viii INTRODUCTION in Software

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L2. Uses Intermediate AutoCAD Skills
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No two comets look the same. Any given comet appears different to Earthbound observers every time it returns to the Sun. Halley s Comet, one of the most well-known of all comets in history, was brilliant when it appeared in 1910, but it was a disappointment to observers who saw and tracked it in 1985 1986.
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to nd fund managers with the same opinion, again a lack of understanding. A short option can never have more risk or margin than the underlying asset being traded outright in the same represented quantity. One hundred shares of the stock carries the same risk as one short stock option, no matter how you slice it. The same goes for an option on a futures contract.
their destinations. In the section on monitors, we learned that increasing numbers of messages in a queue could indicate problems with a connector or network connectivity, but there are many more ways you can manage queues and the messages within them, as we will see shortly.
Part Two dealswith two relatedtopics:root finding and optimization.As depictedin Fig. 1.6a,root locotiorrinvolvessearching the zerosof a function.In contrast, for optimizarion involvesdetermininga valueor valuesof an independent variablethat correspond a to "best" or optirnalvalue of a function.Thus, as in Fig. 1.6a, optimizationinvolvesidentifying maximir and minima. Although somewhat different approaches used,root location are and optimizationboth typically arisein designcontexts. linear algebraicequations Part Three is devotedto solving systemsof simultaneous (Fig. 1.6&). in that they are Such systerns similar in spirit to l'ootsof equations the sense are concemedwith values that satisfy equations.However, in contrastto satistying a single equatiou, set of valuesis soughtthat simultaneously satisfies set of linear algebraic a a equations. Suchequations arisein a varietyof problemcontextsand in all disciplinesof engineeriugand science. particular,they originate in the mathenratical In modeling of Jarge systems interconnected of elements suchas structures, electriccircuits.and fluid networks. However,they are also encountered other areasof numericalmethodssuchas curve titin e l i n g l r n dd i f f e r e n t i a l q u u t i o n s . you will often haveoccasion fit curvesto datapoints.The As an engineer scientist. or to categories: regression techniques developed this pulposecanbe dividedinto two general for in regression ernployed is wherethere and interpolation. described Part Four tFig. 1.6c'1, As is a significantdegree error associirted with the data.Experimental resultsareoften of this of is kind. For thesesituations. strategy to derivea singlecurve that represents general the the matchingany individualpoints. trend of the datawithout necessarily valIn contrast,interpolutionis usedwherethe objectiveis to determineintermediate ues betweenrelativelyerror-freedata points. Such is usually the casefor tabulatedinformation.The strategyin suchcases to flt a curve directly throughthe datapoints and r.rse is the curve to predict the intermediate values. As depicted in Fig. 1.6d, Part Five is devoted to integlation and differentiation.A plrysical interpretation ruurrcricctl of iltegratiott is tlre determinationof the area under a curve. Integrationhas many applications engineering in and science, rangingfrom the determinationof the centroidsof oddly shapedobjectsto the calculationof total quantities In integrationformulasplay an basedon setsof discretemeasurements. addition,nurnerical importtrntrole in the solution of diffbrentialequations. Part Five also covers methodsfor nume.rical difr'erentiation. you know fiom your study of calculus,this involves the deAs terminationof a function's slopeor its rate of change. (Fig. 1.6e). equations focuses the solutionof ordirro'vdi.fterential Finally.Part Si.x on This is bein of and science. Such equations of greatsignificance all areirs engineering are of in cause many physicallaws arecouched termsof the rateof change a quantityratherthan rnodels the magnitudeof the quantity itself. Examplesrangefrom population-forecasting (rateofchangeof population) tlreacceleration a tallin-e of body (rateofchangeofvelocity). to problems. initial-value Two typesof problemsareaddressed: andboundary-value
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