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and mount the phono jack at J1. Finally mount the On/Off switch, the 2 meter/6 meter band switch, the squelch potentiometer, the volume potentiometer, and tuning potentiometer to the front panel as shown in Figure 12 7. For the jumper wire, cut 2 of 22 gauge solid wire, strip 1 4 of insulation off each end and solder to the points indicated. Attach two 4 long pieces of insulated wire to the speaker terminals and solder them. Now solder two 4 pieces of insulated wire to the On-Off switch, use the center terminal and one of the outside terminals on the switch. Next attach three 3 long insulated wires to the volume control on VR3. Next locate the Squelch control (VR1) and solder two 3 long insulated wires to the potentiometer. Take the two free wires and connect them to the PC board. The center terminal from the potentiometer goes to the PC board hole marked (Q), while the other potentiometer lead goes to the hole marked (R). Take the free ends of the two speaker wires and solder them to the circuit board at their respective terminal strip on the bottom left side of the PC board. Now take the two free ends of the On-Off switch leads and solder them to the terminals on the left side of the PC board. Next take the three potentiometer leads and solder them to the PC board. The center terminal of VR3 goes to the terminal marked (D) on the circuit board. The left-most potentiometer terminal goes to the hole marked (C) on the PC board, while the right-most potentiometer terminal

Do not refer to the text when taking this test. A good score is at least 30 correct. Answers are in the back of the book. It s best to have a friend check your score the first time, so you won t memorize the answers if you want to take the test again.

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FIGURE7.I I I ( o )G r o p h l c o l e p i c l i oo f S i m p s o n1 / 3 r u i e l:t c o n s i sos t o k i n gh eo r e ou n d eo p c r o b o l o d n s lf t r c o n n e c i i n g r e e o i n t s(.b )G r c p h i c o e p i c f i oo f S i m p s o n ' s6 r u l e l t c o n s i sos t o k i n gh e th p d n : 3/ if t

Kuo et al. (2005)

Question 6-3

Next, we usevisually orientedarguments developtwo improvedversionsof Euler's to nretlrod-tlre Heun and the midpoint techniques. After this introduction,we formally develop the conceptof Runge-Kutta(or RK) approaches demonstrate and how the foregoing techniques actuallyfirst- and second-order methods.This is followed by a discusare RK sion of the higher-orderRK fbrmulations that are fi'equentlyused fbr engineeringand scientific problem solving. In addition, we cover the applicationof one-stepmethodsto .t-y.r/erns ODEs.Note that all the applications Chap.20 are limited to cases oJ in with a fixed stepsize. ln Chop. 21, we cover more advanced approaches solving initial-valueproblems. for First. we describeadaptiveRK ntethods that automaticallyadjustthe stepsize in response to the truncationerror of the computation. Thesemethodsare especiallypertinentas they are employedby MATLAB to solve ODEs. Next, we discussnrulti,step methods. mentionedabove,thesealgorithmsretain inAs fbrn'ration previousstepsto more ell'ectivelycapturethe trajectoryof the solution.They of alsoyield the truncationerror estimates that canbe usedto implementstep-size control.We describea sinrplemethod-the non-self-starting Heun method-to introducethe essential f-eatures the multistepapproaches. of Finally, the chapterends with a descriptionof ,stiffODEs. Theseare both individual and systems ODEs thathaveboth fastand slow components their solution. a conof to As sequence, they require specialsolution approaches. introducethe idea of an implicit We solution techniqueas one commonly usedremedy.We also describeMMLAB's built-in functionsfor solving stiff ODEs. ln Cha1t.22, we focus on two approaches obtaining solutionsto boundary'-value for problems:theshootingandJinite-dffirencemethods. Aside from demonstrating how these techniques implemented, illustratehow they handleclerivatiye are we boundorvconditions and nonlinear ODEs.

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the vast tracts between the stars and galaxies Suppose that the stars and galaxies themselves are life forms that have evolved to levels of sophistication far higher than we humans so much loftier that we are no more aware of their existence than a bacterium is aware of the elephant in whose ear it dwells Are there life forms like this We do not know the answer to this question We have no idea of how to communicate with such beings The closest we can come in this respect is to turn things over to the clergy and to approach the problem from a spiritual standpoint There exists a psychological split between the church and the scientific community that at times leads one group to criticize the other Let s not question the beliefs of people who have faith in the existence of life on loftier planes than ours.

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