# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

3 Pages

### Take-Home Exam March 2

Course: MATH 442, Spring 2011
School: Texas A&M
Rating:

Word Count: 666

#### Document Preview

442 Take-home Math Exam Due March 2 Texas A &amp; M University Spring 2011 1. Consider the lake purication model: r x (t) = (1 + sin(2t))x(t), v where x(t) is the concentration of contaminant (gr/m3 ), v is the volume of the lake (m3 ), r is the mean outow, t is the number of years since pollution input ceased and 0 &lt; 1. (a) [2 points] Determine the dimensions of r and . (b) [10 points] Assume that...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Texas >> Texas A&M >> MATH 442

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
442 Take-home Math Exam Due March 2 Texas A & M University Spring 2011 1. Consider the lake purication model: r x (t) = (1 + sin(2t))x(t), v where x(t) is the concentration of contaminant (gr/m3 ), v is the volume of the lake (m3 ), r is the mean outow, t is the number of years since pollution input ceased and 0 < 1. (a) [2 points] Determine the dimensions of r and . (b) [10 points] Assume that the annual variation of outow is negligible (i.e. 0). Obtain the time t0.05 required for reducing x(t) to 5% of its initial concentration. Compute t0.05 for Lake Michigan with volume 4, 871 109 (m3 ) and the mean outow 433,092,096 (m3 /D). (c) [8 points] Show that annual variations of outow would not signicantly alter the predicted value for Lake Michigan. 2. [10 points] Two plants are feeding o the same substrate, whose weight at time t is S (t). One of the plants began to feed o the substrate 20 days earlier than the other. Devise a system of dierential equations that describes the plants growth. 3. [10 points] A population of beetles has three dierent age stages: larvae (grub), pupae (cocoon) and adult. Assume constant per-capita death rates for each population class of a1 for larvae, a2 for pupae and a3 for adults. Also assume adults produce larvae at a constant per-capita birth rate of larvae b1 . The larvae turn into pupae at a constant per-capita rate 1 and pupae turn into adults at a constant per-capita rate 2 . Let A(t) denote the number of adults, L(t) the number of larvae and P (t) the number of pupae at time t draw a compartmental diagram and formulate a mathematical model in the form of three dierential equations. 4. For the system of dierential equations: x = y (13 x2 y 2 ), y = 12 x(13 x2 y 2 ). (a) [5 points] Show that the system is Hamiltonian. 1 (b) [20 points] Obtain the equilibrium points and classify them. (c) [5 points] Use Matlab to plot the phase-plane of the system in the range 6 x, y 6. 5. Lateral inhibition a is type of cell-cell interaction whereby a cell that is committed to a particular fate inhibits its adjacent cells from doing likewise. In many developing tissues, lateral inhibition occurs via transmembrane proteins Notch and Delta of the interacting cells. In each cell, Notch is the receptor and ligand is the mediator. For a system consisting of two cells, Delta-Notch mechanism can be modeled with: 1 n (t) = n1 (0)f (d2 (t)/d2 (0)) n1 (t), 1 1 d (t) = d1 (0)g (n1 (t)/n1 (0)) d1 (t), 1 1 n (t) = n2 (0)f (d1 (t)/d1 (0)) n2 (t), 2 1 d (t) = d2 (0)g (n2 (t)/n2 (0)) d2 (t), 2 where f (x) = x2 /(a + x2 ) and g (x) = 1/(1 + bx2 ) for x > 0, ni (t) and di (t) are respectively the level of Notch and Delta activity at time t for the cell i = 1, 2, and and are exponential decay rates of Notch and Delta. (a) [10 points] Nondimensionalize the model such that it is transformed to: x1 = f (y2 ) x1 , y1 = v (g (x1 ) y1 ), x2 = f (y1 ) x2 , y2 = v (g (x2 ) y2 ), and v = /. (b) [10 bonus points] Prove that there exists only one equilibrium. Hint: f, g : [0, ) [0, ) are continuous and f (g (x)) is monotonic decreasing. (c) [10 bonus points] Show that the level of Delta (and Notch) activity at the equilibrium point (x , y1 , x , y2 ) is the same for both cells (i.e. x = x = n and y1 = y2 = d ). 2 1 2 1 2 (d) [10 bonus points] Show that the equilibrium is unstable if f (d )g (n ) < 1. (e) [20 points] It is known that low levels of notch activity in a cell correspond to neuronal dierentiation, whereas the cells with high levels of notch activity remain undierentiated. Use Matlab to nd the solution of the nondimensionalized system for a = 0.01, b = 100 and v = 1 in the time interval [0,25] with initial condition (x1 (0), y1 (0), x2 (0), y2 (0)) = (.8, .7, .7, .8). Based the numerical results and the above statement, determine the fate of each cell. Is such a prediction in agreement with the lateral inhibition? Justify your answer. 3
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

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
York University - ADMS - 2600
CHAPTER 5: EXPANDING THE TALENT POOL:RECRUITMENT AND CAREERSRecruiting Talent Externallyo Labour Market area from which applicants are to be recruited: tight and loosemarket.Factors determining the appropriate Labour Market: Skills and knowledge req
York University - ADMS - 2600
CHAPTER 6: EMPLOYEE SELECTIONSelection the process of choosing individuals who have relevant qualifications tofill existing or projected job openingsSelection Considerations:1. Person-Job Fit job analysis identifies the individual skills, knowledge an
York University - ADMS - 2600
CHAPTER 7: TRAINING AND DEVELOPMENTThe Scope Of Trainingo Training effort initiated by an organization to foster learning among its members.Tends to be narrowly focused and oriented towards short-term concernso Development effort that tends to be orie
York University - ADMS - 2600
CHAPTER 8: APPRAISING AND IMPROVINGPERFORMANCEPerformance Appraisal - A process, typically performed annually by a supervisorfor a subordinate, designed to help employees understand their roles, objectives,expectations, and performance success. Perfo
York University - ADMS - 2600
CHAPTER 9: MANAGING COMPENSATIONPay - is a statement of an employees worth by an employer. It is a perception of worth ofan employee.STRATEGIC COMPENSATION PLANNING Links the compensation of employees to the mission, objectives, philosophies, andcult
York University - ADMS - 2600
CHAPTER 10: PAY-FOR-PERFORMANCE; INCENTIVE REWARDSStrategic Reasons for Incentive Plans:Variable Pay tying pay to some measure of individual, group, or organizationalperformance.Inventive Pay Programs - Establish a performance threshold to qualify for
York University - ADMS - 2600
CHAPTER 11: BENEFITSTHE CHIEF OBJECTIVES OF BENEFITS PROGRAM Improve employee satisfaction Meet employee health and security requirements Attract and motivate employees Reduce turnover Maintain a competitive positionProviding for FlexibilityFlexib
York University - ADMS - 2600
CHAPTER 12: SAFETY AND HEALTHSAFETY AND HEALTH: ITS THE LAWOccupational Injury any cut, fracture, sprain, or amputation resulting from aworkplace accident or from an exposure involving an accident in the work environment.Occupational Illness any abnor
York University - ADMS - 2600
CHAPTER 13: EMPLOYEE RIGHTS AND DISCIPLINETHE THREE REGIMES OF EMPLOYEMENT LAW1. The Common Law of Employment the body of case law in which courts interpretemployment contracts, and the legal principles taken from those cases that guide theinterpretat
York University - ADMS - 2600
CHAPTER 14: THE DYNAMICS OF LABOUR RELATIONSGOVERNMENT REGULATION OF LABOUR RALATIONS: The industrial relations disputes and investigation act (1948) Canada Labour CodeLabour Relations Board Duties:- Administrating the statutory procedures for the ac
York University - ADMS - 2600
CHAPTER 15: INTERNATIONAL HUMAN RESOURCESMANAGEMENTInternational Corporation a domestic firm that uses its existing capabilities to moveinto overseas markets.Multinational Corporation (MNC) a firm with independent business units operatingin multiple
York University - ADMS - 1770
16 March 2012CHAPTER 14: ARGUMENTATIVE ARGUMENTAn Evaluative Critique: Includes both and evaluation of an argument prescribed, plusour own insights about the argument. There are 7 steps to consider in an evaluativecritique.1. Write an Overview of the
York University - ADMS - 1770
The Logical Structure of Arguments: Strong and Weak Arguments Acceptability and Burden of Proof Valid and Invalid Arguments Argument SchemesArgumentation Clarity:Meaning/semantics and structure/syntax of language is important in the production ofre
UCSD - IRPS - 423
Delta Normal Value at Risk CalculationsExample 1: -VaR of a Single Call Option PositionReplicating PortfolioVolatilityRiskless rate rConvenience yield qUnderlying asset price SExercise priceExpiry in years0.150.050.0212412420PriceDelta ()
UCSD - IRPS - 423
F ederalReserveModelParameters2009 -04 -202009 -04 -172009 -04 -162009 -04 -152009 -04 -142009 -04 -132009 -04 -092009 -04 -082009 -04 -072009 -04 -062009 -04 -032009 -04 -022009 -04 -012009 -03-312009 -03-302009 -03-272009 -03-262009 -0
UCSD - IRPS - 423
Midterm ExaminationMay 7, 2009Score boxDo not touch or moveProblem 1Problem 2Total000Please type your name here:GUIDELINES0. Verify that your file is on your desktop. Change the name of this file to lastname_firstname.Example: John Smith will
UCSD - IRPS - 423
Week OneThe Irrelevance andRelevance of RiskManagement!!Copyright Bruce N. Lehmann 2000-2011!The Motivation for RiskManagement Individuals, firms, and governments faceuncertain future outcomes Adverse outcomes can cause persistentproblems like
UCSD - IRPS - 423
Week TwoThe Basics of DerivativeAsset Valuation and Hedging!Copyright Bruce N. Lehmann 2000-2011!Goals Understand how derivatives are priced intheory Understand implications of pricing theoryfor hedging Understand role of imperfections in prici
UCSD - IRPS - 423
Week ThreeThe Basics of OptionsContractsCopyright Bruce N. Lehmann 2000-2006Goals 1. Understand the difference betweenforward and option contracts 2. Understand the payoff patterns ondifferent options and portfolios of options 3. Set bounds on op