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The tirst conditionsare identicalto thoseusedlbr the quadraticcaseTlrat is, they are set up so that the functionspassthroughthe pointsand that the first derivativesat the knots are equal In additronto these,conditionsare developedto ensurethat the secondderivatives at the knots are also equalThis greatlyenhances fit's smoothness the After theseconditionsare developed two additionalconditionsare requiredto obtain the solutionThis is a much nicer outcomethan occurredfor quadraticsplineswhere rve neededto specify a singleconditionIn that case,we had to arbitrarily specily a zero second derivativefor the first interval,hencemaking the resultasymmetric For cubic splines, we are in the advantageous position of needingtwo additionalconditionsand can, therefore, apply them evenhandedly both ends at For cubic splines,these last two conditions can be formulated in severaldifferent waysA very common approaclr to assurne is that the second derivatives the first and last at knots areequalto zeroThe visual interpretation ofthese conditionsis that the function becomesa straight line at the endnodes Specification suchan endconditionleads what of to is termed a "natural" spline It is given this name becausethe drafting spline naturally behaves this fashion(Fig 162) in There are a variety of other end conditionsthat can be specified Two of the more popular are the clampedcondition anclthe not-a-knotconditionsWe will describetheseoptions in Section 1642 For the following derivation will lirnit ourselves natural we to splines Once the additional end conditions specitied, would havethe 4(n - 1) condiare we tions needed evaluatethe4(n - I ) unknowncoefficients to Whereasit is certainlypossible to developcubic splinesin this fashion,we will present altenrative an approach that requires the solutionof only n - I equations Further,the simultaneous will be tridiagonal equations and hencecan be solved very efficientlyAlthough the derivationof this approachis less straightforward than for quadraticsplines,the gain in efficiencyis well worth the effort

As was the case with quadratic splines,the lirst condition is that the spline must pass through all the datapoints J'i: ai I bi6iwhich simplifies to ai : fi (1611) x i ) * c i ( , r r t i ) 2 * d i ( x r- x , ) l

make this their area of specialty, because of the depth of knowledge required to be a good database applications developer.

Therefore,the constantin eachcubic must be equal to the value of the dependent variable at the beginning ofthe interval This resultcan be incorporated Eq (1610): into

DEVELOPING AND MAINTAINING BEST PRACTICES Successful DBAs are proactive in their work, and one of the best ways to be proactive is

s ; ( - v ): -l -,ti) J^i bi(r * ci(x xi)2* di(-r -r;;3

(t612)

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to develop sound database best practices, and to implement them in a consistent manner. The better organized and managed the database operations, the more efficient they will be. One of the many ways that DBAs can perform this task is to create a runbook that describes the organization s best practices and internal procedures. This document is the DBA s bible for performing all DBA-related functions.

There is no pat answer to the question of preparation for this career, and no one route to follow A number of people in training and development have credentials and experience in the eld of organizational development, and formal education in organizational development is available However, there is more to training and development than just organizational development Further, success may depend on whether a person seeks a job inside a company or hopes to operate as a freelancer People who nd employment in training and development inside an organization often begin in another capacity with the company and move quite naturally into a training role They may teach others about a job they have done or are doing, or they may informally help others learn In this vein, experienced computer programmers induct new programmers, top salespeople share techniques and methods with other sales representatives, and veteran stockbrokers break in new members of the rm A fairly common practice these days, when the trainer is an employee, is to assume the role of trainer for a speci ed period and then rotate back into other corporate, service, or manufacturing duties Once in the role, trainers often seek outside instruction for themselves or attend conferences and workshops to gain additional skills Learning new knowledge or skills on the job, planning and conducting training sessions, and getting feedback from participants (and management) provide chances to re ne competence further Becoming a freelance trainer that is, one who works on contract with businesses and industries happens in a number of ways Many freelance trainers start as teachers in schools or colleges, often earning a graduate degree in those roles They also may participate in several special training sessions themselves with groups that specialize in training and development or organizational development, such as ASTD and the National Training Laboratories Once they become employees of a school system or an institution of higher education, they nd opportunities for outside work as trainers, or they become consultants to university departments of indus-.

Next, we will apply the conditionthat eachof the cubicsmustjoin at the knotsFor knot i * 1, this can be represented as J ' i I b i h i - l c y h i - t t ) 1 h l: f i + r (1613)

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