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the Althoughthe composite Simpson'sI /3 rule can certainlybe usedto estimate integral points This constraint equallyspaced it that of givenfunctions, hasthedisadvantage it uses doesnot take into account that somefunctionshaveregionsof relativelyabruptchanges the where more refined spacingmight be requiredHence,tcl achievea desiredaccuracy, fine spacingmust be appliedeverywhereeven though it is only neededfor the regionsof methodsremedythis situationby automaticallyadjustsharpchange Adaptive quadrature ing the stepsize so that small stepsare takenin regionsof sharpvariationsand largersteps gradually are taken where the function changes l/3 rule to the Simpson's are Most of thesetechniques basedon applyin-u corrrposite rule was usedin Rombergintegrain subintervals a mannersimilal to how the trapezoidal tion That is, the 1/3 rule is appliedat two levelsof reflnementand the differencebetween thesetwo levelsis usedto estimate truncationerrorIf the truncationerror is acceptable, the no fi,rrther refinementis required and the integral estimatefbr the subintervalis deemed repeated and If is acceptable the error estimate too large,the stepsizeis r-efined the process levels until the enor falls to acceptable MMLAB includes two built-in functions to implerrrentadaptivequadrature:cluad describes how they can be applied and quad1The following section 1841 MATTAB Functions: quad ond quadl

(continued)

The physician rst called on to attend a patient who has had a closed (blunt) head injury will generally nd the patient in one of three clinical conditions, each of which must be dealt with differently Usually it is possible to categorize the patient by assessing his mental and neurologic status when rst seen and at intervals after the accident In many emergency wards and intensive care units, the Glasgow Coma Scale is used as a rapid reference to accomplish this purpose (Table 35-1) It registers three aspects of neurologic function: eye opening, verbal response, and motor response to various stimuli The scores provided by this scale have been found to correspond roughly with outcome of the head injury, as discussed further on The scale uses a summed score with a maximum of 15; a score of 7 or less is considered to re ect severe trauma and a poor clinical state, 8 to 12, moderate injury, and higher scores, mild injury

by developed Canderand Gautschi MATLAB has two functionsbotlr basedon algorithrns (2000), for irnplementingadaptivequadrature: quad This function usesadaptiveSimpsonquadrature may be more efficient fbr lt low accuracies nonsmooth functions or quadl This function useswhat is calledLobotto quadratureIt may be more efficient for high accuracies and smoothfunctions

4 In the Security page of the WSA Tool, you will see the options shown in Figure 16-7

Patients Who Are Conscious or Are Rapidly Regaining Consciousness (Minor Head Injury)

The following function syntax for the quacl function is the same for the qr-Ladl function:

This is the most frequently encountered clinical situation Roughly, two degrees of disturbed function can be recognized within this category In one, the patient was not unconscious at all but only stunned momentarily or saw stars This injury is insigni cant when judged in terms of life or death and brain damage though, as we point out further on, there is always the possibility of a skull fracture or the later development of an epidural or subdural hematoma Moreover, the patient is still liable to a troublesome post-

in the Users columns Click on the Create User link The Create User page shown in Figure 16-9 appears

g = quad(fun, a, b, taf , trace, pl, p2, )

Figure 35-6 CT scan without contrast infusion showing areas of hemorrhagic contusion adjacent to bony prominences There is also slight subarachnoid blood along the tentorium and in the insular cisterns, both typical of traumatic bleeding

and include a non-alphanumeric character The password used for this example is coffee! with the exclamation point (!) being the sole non-alphanumeric character Be sure to write down the username and password The password is stored in a database, ASPNETDBMDF, in a table named aspnet_Users When you view the table, all of the passwords are encrypted, and if you don t have a record of them, you will likely forget them

Figure 35-7 CT scan (left) and MRI (right) from a patient with diffuse axonal injury There are multiple small hemorrhagic areas (one of which is shown by the dark arrow) in the cerebral white matter The MRI highlights the small amount of blood in these lesions Also shown are a contusion in the anterior temporal lobe (white arrow), which often accompanies the deep type of axonal injury, and blood in the ventricle

bounds,rol : the a where fun is the functionto be integrated and b: the integration (default: l0 6) rra-e is a variablethat when set to a desiredabsolute error tolerance detail to be displayed,and pt, p2, nonzerovalue causes additionalcomputational want to passto f rrnIt shouldbe noted that array operators * / are parameters that yor-r pass emptymatrices rol or fbr and ^ shouldbe usedin the definitionof fun ln addition values tt ace to use the def-ault

(continued)

.

,l85 Adoptive Quodroiure EXAMPLE Problem Stotement Usequadto integrate following function: the (, - q)2+ 001 (x - r)2 + 004

Password coffee!