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### Math417Quiz5

Course: MATH 419, Spring 2011
School: Texas A&M
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417, Math Quiz # 5 Name &amp; ID number: Texas A &amp; M University Fall 2011 1.[10 points] Use the Linear Finite -Dierence method to approximate the solution of the boundary value problem y 4(y = x), 0 x 1, y (0) = 0, y (1) = 2, with h = 1/2. 2.[15 points] Let x, y Rn . Show that xT .y x 2 y 2. 3.[5 points] Let 357 A = 2 6 4 . 028 Compute A 1 and A .

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417, Math Quiz # 5 Name & ID number: Texas A & M University Fall 2011 1.[10 points] Use the Linear Finite -Dierence method to approximate the solution of the boundary value problem y 4(y = x), 0 x 1, y (0) = 0, y (1) = 2, with h = 1/2. 2.[15 points] Let x, y Rn . Show that xT .y x 2 y 2. 3.[5 points] Let 357 A = 2 6 4 . 028 Compute A 1 and A .
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Texas A&M - MATH - 419
Math 417, Homework 31. Let x0 , . . . , xn be distinct points. In Hermite interpolation, the function hj (x) was dened tobe the polynomial of degree 2n + 1 satisfyinghj (xi ) = 0,hj (xi ) = 0, i = j,(a) Verify that hj (x) = (x xj ) j (x)2 , wherehj
Texas A&M - MATH - 419
Math 417, Homework 41. (a) Derive the following rule for estimating ff (x) 1(f (x + 2h) 2f (x + h) + 2f (x h) f (x 2h) ,2h3and the corresponding error term.(b) Use the centered dierence approximation D0 f to estimate f (x) for f (x) =with h = 0.01
Texas A&M - MATH - 419
Math 417, Homework 51. Consider the system of linear equationsx1 + 2 x2 + 3 x3 = 6x1 + x2 + 2x3 = 24x1 + x3 = 5(a) Write the system in the form (A|b). Solve by reduction to triangular form and backsubstitution.(1) (2) (3)(b) Show that detA = a11 a
Texas A&M - MATH - 419
Math 417, Homework 61. Use the nite dierence scheme to solve the 2-point boundary value problem + = 2x + 1,0 &lt; x &lt; 1,(0) = (1) = 0.Use mesh size h = 2n , n = 1, . . . , 8. Take = 103 . Solve Ah u = f using LU factorizationfor a tridiagonal system as
Texas A&M - MATH - 419
Math 417, Homework 71. Consider410A = 1 4 1 ,014(a) Find Bods.,5b= 6 5(B ), where B is the iteration matrix for the Jacobi and Gauss-Seidel meth-(b) Use the theorem given in class to nd the optimal SOR parameter (you should check thatA satise
Texas A&M - MATH - 419
Math 417, Quiz # 1Name &amp; ID number:Texas A &amp; M UniversityFall 20111 (a) [15 points] Use 2 iterations of the bisection method to calculate thesolution of x3 7x2 + 14 6 = 0 on [0, 1].1 (b) [5 points] How many steps are needed to get accuracy 103 ?
Texas A&M - MATH - 419
Math 417, Quiz # 2Name &amp; ID number:Texas A &amp; M UniversityFall 20111 (a) [16 points] Find the Lagrange and Newton form of the Lagrange interxpolationpolynomial that interpolates f (x) =at the points x0 = 0, x1 =x+11, x2 = 2.1 (b) [4 points] Write
Texas A&M - MATH - 442
Math 442Homework # 1SolutionsTexas A &amp; M UniversitySpring 20111. You are a professional modeler at Texas Department of State Health Services. You havebeen assigned to study an inuenza epidemic which occurred in a boarding school in the northof Dall
Texas A&M - MATH - 442
Math 442Homework # 2Due February 23Texas A &amp; M UniversitySpring 20111. Consider the prey-predator modeldx(t)/dt = x(t)(a1 b1 y (t),dy (t)/dt = y (t)(a2 + b2 x(t).a ) [10 points] In terms of conversion of energy from one source to another, is it po
Texas A&M - MATH - 442
Math 442Homework # 4Due April 4Texas A &amp; M UniversitySpring 20111. The simple pendulum consist of a particle P of mass m suspended from a xed point O bya light string of length a, which is allowed swinging in a vertical plane. If there is no frictio
Texas A&M - MATH - 442
Math 442Lab 1 - WorksheetTexas A &amp; M UniversitySpring 2011In this course we will be using Matlab for numerical analysis of mathematical models. A lot ofuseful information about Matlab is available at http:/www.mathworks.com/academia/.To begin we mus
Texas A&M - MATH - 442
Math 442Lab 2 - WorksheetTexas A &amp; M UniversitySpring 20111. Consider a city with population of 3 106 . Suppose that one third of the people livingin that city have been infected with inuenza. In the absence of antibiotics, health ocialsestimate an
Texas A&M - MATH - 442
Math 442, Quiz # 3Name &amp; ID number:(Solutions)Texas A &amp; M UniversitySpring 2011[30 points] 1. (a) What is a chemical reaction? (b) It is known that the mass is conserved inchemical reactions. Considering equation (1.64), explain how it is possible t
Texas A&M - MATH - 442
Math 442, Quiz # 4Name &amp; ID number:(Solutions)Texas A &amp; M UniversitySpring 2011[30 points] 1. (a) What are the main benets of nondimensionalization? (b) Nondimensionalizethe plant growth model (1.15).a) The main benets are: (1) the relative strengt
Texas A&M - MATH - 442
Math 442, Quiz # 5Name &amp; ID number:(Solutions)Texas A &amp; M UniversitySpring 2011[15 points] 1. What is the process of validating a model? When can we accept a model?First we propose a test (e.g. whether the model predictions match with the recorded d
Texas A&M - MATH - 442
Math 442, Quiz # 6Name &amp; ID number:(Solutions)Texas A &amp; M UniversitySpring 2011[15 points] 1. The Poissons equation related the velocity w of uid in an elliptical pipe isgiven by ( 2 w(x, y )/x2 + 2 w(x, y )/y 2 ) = (p1 p2 )/L. What is the solution
Texas A&M - MATH - 442
Math 442, Quiz # 1 (solutions)Name &amp; ID number:Texas A &amp; M UniversitySpring 2011[30 points] 1. What are the main assumptions of the lake purication model discussed in section1.1 of the textbook?1.2.3.4.The lake has a constant volume.The lake is
Texas A&M - MATH - 442
Math 442, Quiz # 2 (solutions)Name &amp; ID number:Texas A &amp; M UniversitySpring 2011[20 points] 1. What is the essential perquisite of using metered models? Why such models arecalled memoryless?Essential Prequisite: The system being modelled must be qua
Texas A&M - MATH - 442
Math 442Take-home ExamDue March 2Texas A &amp; M UniversitySpring 20111. Consider the lake purication model:rx (t) = (1 + sin(2t)x(t),vwhere x(t) is the concentration of contaminant (gr/m3 ), v is the volume of the lake (m3 ), r isthe mean outow, t
York University - ADMS - 3541
CHAPTER 2: TIME VALUE OF MONEYRATE OF RETURN SINGLE PERIODA discount bond an investment that pays no interest during its life; therefore, theinterest you receive on it is part of the final payment.e.g.The equation only holds for a single period with
York University - ADMS - 3541
CHAPTER 3: SETTING GOALS AND THE FINANCIALPLANNING PROCESSDESIRES AND GOALSA financial goal must possess 2 things: first, the goals outcome can be measuredprecisely in dollars; second there is a deadline for its completion.How to Set Financial Goals
York University - ADMS - 3541
CHAPATER 11: PROPERTY, HOME AND AUTOMOBILEINSURANCEPROPERTY INSURANCE Insures your physical properties your home, clothing, furniture, appliances, jewelersand so on against damage or destruction.1. Home Insurance protects the family against the risk
York University - ADMS - 3541
CHAPTER 4: MEASURING AND CONTROLLING PERSONALFINANCESHOW MUCH IS THE FAMILY WORTH?The family balance sheet or statement of net worth is a photograph of the familysfinancial standing at a point in time. The balance sheet is essential for two reasons:1
York University - ADMS - 3541
CHAPTER 5: FAMILY LAWA separation agreement is a contract between spouses in which they agree to liveseparate lives and set various conditions.A divorce is granted by a court upon application by a petitioner. The Divorce Actgoverns all divorces in Can
York University - ADMS - 3541
CHAPTER 6: THE LIFE CYCLE AND FINANCIALINTERMEDIATIONThe Financial Life Cycle - The lifetime pattern of differing financial position andearning power stages.Family Life Cycle Categories:CategoryDescription1Younger, single2Younger couple, no chil
York University - ADMS - 3541
CHAPTER 7: PERSONAL INCOME TAX RETURNGENERAL CONCEPTS OF INCOME TAXATIONCanadian income taxation is based on self-assessment. With few exceptions, everyresident is required to complete an income tax return on prescribed forms. The finalentry on the fo
York University - ADMS - 3541
CHAPTER 8: INCOME TAX PLANNINGINCOME DEFERRAL If you cant use the income for consumption purposes, you shouldnt have to paytax on it until you can use it.Registered Pension Plans (RPP) Is established by an employer to defer incomepayable to employees
York University - ADMS - 3541
CHAPTER 9: RISK MANAGEMENTSpeculative Risk involves a loss and a gain, but in uncertain amounts. E.g. Lottery andInvestments.Pure Risk involves the probability of loss only. E.g. Early death, disability and theft ofa car are all pure risks.THE RISK M
York University - ADMS - 3541
CHAPTER 12: CREDIT AND DEBIT MANAGEMENTDEBT CAPACITYWhy Use Credit? There is no cash available, so credit must be used if the product is tobe purchased. When you borrow, the lender is giving you a credit, or trust, against yourfuture earnings. Borrowi
York University - ADMS - 3541
CHAPTER 13: BUYING A HOME AND MORTGAGEFINANCINGMORTGAGE FINANCINGMortgage financing - traditional way of borrowing money purchase a home.A mortgage is defined as the transfer of an interest in property to a creditor as securityfor payment of a debt w
York University - ADMS - 3541
CHAPTER 14: PRINCPLES OF INVESTMENTSaving is simply the money that you did not spend; it is money left over after your consumption.Investing means using the savings that you have and making it work putting it in investments to earna rate of return.BAS
York University - ADMS - 3541
CHAPTER 15: TYPES OF INVESTMENTSCASH AND EQUIVALENCESFederal Government of Canada Securities:Treasury Bills are short-term debt obligations issued normally in denominations ranging from \$1,000 to\$1 million, and with 91-day, 182-day, and 1-year terms.
York University - ADMS - 3541
CHAPTER 16: MUTUAL FUNDSTYPES OF MUTUAL FUNDSA mutual fund is a financial organization that accepts funds from hundreds andthousands of investors, pools these funds and invests them in bonds, stocks, real estate,precious metals or other investments.O
York University - ADMS - 3810
LECTURE 1: THE REAL ESTATE INDUSTRY1A: THE REAL ESTATE MARKETPLACEThe real estate marketplace actually consists of a very large number of separate marketsdifferentiated by:1. Geographic Location neighborhood, city and region, and national or internati
York University - ADMS - 3810
LECTURE 2: REVIEW QUESTIONS1. What 3 types of physical interests in real estate can be owned?Surface Rights, Above Surface or Air Rights, and Sub-Surface Rights can beowned in real estate.2. Explain the difference between riparian rights and prior app
York University - ADMS - 3810
LECTURE 3: MARKETING, BROKERAGE, ANDMANAGEMENTTypes of Real Estate Marketing Studies1. Market Research (market study) Involves the collection of all relevant data relatingto the product or service being studied. There are two kinds of date:Primary Da
York University - ADMS - 3810
LECTURE 4: VALUATION AND THE APPRAISAL PROCESSIn considering the subject of real estate valuation, two particular questions must be asked:1. Can the specific elements or factors that contribute to the value of a parcel of realestate be identified?2. W
York University - ADMS - 3810
LECTURE 5: REAL ESTATE FINANCEThree Types of Financial Markets:1. Primary Financial Markets a business that raises capital by selling newly issuedsecurities to the general public or the Canadian government selling a new issue ofbonds.2. Secondary Fin
York University - ADMS - 3810
LECTURE 6: REAL ESTATE TAXATIONTax Principles:Equity the basic rule of equity in taxation is the equal treatment of equals.Benefits Received under this principle equity is interpreted as requiring that the burdenof taxation be allocated among taxpayer
York University - ADMS - 3810
LECTURE 8: REAL ESTATE DEVELOPMENTThe Development Process Can be defined as the act of brining an idea or concept to successful completion inbricks and mortar. It is a complex process requiring the coordinated expertise of manyprofessionals.1. The De
York University - ADMS - 3810
LECTURE 9: THE ROLE OF GOVERNMENT IN REALESTATELocal Planning Tools1. Zoning Ordinance involves the use of both a map and a text. The subject area ismapped into a series of zones or districts that are classified as commercial, industrial,residential,
York University - ADMS - 2400
CHAPTER 6: MOVING YOUR AUDIENCE MORAL ANDPOLITICAL REASONINGMoral and Political Arguments When there are facts to accompany argumentation,one can rely on deductive or empirical arguments. Moral and/or political arguments tendto argue how things ought
York University - ADMS - 2400
CHAPTER 1: WHAT IS ORGANIZATIONAL BEHAVIOUR?Organizational Behaviour Field of study devoted to understanding, explaining and improving the attitudesand behaviours of people in an organization.What is an Organization?Human Resources Management - Field
York University - ADMS - 2400
CHAPTER 2: JOB PERFORMANCEJob Performance employee behaviours that contribute either positively or negativelyto the accomplishment of organizational goals. Those behaviours generally fit into 3categories: task performance, citizenship behaviours, and c
York University - ADMS - 2400
CHAPTER 2: SOCIAL PERCEPTIONPerception is a cognitive process that enables us to interpret and understand oursurroundings.Social Cognition the study of how people perceive one another. (Also known asinformation processing.)A 4 STAGE INFORMATION-PROCE
York University - ADMS - 2400
CHAPTER 3: ORGANIZATIONAL COMMITMENTOrganizational Commitment an employees desire to remain a member of anorganization.Withdrawal Behaviour employee actions that are intended to avoid work situations behaviours that may eventually culminate in quittin
York University - ADMS - 2400
CHAPTER 4: JOB SATISFACTIONJob Satisfaction a pleasurable emotional state resulting from the appraisal of ones jobor job experiences; represents how a person feels and thinks about his or her job.WHY ARE SOME EMPLOYEES MORE SATISFIED THAN OTHERS?Value
York University - ADMS - 2400
CHAPTER 5: STRESSStress the psychological response to demands when there is something at stake for theindividual, and where coping with these demands would tax or exceed the individualscapacity or resources.Stressors demands that cause the stress resp
York University - ADMS - 2400
CHAPTER 6: MOTIVATIONMotivation a set of energetic forces that determine the direction, intensity, andpersistence of an employees work effort.WHY ARE SOME EMPLOYEES MORE MOTIVATED THAN OTHERS?Expectancy Theory a theory that describes the cognitive pro
York University - ADMS - 2400
CHAPTER 7: TRUST, JUSTICE, AND ETHICSTrust the willingness to be vulnerable to an authority based on positive expectationsabout the authoritys actions and intentions.WHY ARE SOME AUTORITIES MORE TRUSTED THAN OTHERS?Disposition-Based Trust trust that i
York University - ADMS - 2400
CHAPTER 7: EFFECTIVE COMMUNICATIONCommunication refers to the exchange of information between a sender and thereceiver.PERCEPTUAL PROCESS MODEL OF COMMUNICATIONReceivers create meaning in their own mind.Sender desires or attempts to communicate with
York University - ADMS - 2400
CHAPTER 8: LEARNING AND DECISION MAKINGLearning a relatively permanent change in an employees knowledge or skill thatresults from experience.Decision Making the process of generating and choosing from a set of alternatives tosolve a problem.WHY DO SO
York University - ADMS - 2400
CHAPTER 9: PERSONALITY, CULTURAL VALUES ANDABILITY.Personality the structures and propensities inside a person that explain his or hercharacteristic patterns of thought, emotion, and behaviour; personality reflects whatpeople are like and creates thei
York University - ADMS - 2400
CHAPTER 10: TEAM CHARACTERISTICS AND PROCESSESTeam two or more people who work interdependently over some time period toaccomplish common goals related to some task-oriented purpose.TYPES OF TEAMSWork Team a relatively permanent team in which members
York University - ADMS - 2400
CHAPTER 11: POWER AND INFLUENCEPower the ability to influence the behaviour or others and resist unwanted influence inreturn.WHY ARE SOME PEOPLE MORE POWERFUL THAN OTHERS?Acquiring PowerThere are 2 Types of Power: Organizational and PersonalOrganiza
York University - ADMS - 2400
CHAPTER 12: LEADERSHIP STYLES AND BEHAVIOURSLeadership the se of power and influence to direct the activities of followers towardgoal achievement.Leader-member Exchange Theory a theory describing how leader-memberrelationships develop over time on a d
York University - ADMS - 2400
CHAPTER 14: ORGANIZATIONAL CULTUREOrganizational Culture the shared social knowledge within an organization regardingthe rules, norms, and values that shapes the attitudes and behaviours of its employees.CULTURE COMPONENTS:1. Observable Artifacts aspe
York University - ADMS - 2600
CHAPTER 12: CAUSAL ARGUMENTSEmpirical Evidence characterized by inductive reasoning. (Probable, not certain,reasoning.) With inductive reasoning, conclusions cant be proven (as with deductivearguments).Empirical Research deals with questions such as:
York University - ADMS - 2600
CHAPTER 1: THE WORLD OF HUMAN RESOURCEMANAGEMENTo Human resource management the process of managing human talent to achieveorganizations objectives.Why Study Human Resources?o Staffing the organization, designing jobs and teams, developing skillful e
York University - ADMS - 2600
CHAPTER 2: STRATEGY AND HUMAN RESOURCESPLANNINGSTRATEGIC PLANNING AND HUMAN RESOURCESo Strategic Planning a set of procedures for making decision about theorganizations long-term goals and strategy.o Human Resources Planning the process of controllin
York University - ADMS - 2600
CHAPTER 4: JOB ANALYSIS, EMPLOYEE INVOLVEMENT,AND FLEXIBLE WORK SCHEDULESRelationship of Job Requirements and HRM functionso Job a group of related activities and dutieso Position the different duties and responsibilities performed by only one employe