire region (, ), it is possible for a free boundary to appear. Therefore if < max(, D0 /r) = max(1, D0 /r), then

UNC Wilmington - MATH - 6203

602 Basic Options (E ) = Thus we haveln E [ln S + (r D0 ) (T t)] 2 (T t)/2 T t ln E r(T t) [ln S D0 (T t)] 2 (T t)/2 = T t ln S1 ln S0 + 2 (T t)/2 = . T t max(S , E )G(S , T ; S, t)dS = f (S1 , S0 , t; ).er(T t)EConsequently the conclusion is prov

UNC Wilmington - MATH - 6203

482 Basic Optionsis a linear function of c for c (3.2081, 4.8784). From the data we know (3.2081) = 0.3 and (4.8784) = 0.4. Thus (c) = (3.2081) + (4.8784) (3.2081) (c 3.2081) 4.8784 3.2081 0.1 (c 3.2081). = 0.3 + 4.8784 3.2081Consequently (4.5) = 0.3 +

UNC Wilmington - MATH - 6203

2 Basic Options39 2 p + 1 2 (t)S 2 p + [r(t) D (t)]S p r(t)p = 0, 0 t 2 2 S S Therefore 0 S, t T, p(S, T ) = max(1 S, 0), 0 S.p(S, t) = Ee (t) N (d2 ) (S/E )e (t) N (d1 ) = Ee (t) N (d2 ) Se (t) (t) N (d1 ) is the value of a put option with time-depend

UNC Wilmington - MATH - 6203

2 Basic Options3321. Suppose that S is a random variable which is dened on [0, ) and whose probability density function is G(S ) = 2 2 2 1 e[ln(S/a)+b /2] /2b , 2bSis the solution of the initial-value problem 2u u , < x < , = x2 u(x, 0) = u (x), < x <

UNC Wilmington - MATH - 6203

2 Basic Options2919. Suppose V (S, t) is the solution of the problem 1 2V V V + 2 (S )S 2 2 + (r D0 )S rV = 0 , 0 S, t T, t 2 S S V (S, T ) = V (S ), 0 S.TS , = T t and V (S, t) = (S + Pm )V (, ), where Pm is S + Pm a positive constant. a) Show that V

UNC Wilmington - MATH - 6203

242 Basic Optionsb) Because V = Erer(T t) , t we have V 1 2V V + 2 S 2 2 + (r D0 )S rV t 2 S t = Erer(T t) rEer(T t) = 0. If E is an amount of money you want to have at time T . Eer(T t) is the amount of money you need to deposit in a bank at time t. 16

UNC Wilmington - MATH - 6203

162 Basic OptionsVar [ ] = E 2 E [ ] = = e2b b2 (e 1). a2222 1 3b2 1 e 2 e2b a2 a11. a) Show that if an investment is risk free, then theoretically its return rate must be the spot interest rate. b) Using this fact and Its lemma, derive the Black-Sc

UNC Wilmington - MATH - 6203

2 Basic Options9b) Due to the fact that the sum of two normal random variables is a normal variable, it is easy to show that the sum of n normal variables, 1 t + + n t, and the limit of the sum as n are normal variables. BecausenE [X (t)] = lim En i=

UNC Wilmington - MATH - 6203

2 Basic OptionsProblems1. a) Show 2 1 ex /2 dx = 1. 2b) Show that 2 2 1 e(xa) /2b dx = 1 b 2holds for any a and b. (Because this is true and the integrand is always possitive, it can be a probability density function.) c) If the probability densit

UNC Wilmington - MATH - 6203

1 IntroductionProblems1. What is the dierence between taking a long position in a forward contract and in a call option? Solution: Taking a long position in a forward contract is an obligation to buy an underlying asset at a xed price. Taking a long pos

UNC Wilmington - MATH 6203 - MATH 6203

1Homework Problems (Part I) for Derivative Securities and Dierence MethodsProblems31 IntroductionProblems1. What is the dierence between taking a long position in a forward contract and in a call option? 2. Suppose the futures price of gold is curre

UNC Wilmington - MATH 6203 - MATH 6203

Main Subjects of Chapters 3 and 41. Closed-form solutions for European barrier options, properties of European and American barrier options, and relations among knock-out, knock-in and vanilla options, Problems 1*1 , 2a,b,d,e, 3* (Chapter 3) 2. Asian opt

UNC Wilmington - MATH 6203 - MATH 6203

2 Basic Options87P (S, t) and Sf (t) are known functions obtained from S P the solution of the American put option problem. Let P = and P . For them, the formulations are P D0 = D0 1 2 P P 2P P + 2 S 2 + (r D0 )S rP + S 2 2 = 0, t 2 S 2 S S Sf (t) S, 0

UNC Wilmington - MATH 6203 - MATH 6203

3 Exotic OptionsProblems1. Consider the following problem: 1 2 2 2V V V t + 2 S S 2 + (r D0 ) S S rV = 0, 0 S, t T, where 1 (S ) and 2 (S ) are continuous functions and 1 (B ) = 2 (B ) may not hold. a) Try to nd such a relation between 1 (S ) and 2 (S )

UNC Wilmington - MATH 6203 - MATH 6203

1263 Exotic Options Consequently, noticing Co (S, tK ; Bl ) = Co (S, tK ; Bl ) = Gc (S ), we obtain Co (S, tk ; Bl ) = max ert Bl Co (S , tk+1 ; Bl )G1 (S , tk+1 ; S, tk , Bl )dS ,Gc (S ) max ert Bl Co (S , tk+1 ; Bl )G1 (S , tk+1 ; S, tk , Bl )d

UNC Wilmington - MATH 6203 - MATH 6203

3 Exotic Options129c(bE ) , t; r, D0 + 2= er(T t) f =e =cr (T t)= c(S, t; r, D0 ) f(bE )2 (D0 +)(T t) e , 2 (T Eer(T t)2 Bl (t) D0 (T t) Se , 2 (T Eer(T t) t) t)2 Bl (t) , t; r, D0 . SConsequently, we nally have c0 (S, t) = c(S, t; r, D0 ) Bl

UNC Wilmington - MATH 6203 - MATH 6203

3 Exotic Options1371 + rT A, i.e., (1 + D0 T )S + (1 + rT )A < 0. Thus 1 + D0 T 1 + rT 1 A if < , then when S > , the PDE cannot be used. If 1 + D0 T 1 + rT 1 1 + rT > , then when S > A, the PDE cannot be 1 + D0 T 1 + D0 T 1 + rT A <S< A, we have (1 + D

UNC Wilmington - MATH 6203 - MATH 6203

1823 Exotic Optionsc) Let V (S, H ) = SW ( ) and = H/S . Then V S 2V S 2 V H V (S, H ) H Thus 1 2 2 2V V S + (r D0 ) S rV 2 2 S S dW 2 2 d 2 W rW + (r D0 ) W =S 2 d 2 d dW 2 2 d 2 W =S + (D0 r) D 0 W 2 d 2 d and V dW (S, S ) = (1). H d dW H dW 2 = W , d

UNC Wilmington - MATH 6203 - MATH 6203

1843 Exotic Options C+ + C = 1, C + C = 0, + + From the rst two conditions, we have C+ = and W = C++ C + + + C = f 2 , f2 f2 C + + C = . + + f2 f2 f2 + , and C = + + f 1 + C f 1= + f 1+++ + f 1.Subtracting the third condition from the

UNC Wilmington - MATH 6203 - MATH 6203

2023 Exotic OptionsTherefore according to these relations above, for the integral given we have er = S1 S0 0 S1TS1T (S1T , S2T ; S1 , S2 , t)dS2T dS1T1 2 det P1 2 T 1 1 e(1 Pe1 ) P (1 Pe1 )/2 dS2T dS1T S1T S2T 1 = S1 2 1 2 201 = S1e[1 (z21 )2201 1

UNC Wilmington - MATH 6203 - MATH 6203

3 Exotic Options2251 2 and being . . . . n b) For the European option with a payo min(S0 , S1 , , Sn ), its price is Vmin (S1 , S2 , , Sn , t) = S0 Nn B10 , B20 , , Bn0 ; 120 , 130 , , (n1)n0 +S1 Nn (B21 , B31 , , B01 ; 231 , 241 , , n01 ) . . . +Sn Nn

UNC Wilmington - MATH 6203 - MATH 6203

4 Interest Rate Derivative SecuritiesProblems1. a) Suppose the spot interest rate is a known function r(t). Consider a bond with a face value Z and assume that it pays a coupon with a coupon rate k (t), that is, during a time interval [t, t + dt], the c

UNC Wilmington - MATH 6203 - MATH 6203

4 Interest Rate Derivative Securities243with A(T ) = B (T ) = 0 and determine the system of ordinary dierential equations the functions A(t) and B (t) should satisfy. Solution: Substituting V (r, t) = eA(t)rB (t) into the equation yields dA dB r + (a0 +

UNC Wilmington - MATH 6203 - MATH 6203

4 Interest Rate Derivative Securities251 = = =2 + ( + )2 e(T t) ( + ) ( + )e(T t) ( ) 2 ( + )e(T t) ( ) 2 e(T t) ( + )e(T t) ( ) 2 ( + )e(T t) ( ) 2 e( +)(T t)/2 ( + )e(T t) ( )2/ ( + )/ ( )/( + )/2/e( +)(T t)/ ,the two expressions are identical.

UNC Wilmington - MATH 6203 - MATH 6203

2544 Interest Rate Derivative SecuritiesT+V (r, T + ) V (r, T ) =TV dt = tT+ (t T )dt = 1.TThat is, V (r, T ) = V (r, T + ) + 1 = 1. In the rst problem V (r, T ) = V (r, T + ) is also identically equal to one. Consequently, from T to any t < T ,

UNC Wilmington - MATH 6203 - MATH 6203

4 Interest Rate Derivative Securities261Then Vf (r, t ) gives the value of the oor and the premium of the oor is given by Vf (r , t ), where r is the spot interest rate at time t . 19. a) S is a random vector and its covariance matrix is B. Let S = AS,

UNC Wilmington - MATH 6203 - MATH 6203

2804 Interest Rate Derivative Securities r = (u w). Therefore the equation for any convertible bond is 1 2V 2V 1 2V V + 2 S 2 2 + Sw + w2 2 t 2 S Sr 2 r V V + (u w) rV + kZ = 0. + (rS D(S, t) S r In this equation, only the market price of risk for the i

UNC Wilmington - MATH 6203 - MATH 6203

2844 Interest Rate Derivative Securitiesand using the nal condition, we arrive at b0 (t) = kZ 1 er(T t) , rwhich is nonnegative for t T . Dene B c (S, t) = Bc (S, t) b0 (t). Thus Bc (S, t) = B c (S, t) + b0 (t). Substituting this relation into the orig

UNC Wilmington - MATH 6203 - MATH 6203

1Mathematics 2Y Spring 1995 Probability Theory Contents x1. Basic concepts. Sample space, events, inclusion-exclusion principle,probabilities. Examples. x2. Independence, conditioning, Baye's formula, law of total probability. Examples. x3. Discrete ran

Quebec Trois-Rivieres - MA - 141

1. (a) Find parametric equations for the line that passes through the point (2 , 0,1) and is perpendicular to the plane with equation 4 x y 2z = 1. Solution. The direction vector for this line is v = (4,1,2) and it must pass through the point (2, 0,1). Th

Quebec Trois-Rivieres - MA - 141

whose equations are: L1 : 8< : x=t y=2t z=3 , L2 : 8< : x = 1 + 2t y = 3 2t z = 3t. Solution. Since the plane contains the two lines, their direction vectors (1 ,1, 0) and (2,2, 3) are parallel to the plane. Hence their cross product will be a normal vect

Quebec Trois-Rivieres - MA - 141

(1,1, 0) (2,2, 3) = _ ijk 1 1 0 2 2 3 _ = 3i 3j + 0k = (3,3, 0). To get a point in the plane, we can take any point in either line, so just set t = 0 in the equations for L1 to get the point (0, 2, 3). The equation for the plane is

Quebec Trois-Rivieres - MA - 141

z), and then graph the surface z = y2/x for z _ 0. Be sure to label your axes. Solution. Setting z = c 6= 0, we can solve for x to get x = y2/c. These graphs are (sideways) parabolas in the xy-plane, that get less steep as c gets large, and more steep as

Quebec Trois-Rivieres - MA - 141

that these level curves all have a hole where x = 0 since z is not defined there. (See the link to the level curves picture.) In graphing the whole surface, we sketch two cross sections for x = 1 and x = 2. These again are parabolas with equations z = y2

Quebec Trois-Rivieres - MA - 141

3. Calculate the following limits, or show that they do not exist. (a) lim( x,y)! (0,0)e2xyy2 x2 + y2 Solution. As (x, y) ! (0, 0), the numerator approaches e0 = 1, since it is a continuous function of x and y, while the denominator approaches 0 and is

Quebec Trois-Rivieres - MA - 141

(b) lim( x,y)! (0,0)2xy2 x2 + y2 Solution. Convert to polar coordinates to get limr! 0+2r3 cos _ sin2 _ r2 = limr! 0+2r cos _ sin2 _ = (2 cos _ sin2 _) limr! 0+r = 0. (c) lim( x,y)! (0,0)sin(x

Quebec Trois-Rivieres - MA - 141

Solution. W e take the limit as (x, y) approaches (0, 0) along two different lines with equations y = cx. First, let (x, y) approach (0, 0) along the line y = 0. We get lim( x, y) ! (0, 0) y=0sin(x + y) 2x y = limx! 0sin x 2x = limx! 0cos x 2 = 1 2

Quebec Trois-Rivieres - MA - 141

using lHospitals rule for the second equality. If (x, y) approaches (0, 0) along the line y = x instead, we get lim( x, y) ! (0, 0) y=ssin(x + y) 2x y = limx! 0sin(2x) x = limx! 02 cos(2x) 1 = 2, using lHospitals rule for the second equality. Since

Quebec Trois-Rivieres - MA - 141

4. A function y = (y1, y2) is defined by y1 = 3x21 + x22 and y2 = x1x2 1 x1 + 2 . (a) Find the Jacobian matrix _ @yi @xj _ , and say where y is differentiable. Solution. yx = _ @yi @xj _ =@y1 @x1 @y1 @x2 @y2 @x1 @y2 @x2! = _ 6x1 2x22x2 +1 ( x1+2)2 x1 x

Quebec Trois-Rivieres - MA - 141

Approximate y(1.01, 2.02). Solution. Let _y = y(1.01, 2.02) y(1, 2). We know that dy at (1, 2) approximates _y, so we have _y _ dy|(1,2) = yx|(1,2)dx = _ 6 4 5 1 _ 0.01 0.02 _ = _ 0.14 0.07 _ . Here we have taken dx1 = 1.01 1 = 0.01 and dx2 = 2.02 2 = 0.0

Quebec Trois-Rivieres - MA - 141

5. Suppose we have functions z(y1, y2, y3) : R3 ! R2 and y(x1, x2) : R2 cfw_(0, 0) ! R3 given by z= _ z1 = y1y2y3 z2 = y1y2 2 + 2y2y 23and y = 8< : y1 = x2 cos(_x1) y2 = x2 sin(_x1) y3 = ln(x21 + x22 ) (a) Express the Jacobian matrix _ @zi @xj _

Quebec Trois-Rivieres - MA - 141

of the composition z _ y as a product of two matrices (do not evaluate this product). Solution. The chain rule says zx = zyyx. So zx = _ y2y3 y1y3 y1y2 y2 2 2y1y 2 + 2y2 3 4y2y 3 _0 @ _x2 sin(_x1) cos(_x1) _x2 cos(_x1) sin(_x1)2x1 x21 +x22 2x2 x21 +x221

Quebec Trois-Rivieres - MA - 141

Find _ @z2 @x1 _x2(3,1) and simplify your answer. Solution. To get _ @z2 @x1 _x2we must multiply the second row of the first matrix above by the first column of the second matrix, and then we need to evaluate at (x1, x2) = (3,1). We get _ @z2 @x1 _x2

Quebec Trois-Rivieres - MA - 141

Notice that we have y1(3,1) = cos(3_) = 1, y2(3,1) = sin(3_) = 0 and y3(3,1) = ln 10. Thus plugging in x1 = 3 and x2 = 1 in the above, the first and last terms of the sum become 0, and we are left with y2 3_x2 cos(_x1) =

Quebec Trois-Rivieres - MA - 141

(ln 10)2_(1) cos(3_) = _(ln 10)2. 6. Suppose f(x, y) and g(x, y) are differentiable functions, and define h(x, y) = f(x, y)g(x, y).

Quebec Trois-Rivieres - MA - 141

Show that dh = fdg + gdf. Solution. By definition, dh = hxdx + hydy. By the product rule, hx = @ @x (fg) =

Quebec Trois-Rivieres - MA - 141

fxg + fgx and hy = @ @y (fg) = fyg + fg y. Thus, substituting these expressions into the equation for dh and rearranging the terms, we have

Quebec Trois-Rivieres - MA - 141

dh = (fxg + fgx)dx + (fyg + fgy)dy = g(fxdx + fydy) + f(gxdx + gydy) = gdf + fdg. 3

Cal Poly Pomona - DFS - dsfsd

A.P. Biology: Chapter 12 & 13 Test1. The centromere is a region in which a. chromatids are attached to one another. b. metaphase chromosomes become aligned. c. chromosomes are grouped during telophase. d. the nucleus is located prior to mitosis. e. new s

NJIT - MGMT - 691

NEW JERSEY INSTITUTE OF TECHNOLOGY Instructor: Diana Walsh, Esq. Tel.: (973) 596-6418 Fax: (973) 492-5347 E-mail: diana.walsh@njit.edu Webpage: http:/web.njit.edu/~walshdDear Students: As your instructor for MGMT 691 I would like to welcome you to our vi

NJIT - MGMT - 691

a. How should (ethics) we regulate our energy? whom do you think does this well and who benefits?Energy must be controlled by the government.Businesses won't operate without profits motive or without keeping in mind their objective, may be long term. So

NJIT - MGMT - 691

after all the readings of various articles and case law opinions.argue your decisions from a ethical perspective ( motives/consequences of the parties to these cases and is your decision enforcing what is good behavior for the greatest good for the grea

NJIT - MGMT - 691

New meningitis vaccine from India An Indian company called Serum Institute of India Ltd (SIIL) has, in collaboration with the World Health Organization (WHO) and Meningitis Vaccine Project (MVP), developed a new and affordable vaccine for meningococc

NJIT - MGMT - 691

After reading and debating this issue, who do you think is responsible for what goes on in the corporate world? Who, if anyone, should be held accountable and how come? With whom do you agree?Circumstances and pressure have some effect on the decision an

NJIT - MGMT - 691

NEW JERSEY INSTITUTE OF TECHNOLOGY School of ManagementSyllabusDiana Walsh, M.A., J.D (N J Bar) Email: diana.walsh@njit.eduCourse Title: Legal and Ethical Issues Semester: Fall 2007Webpage:http:/web.njit.edu/~walshd/Course No.: Mgmt 691 -851Class T

UC Irvine - CEE - 81B

CEE 81B Lab Report Wells Tsai, 901961031.On the first graph, its easy to see that when the speed is around 40-60 the volume stacks up, and this is for upstream and downstream. This would make sense since there shouldnt be too much of a difference betwee

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History 2055 (Spring 2010)Wednesday, January 20 Went over syllabus. o Need to buy books. Assistant: Spencer McBride o Himes 313 o Monday & Wednesday: 12-1:30 o Smcbri4@lsu.eduFriday, January 22Early European Exploration and Settlement and Indians Exp