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  "text": [
    null, 
    "Let us summarize what we&#39;ve\nlearned so far.", 
    "So we started out with building\nthis playground, this", 
    "EECS playground.", 
    "And within this playground,\nwe&#39;ve all decided that we will", 
    "abide by the lumped matter\ndiscipline, the LMD.", 
    "And these are simply constraints\nthat we impose", 
    "upon ourselves to simplify\nour analysis.", 
    "Notice that, you really\ndon&#39;t have to do that.", 
    "You are welcome to hang out here\nand do whatever you want.", 
    "But you might have a\nlot of fun as well.", 
    "But, you will not be able to\nbuild things as simply as you", 
    "would if you were inside\nthe EECS playground.", 
    "But, Within this playground\nyou have promised that you", 
    "will follow the lumped\nmatter discipline.", 
    "Lumped matter discipline has\nthree components to it.", 
    "One is that the elements will\nhave del phi b by del t equals", 
    "zero, outside the elements.", 
    "In other words, when you build\ncircuits, you want to make", 
    "sure that the del phi b by del\nt is going to be zero.", 
    "And inside the elements, we are\ngoing to make sure that", 
    "when you define something--\ndescribe something as a lumped", 
    "element, del q by del t,\nfor that element--", 
    "the net del q by del t for\nthat element inside the", 
    "element is going to be zero.", 
    "And that&#39;s going to be true\nfor all your elements,", 
    "registers, sources,\nwires, and so on.", 
    "And the third element is that\nyou will only focus on signal", 
    "speeds of interest that\nwill be way lower than", 
    "the speed of light.", 
    "Now one of the interesting facts\nof life is that as our", 
    "microprocessors get faster and\nfaster, some of the chips", 
    "inside your iPhones, and your\ndesktops, and so on, are", 
    "clocking at speeds in excess\nof three to four gigahertz.", 
    "When signal speeds are that\nfast, we are now getting to a", 
    "point where the signal speeds\ninside our chips are", 
    "approaching the speed\nof light.", 
    "So they&#39;re not all\nthat far off.", 
    "And so therefore, over the next\ndecade, as people try to", 
    "push speeds to even higher\nvalues, various things are", 
    "going to start breaking unless\nwe change things", 
    "dramatically somehow.", 
    "What this does is these\ndiscipline elements, the", 
    "lumped matter discipline,\nenables us to create the", 
    "lumped circuit abstraction.", 
    "Look at our lumped elements.", 
    "Lumped elements will\nbe described", 
    "by their v-i relation.", 
    "So each of these lumped elements\nof that sum i, that", 
    "would be sum function of\nv, the v-i relation.", 
    "The relation could be linear,\ncould be non-linear.", 
    "Could be, in general, could be\nanything, just that they have", 
    "some v-i relation.", 
    "For the register you saw that\ni was v divided by R.", 
    "For some other element, it could\nbe that i is 6.7 times v", 
    "squared plus v divided by\n2 plus some constant 1.", 
    "I mean, who knows.", 
    "That could be some function of\nv. Could be linear, could be", 
    "non-linear.", 
    "And for this element, the power\nconsumed by the element", 
    "is given by vi.", 
    "Finally, we showed that when\nyou make the lumped matter", 
    "discipline assumptions,\nMaxwell&#39;s equations simplify", 
    "to extremely simple\nKVL and KCL.", 
    "So, for example, KVL simply\nsays that the sum of the", 
    "voltages around a\nloop is zero.", 
    "While KCL says that the sum of\nthe current that go into a", 
    "node is zero.", 
    "You can also say the currents\ncoming out of a node are zero", 
    "by the same principle.", 
    "What is amazing about this is\nthat by making the lumped", 
    "matter discipline, by abiding\nby the lumped matter", 
    "discipline, we have been able\nto convert the use of", 
    "Maxwell&#39;s equation into the use\nof very simple algebra.", 
    "So we replaced our del phi&#39;s and\ndel t&#39;s, and all of that", 
    "stuff, with extremely\nsimple algebra.", 
    "And in the next set of segments\nI&#39;m going to show you", 
    "how we can simplify and analyze\ncircuits extremely", 
    "easily using very, very\nsimple algebra.", 
    "And, in fact, for the first half\nof this course, you are", 
    "not going to see any\nsquigglies at all.", 
    "It&#39;s going to be very,\nvery simple.", 
    "And even later, we&#39;re not going\nto be seeing any partial", 
    "differential equations.", 
    "We will see some fairly simple\ndifferential equations, but by", 
    "making the LMD assumptions, we\nhave really gotten rid of a", 
    "lot of the complexity.", 
    "And things are going to be\nreally, really, really simple.", 
    null
  ]
}