Welcome to the 2016 Conference of the Mormon Transhumanist Association. My name is Lincoln Cannon. I am a director and founder of this association, and I've served as its president for the last 10 years. Three years ago at this conference, the renowned historian of Mormon origins, Richard Bushman, spoke here. He proposed that the mission of this association is to take the place of B.H. Roberts and John Witso. Roberts and Witso are now long deceased, but they were Mormon apostles who were champions of science. In 1908, Witso published a book. It was entitled, Joseph Smith as Scientist. In it, he claimed that truth is truth forever. Scientific truth cannot be theological lie. Then of similar mind, Roberts wrote in 1931 that to pay attention to and give reasonable credence to science, is to link the Church of God with the highest increase of human thought and effort. Of course, Roberts and Witso weren't the first Mormon apostles to champion science. One of their predecessors was Parley Pratt, who was among the first 12 Mormon apostles organized by Joseph Smith. In 1855, Parley published a book entitled The Key to the Science of Theology, and that's precisely what he considered the potential of theology to be, a science. I'd like to read to you the first words from his book, the preface of that book. I think that you'll find that these words are words that will resonate with just about any transhumanist, Mormon or otherwise. Here are his words. The present is an age of progress, of change, of rapid advance and wonderful revolutions. The very foundations of society, social, political, commercial, moral and religious seem to be shaken as with a mighty earthquake from center to circumference. All things tremble, creation groans, the world is in travail and pains to be delivered. A new era has dawned upon our planet and is advancing with accelerated force, with giant strides. The railroads and the steamboats with their progressive improvements in speed, safety and convenience are extending and multiplying the means of travel, of trade, of association, and intercommunication between countries whose inhabitants have been comparatively unknown to or estranged from each other. But as if even these means were too slow for the godlike aspirations, the mighty throes of human thought and its struggles for light and expansion, humanity seizes the lightning, tames and subdues it and makes it the bearer of its thoughts and dispatches. While these things are in progress by one portion of humanity, another learns to seize and control a sunbeam in a manner subservient to the progress of the fine arts and by which means one performs in a minute the work which a short time since would have employed the most active years of a lifetime. Those are the words of Parley Pratt that he used to introduce what is in his estimation a science of theology and what was in his estimation the heart of Mormonism. Another Mormon apostle that championed science was James Talmadge. He was a contemporary of Robertson Whidsoe and echoing Pratt in 1899, Talmadge wrote these words, to count the ticking of a watch thousands of miles away, to speak in but an ordinary tone and be heard across the continent, to signal from one hemisphere and be understood on the other though oceans roll and roar between, to bring the lightning into our homes and make it service fire and torch, to navigate the air and to travel beneath the ocean surface, to make chemical and atomic energies obey our will. Remember this is 1899, are not these miracles. At some point in his life Talmadge had acquired a copy of Pratt's book, The Key to the Science of Theology and I happen to know that because I have the book here with me today. I received this book from my step-grandfather and his name was Wayne Wiscombe. He was married to Helen Bradley Wiscombe as his first wife. When she died he inherited it and he gave it to me. She was the granddaughter of Talmadge and inside the front cover of this book is the stamp of Talmadge's personal library. He had acquired it from the Deseret News Corporation at some point in his life. For me this book embodies Mormon transhumanism. For a few reasons. First of all, both Mormon transhumanism in this book advocate the ethical use of technology and religion to extend human abilities. Second, both envision a future of unlimited human potential in compassion and creation. And third, both are an inheritance from past champions of science that were inspired by their Christian discipleship. And then finally, one of the reasons why this book embodies Mormon transhumanism for me is that today both the association and this book are going to move on to their next caretaker. A few months ago I told the board of directors of the association that I felt it was time for us to have a new president. While I admit to some sadness in telling them that, I believe that 10 years is long enough for anyone to be the leader of an organization like ours. As transhumanists we know better than most that change is essential to progress. And as religious transhumanists we know better than most that change is too often resisted most when it's needed most. So last month the other board members and I, all of us democratically elected to represent the voting members of the association, we met together to select a new president and the outcome was a unanimous vote for Christopher Bradford. I'm proud to call Chris my friend. Over 15 years ago he and I met in online philosophy discussions at Belief Net. It was a forum, it's still around but not as popular as it once was. And since that time I've spent countless hours with Chris discussing just about every topic that I'm capable of imagining. Over the years he has been involved and I have been involved in each other's projects. We've worked together. Most importantly he was one of the 14 founders of the Mormon Transhumanist Association along with me and several other people in this room. He's also served as a director and vice president of the Mormon Transhumanist Association and he knows Mormonism and transhumanism and this association as well as anyone and better than most. Chris has my full support and confidence to be our new president and Chris I'd like to invite you up with me. Chris I'd like to give you the key to the science of theology and I trust that it will inspire you as it has inspired me. Chris and I are going to take questions from you that any questions you might have regarding the change in the leadership of the association or regarding its past or its future whatever you might have on your mind for the next few minutes. And before we do that I would like to invite everyone to show our appreciation to Lincoln for his leadership. I figure it might as well it's an appropriate moment for us to share with Lincoln a token of our appreciation. We've we're preparing for him a crystal sear stone engraved engraved with the logo of the association and his tenure as president. And I just want to express my own gratitude for Lincoln. We've really looked up to him and gained so much from his leadership. It's been incredible to witness for me the way he empowers us and inspires us to take things and run with them and to grow personally has really been a life changing experience for me and I'm so grateful for his friendship. That's in earnest of the actual gift by the way. May we answer any questions? Yeah so to repeat question for the recording what are the major duties and aims of the president of the association apart from the annual conference? So the president of the association is very much the public face of the organization in many ways and so there's participation in other conferences. There's participation in online forums. We hold regular monthly meetups and we're working right now on making those a little bit more structured and so helping people who are new to the ideas of the organization with introductory material helping them kind of get their footing in what Mormon transhumanism is. In addition the constitution has the president acting also as the CEO of the organization. We have a separate management team that manages marketing finances and so forth legal affairs and so the president also is responsible for those regular meetings and for ensuring that we maintain our non-profit status and all of those types of things as well. Does that sufficiently answer your question? I'll be sad if this happens but can we expect Lincoln to not be active in writing on a lot of different forums about Mormon transhumanism and I'll be delighted to see if Chris might be more active in... So the question was should we expect to see Lincoln become less active in writing about Mormon transhumanism and should we expect Chris to become more active in writing about Mormon transhumanism? Is that a fair restatement? I'll only answer the first part of that question. I'll let Chris answer the second part. I suspect you will see me writing more about Mormon transhumanism going forward. When running the association a lot of time and effort goes into tasks behind the scenes where you know there are websites and conferences and all sorts of things to organize and run and make sure operating effectively and efficiently and so the time that I have historically put into those sorts of things I imagine we'll start going into more writing about the MTA and Mormon transhumanism. In particular I have three open invitations to write for some peer-reviewed journals about Mormon transhumanism that I've not been able to satisfy and I'll be working on all of those in the near future and those should be available hopefully and I think they'll be good tools for the association once they are available. So I think the answer to your question is that you should expect more of the writing about Mormon transhumanism from me. And I can address the second part of the question. Yes you should expect to see more from me in particular in online forums. My public involvement with Mormon transhumanism has been less online and more in conferences and last 12 months I've presented at four different conferences on Mormon transhumanist topics but I do have plans to be more active in the online forums and I have a number of things in the works that you'll see coming soon. Other questions? Any parting advice you want to share with the group? Well I'm not going to go away so it's not that sort of parting advice but parting advice perhaps as having been the leader of the organization. I wrote a blog post about this a month or two ago and one of the things that comes to mind as you ask the question is my experience with interacting with others both Mormons and non-Mormons about Mormon transhumanism and the types of reactions we get and what my opinion is about good ways to respond to those types of reactions. As probably most of you know because I'm sure you've interacted about Mormon transhumanism with other people we get a wide range of responses. We get very enthusiastic responses from some people and you know a lot of people are more likely to be most people are probably more likely to be cautiously interested like wow that's kind of different interesting and then of course there's the subset of people probably small but loud that really really dislike what we do and of course there are there are two main types of those people there are people who really dislike what we do because it runs counter to their understanding of religion and they tend to think of us as the antichrist or something like that and then of course there are secular persons who are quite anti-religious generally and we kind of epitomize the horrible like effort to make religion persist in the face of their clear dominant intellectual superiority and of course the approach they take is one of ridicule usually where we're we're stupid and not worth listening to and so my advice regarding these things and and you know my own mileage has varied in my ability to to exemplify them but my advice would be that a good sense of humor is good along the way it's probably not particularly effective to demonize them in return speaking of the more religious fundamentalist types and it's also probably not particularly useful to ridicule them in return although I think it is worth saying why we believe that the positions we take are better than the positions that they are taking why we why we believe that religious fundamentalism sectarian fundamentalism has detriments why we believe that secularism probably isn't the strongest way forward things like that I think are definitely worth saying I don't think we should shy away from saying them but I think that they're that they're I know that there are constructive and friendly ways to say these things and so that that I would I suppose is the advice I would give to members of the association is to to try to exemplify that friendly constructive but not frightened position of expressing you know the kind of religious vision the kind of scientific and technological vision that that the association stands for all right I think our time for questions is up thank you very much for being here this morning and I'll turn the rest of the conference over to our excellent new president Christopher Bradford


Let us continue our discussion of centroids and now let's step away from the easy, discrete setting and let's try to go towards the continuous setting. Suppose next that we have a region R that's bounded by some function f of x. And so if we have just our typical x-axis and y-axis and so we have some function f, which maybe it looks something like this. So we have some function f and then maybe we have some bounds on x. We have some x equals a and x equals b. And so consider this region that's below the curve, it's above the x-axis and it's bounded left and right by x equals a and x equals b. So this is a region on the interval a to b. And so this is what we mean by this region R, like so. Now we know how to calculate the area of such a thing, right, the area of the region R is going to be the typical formula, a equals the integral from a to b of f of x dx. We're used to that type of calculation. Now what I want to do is let's try to approximate R by in many rectangles, all right? So we've done this many times in the past, let's subdivide the interval into pieces and then we can construct rectangles and then for simplicity's sake, we'll make the height of the rectangle be determined by the midpoint, like so we get the height right here, we get the height right here, midpoint, we get the idea, we get all of these midpoint rectangles, like so I do apologize for the crudeness of the drawing but this is just for illustrator purposes just to give you the idea. So we can approximate the area under the curve using these rectangles. Now kind of like this when we approximate the region as this system of rectangles, what we can do is we can consider for each rectangle, what if this was just a single object? We're gonna assume each one is an object all by itself, right? Where would the centers of each of these rectangles be? Well if you take a typical rectangle between xi and xi minus one, so xi bar is the midpoint right here, well that's where the similar mass is gonna be, its x-coordinate is gonna be xi bar, which of course is namely just xi plus xi minus one over two and then the y-coordinate, the y-bar is just gonna be halfway up this thing which the height of the whole rectangle is f of xi bar and then we're gonna take half of that, like so. So the center of mass for a single rectangle is xi bar and one half f of xi bar, we get that center. Well how massive is one of these objects? Well assuming the entire lamina here is uniform density, then we could actually equate the mass of a single rectangle with the area of a single rectangle and we know what the area of this thing is gonna be, it's gonna be f of xi bar times delta x, like so that's the mass of a single one, the area of a single one. And so what we wanna do is think of this as a system with n points in it. The location will be the centroid of the rectangle and then the mass will be the area of the rectangle and so if we start to try to compute this, we're gonna take x-bar, it'll be approximately, it's gonna be the moment where i equals one to n, we're gonna take the masses of all of these things and the mass remember is this f of xi bar delta x, then we'll multiply this by its location which is just xi bar and then we're gonna divide this by the sum of the masses which is f of xi bar delta x. Now this is an approximation of x-bar. If we take the limit as n goes to infinity, well the one on the bottom, we know this one super well, the region on the bottom, this is the Riemann sum which we're just using the midpoint rule approximation. As n goes to infinity, this is gonna go towards the true area under the curve which is the integral from a to b f of x dx. That we've seen before, what happens on the top? Well on the top as n goes to infinity, f of xi bar, that's gonna converge to just f of x, the delta x is gonna converge to a dx, this xi bar will just become an x and then our Riemann sum becomes an integral from a to b and so there you have it, this gives a formula for the center x-coordinate x-bar. You're gonna get one over the area which the area is the integral of f of x and then you get the integral from a to b of x f of x dx, there's this extra x that pops out here and so this process of accumulation which we've seen many times comes down to the fact that when you have a continuous problem subdivided into smaller linear or so to speak discrete problems, solve each of the discrete problems and take the limit and that will give us the solution to the continuous problem, we get this x bar right here. So it's one over a the integral of x f of x dx. Now the y-bar is a little bit different and that's because the geometry is a little bit different here and so let's illustrate what that would look like. Let me clear off my board. If we repeat this example for y-bar, well it's basically the same idea, the denominator is gonna be the sum of all of the masses so I equals one to n, the area of each rectangle will be f of xi bar delta x. In the top, we take this sum where i equals one to n, we have to take the mass which is f of xi bar delta x and then we have to dine it by the y-corner which is gonna be one half f of xi bar and so when you put these things together as n goes to infinity again, right? As n goes to infinity, the bottom will again converge to the integral from a to b of f of x dx. The top on the other hand, it'll approach one half the integral from a to b of f of x squared dx or sometimes they stick the one half inside here, right? And so when you put those together, y-bar is gonna be one over the area divided by one half f of x squared dx. And so we get these formulas for, we get the formula for x-bar and y-bar and these are just come from this idea of taking limits of this system of discrete problems putting together. And so in the next video, we're going to take a look of how one can use the centroid formless x-bar and y-bar to find the center of mass of various regions. So take a look for those videos.


It's The Cube, coming to you from San Jose, California. Here's your host, Jeff Rick. Hi, Jeff Rick here with The Cube. We are on the ground at the Fairmont Hotel in San Jose, California at the Silicon Valley Business Journal Corporate Philanthropy Awards. It's a big event where they're going to honor 50 companies here tonight that have given back to the community, both in terms of money and time and volunteers. And it's also an opportunity for the nonprofits to come out, to face to the name and really highlight what they're doing in the community. So we want to grab a couple, have them give us an update. So I'm really excited here to have Katherine Cook from the Boys and Girls Clubs of Silicon Valley. Okay, excellent. It's a big national organization, right? It is a big national organization, although Boys and Girls Club of Silicon Valley is its own autonomous branch of the Umbrella Organization, which is Boys and Girls Club of America. Now, is that a unique situation? It is not. So we have 4,000 clubs across the United States. So everybody runs their own Boys and Girls Club organization based upon their demographic and their sort of area and the population that we serve. So I hear, I watch a lot of sports. They talk about Boys and Girls Clubs all the time and giving back. What exactly are some of the services that you guys do of Boys and Girls Clubs? So the Boys and Girls Clubs of Silicon Valley serves about 3,000 youth in our area during the regular school year as well as 15,000 other youth that don't attend our regular program. We're an out-of-school program that provides services in five core areas. We have healthy lifestyles. We have a rigorous academic program. We used to sort of Boys and Girls Club started as the boys club and it was kind of to keep them off the street after school. That's exactly what it was. Keep everybody off the street and out of trouble. And it's turned into a very rich, robust program, after-school program that really serves children in our community. And our mission statement is to serve those children who need us most. All right. In what areas do you guys cover geographically? So the Boys and Girls Club of Silicon Valley has ten club houses in Santa Clara County. Nine of them are in San Jose. One is in Morgan Hill and we're expanding all the time. We're actually getting ready to expand it to Evergreen. So, yeah, growing our organization. Excellent. So kind of San Jose South. East side, San Jose South. Okay, awesome. Yeah. So talk a little bit about corporate philanthropy and what an event like this means to you guys and for corporations to give. So we actually could not run our organization without the corporations in Silicon Valley and their support. We have the support of several big corporations. Macy's is one of them, which is, of course, national, but we have Wells Fargo, Galena, Plot Construction. It's a very, very long list of people that support Boys and Girls Clubs and our operating budget is such that if we did not have that support we would not be able to offer services. That's great. So, do they get mainly money or are there other ways that people can contribute besides money? We also have volunteers, corporate volunteers. So we have volunteers at the high school level, the college level, and then corporate volunteers. So they'll come in. For example, they just came in and had a large group of volunteers came in and painted a map on the block top of one of our clubhouses. So we're always looking for volunteers to come in initially and then hopefully they'll come in and volunteer on a regular basis. Great. So I'll give you the last word. People want to contribute. People want to help. Where should they go? They should go to the Boys and Girls Club of Silicon Valley website, which is bgcsv.org. Awesome. Yeah, and there's a donate there button, and we appreciate everything that anybody can do for us. All right, awesome. Well, Catherine, thanks for stopping by. Again, Jeff Rick here on theCUBE. We are on the ground at the Fairmont Hotel in San Jose at the Silicon Valley Business Journal Corporate Philanthropy Awards.


So I'm going to, I want to start up with a piece that I dedicate to Michelle and so I write the, I write from these rituals called Sematics and they come out of the fact, I'm just going to be very brief with this, I was raised in a factory town in rural Pennsylvania and oh, I just, I wanted nothing to do with this factory town, I saw, I saw pretty early on my grandmother had a shelf in her living room with artwork from all of her nine daughters and sons and I, but the artwork, you know, little paintings and pieces of pottery and I asked her, I said, well, everything on the shelf, they did when they were five so where is the work they're doing now? And she said, they don't have time for art, they're busy working and I thought, oh, I have to get out of here. And so I didn't, you know, I felt pretty good about my decision moving to Philadelphia. No, really, it was great. I loved it. I was writing from, for about 20 years from the mid eighties to about and then when 2005 rolled around, I went back out for a family reunion and, you know, it was whatever, it was just, it was dreadful and whatever, but nothing that unusual happened at the reunion except, you know, it was just, it was just that of the train ride home is when I started thinking about what I was doing and I realized that I had turned everything that I was doing into a factory the way I was writing. I had seeped into my work and I was horrified by this and as soon as I got home, I looked at, I threw up on my door. I just couldn't believe it and I wanted to see my desk and I could see it. I could see the factory on the desk what I was doing. The way I was writing, the way I was getting poems ready for magazines and all that shit you do and I just hated it and so for about about a month, I stopped writing and I started making a list one morning of the problems with the factory and that is a very long list. If you have anybody in your family who works in factories, you know what the factories do to your to your family members. It just destroys them and so I could see what was happening and this is a long list that manifold it back into itself and but at the top of that list was the phrase the inability to be present and that was what I went after. So for the next seven days, I wrote a single color, a single poem a day while eating a single color of food, red, orange, yellow, green, purple and white. I ended with white because the EPA had just finished the study of finding asbestos all over lower Manhattan after everybody had been lying about asbestos in the World Trade Centers, but that's a whole other story. But it worked. That was the great thing. It worked. I created this place of extreme present with the rituals and I loved it and it changed my life immediately and I had the great honor and pleasure of going with Michelle and a lot of other people to Mexico for the radar retreat and I just couldn't believe how beautiful this was. So I did a ritual down there where I would wake up every morning and listen to a different print CD from beginning to end and mix prints into my dreams that I did this dream therapy to remember my dreams and I loved prints coming into my dreams and then I would go down to the beach and I would sit a foot closer to it. I went down there for nine days so I measured how many feet to the surf and I had a special, I did research to get a special kind of ink and paper so that I, you know, because the last day I was riding in the break the water was, I was right where the waves were breaking and it was so exciting to rate inside the break and I had this crystal that I would put in and the crystal would, these little silver fish that live in the water, the breakwater would come in and surround and kiss my crystal. But that's, there were other things I did but that's, but then so that we take notes then while doing these things and then the notes were put into poems and so I'm gonna read just a few of those poems for Michelle. We love you, Michelle. We're all gonna give her a standing ovation at the end of this, right? I was trying to get you to do it in the beginning. We got to do it. Let's do it now.  We love you.   I would win. I would win. I would win. Sort of act like Paul Bearer was sofa cushion. He's straight. So I guess he's not in the fat guys.  Is there more death or semen in my first book? I'm afraid to calculate.  No, no, you assure me. He likes your poems. He's just straight.  That was this really lovely man who was showing us the, remember he was helping the baby turtles run to the water and which was really nice until the frigate birds would come down and eat them off the surface right over. Act like administered by syringe to the dying. You ask if I'm a man or a woman. You only know how to talk to men to women making me a small, wild room. I'm intensely acutely, exceptionally and then exceedingly. Oh, you say now you don't annoy me in the morning, the afternoon or evening. I have no annoyance free home. It's all breaking up on the phone. No, not the signal. Us, us, us. What else sails backwards through my throat but your name. Kota Monty Center, golden twilight, betting against the wild, surviving our efficiency. Act like flowers pulling his petals out. Let me know if you need anything. I'm here to serve you. And just so you know, we're having a sale on our newest model. It's very nice. It's where your hand gets held through the difficult currents. Later, the small ones seem bigger. But our test results show that everyone who hangs in there winds up a jar of their former top secret desires. So please let me know if you need anything.  Act like polka dot on Minnie Mouse's skirt.  I tell your children about war, about their tedious future careers.  I'm the faggot at dinner, asking to be alone with children. Tell them their future happiness depends entirely on how well they cultivate rebellion against any structure that does not hold their autonomy and creative intelligence as a priority. Children, your bliss is at stake. Children, listen carefully for the lies your parents tell you. Children, prepare for joy in ways none of them will ever imagine prepared to live with no regrets. So this is a tiny new book that the artist Jason Dodge just published. I had a boyfriend named Mark Holmes. He had changed his name to earth. And he was an environmental and an AIDS activist who was murdered in 1998 in Tennessee. And if there's a queer community down there that he was living with at the time, and he was kind of burned out. He was working with a gardener. And he was well, he was bound and gagged, raped, covered in gasoline and burned alive. And the police who either didn't want to deal with hate crime, or they knew who did it and they were trying to protect them, or they just didn't care about faggots covered up this crime. And they wrote his death down as a suicide. And I had I had a hard time. It was hard enough dealing with the fact that somebody you love has been brutally assaulted and murdered. But dealing with the police, it was so horrible. I mean, the sheriff in particular at the time, the sheriff, by the way, is now that sheriff from 98 is now in prison. That's a whole other story. He's a creep. And and his deputies. And yeah, and the and the district attorney from back then was disbarred and fired for corruption.  And like the sheriff would say to me on the phone from Philly, he would say he just didn't want me to come back down there and start this all over again.   But there's a film crew, a film house called Delinquent Films, they're making a documentary about my books and life. And they didn't exactly believe me.  And then they spoke to the coroner and then they spoke to the paramedics and they all were like, there's just not, you know, four year old could tell you this was a homicide. So and the death certificate says the victim's death was caused by the inhalation of the accelerant, etc. And so I've started to change. I did several of these rituals trying to deal with my trauma around this and it wasn't working. And then finally, this one was amazing. And I'm very happy. These are new pieces. The last time I saw Earth, he gave me a crystal that had been on hit that he had been carrying around for about a year and a half every day. And I took that I didn't touch that crystal after he was murdered for many years, because it was like a force field around it, like I can't touch this thing. And then I started putting it in my hair wrap. And every morning, it was at McDowell Colony in New Hampshire. And, and this very angry movie that had been in my head for 15 years, where it's this invention where they catch the murderers and there's a courtroom drama, it looks like this room a little bit.  And but the film vanished about a week and a half into working with this crystal, and it has not returned. So it does work. I believe, I think there's been this dirty rumor and poetry in the last 30 years, that first of all, there's this sort of misogyny behind this whole idea of philosophy needing to buttress poetry that poetry is too weak, too feminine to stand on its own. And I think poetry is strong.  First of all, and second, I firmly believe that poetry can heal us. And this worked for me. I'm just gonna read a few of these. So it's called Mount Medadinox transmissions, the ritual. And then the poems are titled, Sharky of the Bird Cage. Quote, if a poem is a prayer that it rise out of my hair, unquote, Robert Seidel, a beautiful moving target is all you wanted to be aspiring future wilderness. You must know by now of the dark quiver my wand genius shot back through same hole. Not everything allows for indulgence analogous to being open by morning fall forward, fall conjuring, tell the farmer we cannot taste his milk but wish to. So one of the things I was doing was also taking a very small, soft, crisp look, you know, I mean, it was like not sharp.   And I said, yeah. And she said, that's awesome.  Few things tire me more than imagining reincarnation, a child struggling all over again to not favor war, not surrender to greed, a finger in the web to give it back 10 fold. Holding our gourds fragment is promised to change if we want change. Another evening of faults are under the chrysalis. A wayward protein bloodletting from unforeseen orifice gathers us to elongate a grass fed hours falling victim to the song and it's silk encasing too urgent for punctuation coping with an inferior century foaming over the rim. A smile hanging on the face as though it will pay off. But then it does pay off. We didn't think we could open up like this. Here we are living in the better place to know. The mountain throat temple is our uncontrollable humming from meditating on mountain mad knock paint over the dead end sign. Our police writers. Yes, they are writing into books our little cherub of misunderstanding of thinking to push us back into body of the whole. Love yourself more next time their reports read stone sink as they please a lit cigarette and our dark hello. So I want to read. So I've recently published for the Poetry Foundation this just days ago this essay on Whitman. And I as a young queer person Whitman was very important to me. And like a lot of people I had naps and a soft beard grandpa poet.  And and and saying that Native Americans and African Americans will be eliminated because he had this crazy idea about eugenics that that you know, he assumed that Darwin meant that they should all be wiped out with like eight off Hitler.   I don't care anymore. I'm just I have and you know what? It's like everybody. So I've been getting a lot of hate mail. And sometimes it's just people wanting to say but what about this like they just can't like I understand that like is this real?   You want all the morality, you know, to be around these people.   And then I said, and then people were saying to me, well, but that's the way things were in the time period back in the 19th century. Everybody was reading on blah, blah, blah.  Okay. So how about people in early 20th century Germany who hated Jewish people? So we just say, well, the Holocaust, you know, it's like, well, that's what the way they were feeling that way about they were in a bad mood.  Like getting grandma on board, like you were saying, get it up here.  So this is the ritual is titled, you don't have what it takes to be my nemesis. So I'm going to read the ritual and the resulting poem to the friend that so these are real things that happened to the friend you thought was a friend until they tried to sabotage the publishing opportunity to the one who ripped your book in half on stage, then wrote patronizing letters to the newspaper about how you should be writing and the poets you should be reading to become a real poet to the creep who deleted your MP3 file because your reading was better than his. There are others lying conniving, envious sour pusses without the courage to be loyal to the love of friends and shared ideas.  Even still, they are given the parting words, you don't have what it takes. Take notes about each of them for the poem, their names are unimportant, as such cowards are rarely remembered. Create a line of tiny photographs of their faces on your computer, all in a row, then print it out. This will be the rolling paper for a cigarette. Cover their faces with equal amounts of the following dried ingredients, fennel seeds, pine needles, rose petals, mugwort, basil, white sage, red sandalwood powder, perique tobacco and marijuana.   Notes about the ones who didn't have what it takes to beat you down the ones who never deserved your friendship in the first place, exhaling their faces on a braid of smoke is more satisfying than the usual forms of forgiveness. Find your poem in the notes and utterly relish your day. So the poem is titled, I feel so lonely when you touch me. Like most people ghosts want listeners, inquiring gender of tree quaking in shade rips your collar to pieces. We meet ourselves whole at same time, order of the way some will ruin themselves, gentleness thrust into a clean glass, IDS, yes, angling a wider indulgence, you and your broken pencil, right, it's a writing world, but do get on with it. Listen to blood of trees and viewing interest rate with sunshine, suffering past to a hired hand. So I want to read a new poem that my mother contacted me, I'm on the road doing this huge project right now, across the nation where I listen to extinct animal sounds, you know, 52% of all the wild animals have vanished in the past 30 years, we found out last September with the World Wildlife Fund, Planet Index report horrifying news. So there are there are field reports and I've been saturating myself with these wherever I go and sleeping in Walmart parking that's called from Whitman to Walmart. I started women's races front door and scumbag and then I go across the nation and sleep in Walmart because I believe Walmart is the best example of the results of his love of manifest destiny. And but my mother called me up in late March and she said, happy, happy, half century. I said, mom, my birthday is January 1st. She's like, I know that's and she was a little high with breakfast, a little, you know, and I said, so I thought there was something with that, you know, but she's like, no, this was the day you were conceived silly. I was like, Oh, okay, cool. So I, I was in Kansas and I did this thing. I was born in Topeka, Kansas. I did this there for my half century, whatever.  And a Kansas field I spent several hours bearing my feet in the soil while listening to insects, birds and cars on the highway beyond the trees. I was born January 1st 1966 at the 838th Tactical Hospital Ford Forbes Air Force Base of Topeka, Kansas. My mother said the doctor held me by my ankles and announced, another fine soldier for Jesus.  We drank from the same aquifer. The sky was as big as it is today.  And in that order, I apologize for being alive. I apologize for the animals I shot and killed to prove I could provide dinner. I apologize for having no answers on how to stop the hyper militarized racist police on the streets of America, while the racist US military is on the streets of Arab nations. I apologize for paying taxes that purchase the bullets, bombs and drones. I am a citizen of the United States. My nation is guilty of war crimes. I apologize for not convincing my queer sisters and brothers. They're repealing don't ask don't tell was putting a sympathetic face on a multi trillion dollar military industrial complex. I apologize for not finding a way to protect Chelsea Manning. I apologize for not preventing my boyfriend Mark from moving to Tennessee where his murder is awaited. I am a citizen of the United States. My nation is guilty of hate crimes. I apologize for many things for a long while then I covered the hole with my offerings and took more notes for the poem.  The first time someone sent Homer through the internet dot dot dot. We are all falling in love while standing in line for death.   If you feel destroyed let us talk do not turn it off yet. We dreamed our obliteration for centuries. Then Hollywood said this is what it will look like or maybe this or maybe this.  The disgraced hairdresser pours us another shot. We will figure it out my friend. The ocean is never far when you feel your pulse. I want to end with one piece that I wrote. It's from my new book. It's the first piece I wrote it in anticipation of the 30th anniversary of inventing my gender neutral name C. Conrad and it's called M.I.A. escalator for Jen Benka and Carol Miracov and I'm going to read the ritual in the poem. I wrote several of my favorite escalators in Philadelphia taking notes up and down the advantages. At the top and bottom of the ride I would show photographs of myself to strangers and ask excuse me have you seen this person? Sometimes there was confusion. Isn't that you? I'd reply no. Many people think I look like her but have you seen her? I feel very fortunate to been born before the ultrasound machine. My generation was the last generation to have a male and female named waiting at the other end of the birth canal. My generation is the last to have our mothers touch their bellies talking to us as male and female pink or blue both pink and blue. Have you seen this person? I enjoyed my conversations with strangers and made at least one new friend. A handsome man who knew I was the person in the photograph that person I am that person and agreed. The ultrasound machine gives the parents the ability to talk to the unborn by their gender taking the intersex nine month conversation away from the child. The opportunities limit us in our new world. Encourage parents to not know. Encourage parents to allow anticipation on either end. Escalators are a nice ride slowly rising and falling, riding while riding, notes for the poem meeting new people. Excuse me my escalator notes became a poem. My poem is titled I hope I'm loud when I'm dead. I have a mannequin for a paperweight. It is difficult to type with such a large paperweight. I reach around lovers late into night typing. From behind, it is impossible to tell which is Virgil. Poetry can be of use. The field of flying bullets the hand reaches through loving the aftertaste finding a deeper third taste. Many are haunted by human cruelty through the centuries. I am haunted by our action since breakfast. You said too much poetry. I said too much war. The biggest mistake for love is straining. There was a door marked mistake we entered. You said too much falling around.  Thank you.


So, in the last lecture we were studying about interesting problem from population growth and we first introduced the linear model and we have seen that linear model is not suitable when the population is high. And then we derived the non-linear model it is also known as logistic model curve curve we have not yet plotted. And then the equation which we have seen is d y by d t is equal to a of y minus b of y square with the initial population by the t naught is equal to y naught. And we have seen that a solution under we are given provided few exercises I hope you have already done the exercises by now. And you have produced a solution in the format y of t is equal to a of y naught by b of y naught plus a minus b y naught into e power minus a into t minus t naught is valid for t greater than t naught this is what the solution you have obtained it. And what we have done is that if you recall the previous lecture we have seen two equilibrium point this is the curve t and this is the curve y. And y equal to 0 for this equation y equal to 0 and y equal to a by b are equilibrium points equilibrium points you will see the exact definition of equilibrium points at a later time. But what the equilibrium so and so that y identically 0 is a solution to the system similarly y identically y t equal to a by b the constants that are solutions to the system. And from the theory we you will eventually understand more and more that when you have two solutions it cannot cross each other you will see all that. So, whenever you start a t here y at t equal to 0 it will remain there only. So, you will move along only this line similarly if you mark y equal to a by b which is an equilibrium solution. So, if you start anything here it will remain there and that is all we have explained in the last lecture and we also asked you to work out the details.  And this is a positive quantity and hence as t tends to infinity this entire term goes to 0 once it goes to 0 t tends to infinity this will be. So, you will get this fact limit t tends to infinity y t is nothing, but a by b sorry you see. So, you have an analysis of that one. Now we want to understand different cases. So, we will we will come to the next thing. So, we will what you do a some further analysis you want to do some further analysis quickly. So, whatever I left out you should go back home and work. So, consider the case 1 first case 1 case 1. So, 0 less than y naught less than a by b this the case situation is something like this here.   And you look at the one of the thing here immediately what we have seen is that the solution because this is y equal to a by b y t equal to a by b is a constant solution. And y equal to 0 is also a constant solution as t moves y t has to remain here this is what the exercises I have given in the last lecture. So, this is also true that 0 less than equal to y t less than a by b all the time it will remain you can never touch these two lines. So, I want to understand the how the curve looks like and we also seen that in the previous slide if you see you see the limit of this one is also is a by b the limit it approaches there. So, we will go there we will do that one. So, what will happen we want to understand. So, look at now this case interesting case. So, we want to the analysis we want to understand some how the curve how is the shape of the curve. So, let us try to the to understand the curve better you have to understand its derivative you have to see the sign of its derivative d y by d t is equal to a y minus b y square. So, this can be written as y I can take it out I will take b also outside. So, you will have a by b minus y you see y at t, but y at t y at t for all time t is less than a by b. So, that shows that this is always positive y is already positive therefore, this is positive that immediately implies this is this case do not forget this case it is here somewhere here below a by b. So, this implies y t is an increasing function y t is an increasing function that is a one observation. So, y t increases.  So, one should do that one here is an exercise now for you in the same situation the exercise is that I want to understand if you want to. So, I got some information that y t is an increasing function. So, I have an information that y t is an increasing function, but I want to understand little more about it if you want to understand not you have to understand more and more of its derivative. So, you just to compute d square y by d t square you can immediately see that d square y by d t square you just do computations a plane differentiation computation you can write here it is in a nice way y into a minus b y into a minus 2 b y a minus 2 b you say you can do this is a simple computation which a thing now you observe some fact. So, let me think what we have seen that this is a positive number this is positive now to determine the sin of d square v by d t square it depends on the sin of a minus 2 b y. So, let me write d square y by d t square is equal to y into a minus b y into a minus 2 b y here since this is positive the sin of this is determined by this will be positive d square y by d t square will be positive if y is less than a by 2 b and it will be negative if y is greater than a by 2 b you see. So, the sin changes of the d square d by by d t is always positive, but d square y by d t square changes sin when it reaches a by 2 b you see a by 2 b is the half of the limiting population if you look at it see what is a by b a by b is the limiting population that is what you have seen the population cannot grow beyond a by b limiting population. In fact, in it cannot achieve like in linear case where unlike in the linear case where in the linear case it can go to infinity, but in this case it cannot go to infinity. So, a b 2 b is half of limiting population half of limiting population.  So, up to this area up to a by 2 b d y by d t is positive. So, if 0 if 0 less than y less than a by 2 b in this interval d y by d t is positive and d square y by d t square is also positive what does that indicates it actually indicates if both are positive it is not only the function is increasing this is basically you can think it as its acceleration. So, it is you have an accelerated growth. So, the function is increasing in a very accelerated growth, but if you reach if the population reaches half of the population say a by 2 b and then if the population reaches here up to it never reaches a by b in this situation you have d by d t is still positive that means the population is still growing, but then the growth of the rate of growth of the population it is a decelerated growth. So, this is an accelerated growth here this is a decelerated growth you see. So, you get basically get if the population starts from here it will go very fast growing the growth is very fast and then after that still growing, but the growth slowly reduces the growth rate reduces. So, you get a logistic curve. So, this is called the S shaped curve called logistic curve you see. So, this is a more or less a complete analysis of this problem when your initial point why the case 1 where y naught is between 0 and a by b. So, it starts immediately the grow population do not grow much it a growth will be decelerated. What will happen if your initial population itself is huge what is the analysis and that is an exercise for you. So, here is a final exercise in this problem study the case study the case when y naught is greater than a by b is a one more program to be study you can see immediately you can in fact see all that you can derive. In fact, there is no separator grade d by by d t is negative and d square y by d t square is also negative. So, that means it is a population decreases. So, the moment you have population above the limiting value then the population decreases and this is a very decelerated decreases. So, it is faster again you the limit will be still a by b the limit of the population will still be a by b. So, understand this case. So, the once the you understand this problem completely you will n draw sketch the graph the graph more or less looks like, but you prove it. So, if you start your initial population at a time t naught is equal to y naught then the population will. So, you get that picture completely alright. So, the some comments as I said in the beginning of this example the parameters a and b appearing that one is vital coefficients and that varies this vital coefficients a and b varies according to which population you are studying. So, there is no definite way of determining a and b you have to study the population over a long period of time and you have to do the kind of data analysis in that to determine a suitable a and b and even this a and b will not remain the same for a same population as the time goes. So, for a certain period of time even including the human population a certain a and b will be good enough, but then you have to re evaluate the a and b after a certain period of time. Secondly, the population model we are given where we have taken into account only the interaction between the species themselves that is the term you got it by square, but in the natural thing that is not the case you have to live with other species even within the single species there will be other issues like national disasters, epidemic and so many things in a population can come into picture. So, you have to define the model according to the situation taking into these kind of facts. For example, let me tell you one example which you probably see in our course or you can not that as I said initially it is not possible to explain to you every problem in this course, but let me tell you one important prey predator model. I will just take the equation I will not give you anything much, but you can see now since the other model is explained neatly you will it is also called Lodka Volterra prey predator model. So, in this example you have two species x t is the species one you can say the prey you can think is a rabbits ok. So, prey and y t is the population x t is the population of the rabbits prey and y t is the population of the predators foxes if you want is just one thing. So, the prey predator model one interesting this you can see that in analogy with the previous model d x by d t you will have a x this is the population is growing linearly with respect to the prey.  So, you have a term the interaction between x and y. So, you will have a term of this form and the rate of population of the d y by d t you will have the c x y minus d x square d y square. So, you see this is an interesting again a non-linear model which you know d y square there is no this is the growth corresponding to that one it is because one is eating the other one. So, to understand that one that is why this is positive sign and this is the negative sign on the other hand this is the negative sign. So, this is the again a non-linear system you will come across with some non-linear system if not this one some other non-linear system and its qualitative analysis will be studied in the coming lectures we will do that. So, there are a lot of interesting examples we can do it now I want to go to a next example as I told you this lecture and lecture will be examples from the standard nice example initially two three examples I will explain in detail and then this is a very nice problem it is actually happen is called atomic waste disposal problem atomic waste disposal problem as I told you all these are all very standard problem probably to see these examples which are explained here you can do the book by Brahm which is given in the literature which is given in the references. So, you can look into the book that there will be lot more examples. So, it is a very nice problem it is actually happened in US where the environmental registered issue about the disposal of the atomic waste is a very powerful atomic waste radioactive material what they have were doing is that you have the atomic waste radioactive waste put it in drums and sealed it very strong drums sealed it and then they used to dispose it in the sea. So, you will have a dispose it sea the environmental is this is the sea level. So, what you are doing it they were disposing this atomic waste in a place where the depth was around 300 feet this was the total 300 feet. So, the issue was that when there when they were disposing this atomic waste at the sea level it will acquire the velocity due to gravity and when the thing is that these drums will reach certain speed when the drums reaches at the bottom of the sea level and it is possible that the impact the velocity the impact when the drums reaches the boundary may be so high that the drums can break. So, the environmentalists were protesting against the this one the disposal of the atomic waste problem. So, this problem was given how to understand this problem and this we want to see even this through this problem you can see even how you attack the problem is also important you may get the solution you may as I said earlier getting the solution itself may not actually solve the problem what you are set out. So, let us calculate. So, calculate let y t be the position at time t position at time t. So, you are disposing the thing and you will the at time t your drums are here this is this length is y t. So, it is all Newton's second law you will apply Newton's second law Newton's second law how do you apply. So, you have the mass of this one mass m and then you have the acceleration d square y by d t square equal to the total force. So, it is a question of first computing the total force how do you compute the total force what are the forces acting here what are the forces acting which you can immediately write because n is a simple physics which you have studied. So, you have a gravitational force w and then you will have a because it is a water. So, there will be a buoyancy force called and this buoyancy force will act against the motion that is what you have to understand. So, you have a buoyancy this one is coming under gravity down. So, there is a buoyancy force and then this acquiring the velocity and you will also have a drag force. So, this is the due to gravity that is nothing, but m g and this is the buoyancy force and that you know for water this is the drag force, but normally the drag increases proportional to the velocity. So, if I introduce velocity here. So, velocity let me introduce here if I introduce velocity v t that is equal to d y by d t and the drag force will be proportional to v. So, the d will be something like c v for some parameter. So, it will be proportional to the velocity. So, you will get that one. So, how do I write this equation? So, if you combine this equations fully in the terms of v. So, you will have m into. So, let me write instead of the second order in terms of the velocity I can write it as the first order equation. So, m into d v by d t is equal to the total force what is that one w minus b minus c v. This I will write it as v in suitable form I want to write suitable form. So, you can solve it easily that is why. So, I will write it d v by d t is equal to 1 over m into w minus b minus c v. So, you see that you will have it. So, but I can write this is equal to m g is equal to w because this form I need it that is why that you can see that you can solve it from here itself, but this good form of writing. So, this is m g w. So, I can write multiply and divided by g you get m g. So, you get a w w minus b minus c. So, this is. So, let me write it in a form many of you are familiar I will combine all that there and I can write it in a nice way d v by d t plus c g by w into v is equal to g by w w minus b. And the velocity you are just dumping it. So, initial velocity is 0 at time t equal to 0 the velocity is equal to 0. So, you see this is a first order equation first order linear equation. Of course, those who are attending this ODE course for the listening to this ODE course for the first time they may not know how to solve this thing, but most of you I am familiar those who have seen some ODE notions you know how to solve it. Anyway, in our coming lectures you will see how to solve these equations in your equation. So, let me not spend time how to solve it here because we are going to explain to you how to get the solution later. So, what I am going to do is that I am just plainly writing my solution. So, the solution will be v t is equal to I can immediately this also a non homogeneous equation there is a non homogeneous term. So, it is a first order linear non homogeneous equation.  And we will explain in detail how to solve it when we study the first order second order all that equation. But let me write down the solution very nicely the solution is w minus b by c 1 minus e power minus c g by w t this is the solution. So, what is our aim as far as our problem is concerned the aim is to see that the velocity does not reach where the breaking level. And that was calculated that is calculated by the people if the velocity v t is approximately something like 40 feet per second these are computation done by the people environmentally minister. If the drum you drop the drum and reaches the bottom by the time it reaches the bottom if the velocity reaches crosses 40 then there is a chance that these drums will break. So, we want to see that by the time it reaches the velocity will keep on increasing whether that is why the analysis is now required whether if your solution never reaches 40 then there is no problem it is not going to reach and 40 and then. But then now you compute this as t the an immediate analysis you can do limit t tends to infinity v t is equal to this as t tends to infinity this term goes to 0 all right. So, let me mark it with a color this term goes to 0 as t tends to infinity. So, immediately you see that the limit goes to w minus b by c and these are all known quantities w b or all and c these are all known quantities because w is m g b is the buoyancy which is has a value c has the proportionality to the drag force to the velocity and these are all computer, but this is approximately happened to be 700 you see. So, the velocity indeed will cross 40 as t tends to infinity, but there is nothing to completely ignore the problem here it only says that the velocity can cross 40 at certain time, but that does not mean the velocity will reach 40 by the time suppose it hits much earlier time the ground. If it reaches and hits the ground which is only 300 feet at that time it may not reach 40 then you are fine, but from here from this computation we are unable to judge at the time it reaches because we do not know the time what time it will hit because you have calculated the velocity in terms of the time we have not calculate the velocity in terms of the distance that is where the a different approach. So, this approach even though it looks like your problem is solved completely we are unable to predict what the actual problem was actual interest was about the problem. So, we have to view this problem we have to analyze this problem in a slightly different way and that is what we are going to do it now another approach. So, this is again to indicate solving just differential equations may not be the entire aim and in fact solving may not give you what you want and quite often it may not be necessary to solve a get the solution explicitly the aim of the problem will be quite different which you have to learn it. So, the idea is that you have this problem and you are dumping it you want so far you calculate the velocity as a function of the velocity is your independent variable and time was your independent variable. Now what we are going to see is that you have viewing this distance y is the distance indeed the distance earlier also, but you have seen the difference was that you viewed the distance y as a function of time. Now I am trying to view y as a independent variable and then you calculate the velocity so you are going. So, you are calculating the velocity v of y velocity at distance y. So, the time is not coming into picture in this formulation now. So, but we need that one. So, v is the velocity at a distance y. So, we are computing in the downward direction which you understand I hope at a distance y you see. So, that is why. So, y is your independent variable now v of y is the velocity as a function of the distance is the dependent variable. Of course, at time t you already have. So, y equal to t is the distance at time t that you still exist. So, if you come so if you derive my relations v is the velocity at time t at time t your distance is y t.  So, this relation you already have it you see. So, at time t you are at a distance y t and then the velocity at that time function v t. So, you compute this thing.   You substitute. So, you compute d v by d t in this equation. You substitute that equation substituting in the earlier equation. You get it substituting. What do you get it? v into d v by d y is equal to let me just write equation. The same equation I want to the c g by w v equal to g by w w minus v. You can derive to this form. So, if you do not get it, you can get this equation. These are all simple computations which you should do it. You substitute or do the computation as I said do the computation. I write this equation in a slightly here there is a problem. The problem is something serious now because this is. So, earlier in v the equation you go to as a linear equation linear homogeneous first order equation, but look at this term. This is a non-linear term. So, the moment non-linear equation the moment we have changed the way you view it that is why the other model derived first thinking that that will give you the answer, but the required answer we did not get it. So, we have when we change the model and view this v as a function of the distance we have a non-linear model and we have to analyze this model quickly nicely.  So, I will write this exercise. This is a simple computation you do not have to worry, but you should get familiarity with the computation. Write the equation as I want to form even though it is a non-linear equation I want to write it in the solvable form. Write the equation as this is easy to do it equation as let me write it v by w minus b minus c v into d v by d y. This is not difficult to write is equal to g by w. So, in non-linear equation solving is there are no general methods at all. So, you have this equation. Now, this is an equation in v d v d y you can take it out the other side and of course, the velocity initially is an initial value problem. So, you have a v 0 is equal to solve this equation can be integrated solve it this is a solve it. This is standard integration problem it may look complicated does not matter what you can add is that you can add you can make a numerator similar to this one first you multiply something you can take c outside and do all kinds of things. If you take c outside you get w minus b by c and v is the you add and subtract something. So, you can decompose it in a partial fraction or whatever form it is which you can solve it and solve it to get. If you do not get it at least after few lectures in differential equations after studying the basics of differential equation you should be able to solve it, but you need not have to know any differential equation to solve this one. So, this is an integral problem. So, you have to just integrate it which you can do it because d y this is in a at least way even though it is non-linear it is a this is a constant. So, g n g w this is a constant. So, you do not have to worry about it. So, d y you can take it it is a separable form and integrate this function. So, basically want to integrate this function you are in the you have to integrate this function and substitute this thing to get it. So, let me write down my solution in a you get a solution in an implicit form g y by w this is an implicit form equal to minus v by c minus w minus b by c square. Anyway do the computation if I have not make any error I am not sure there may be some minor error of sign or something, but it is nice to correct the error of the lectures and that is the best way to learn in fact. So, you see is the thing. So, that is the final form of the solution. So, earlier you have a better form you have a better thing, but this is a more complicated form of solution more complicated solution, but and you cannot separate it even you cannot represent. So, you see this is an implicit equation there is no easy way of representing v in terms of y, but what is interesting they have done is that that is a final tail tail to the tail tail to the tail if you want the both tails are different. What they have done some numerical computation and what is your aim do not forget the aim the aim has to compute v the velocity when it reaches a distance 300 right that was the initial aim. You want to know what is the velocity when it reaches here and there did some computation it happened to be approximately 45 greater than 40 you see. So, you wanted that to be less than 40, but unfortunately it happened to be 45 and then eventual result was that they have to stop them we get. So, it was a protest from the environmentalist and they have to see how the mathematical simple analysis one has to deal with to solve problems. With this example I will now go to I will not give you the details here I want to give you two more examples I will not be able to complete the analysis, but these two more examples are extremely fundamental in two of the fundamental areas of engineering one from mechanical engineering mechanical and another from electrical and these people the mechanical engineers electrical engineers regularly use these examples. In fact, any automobile any things you do do it any construction even civil or whatever mechanical construction thing these examples will work. So, I will today I will try to give these two examples how they produce the interesting aspects of these examples are that both leads to the same differential equation. If you recall my first lecture the aim was even though the differential equations may be coming as modeling of different physical phenomena the mathematicians always want to study in a very general perspective it may have common features this one of the interesting very simple examples which most of you are familiar those who are again taken a course on ODE will be familiar. It gives you a non homogeneous second order linear all simple equation with constant coefficient which you can solve it you see we both leads to. So, we will derive it the equation we will show you that equations how the equations are coming and may be in the next lecture we will do an analysis of that and this is the complete thing after that we will explains few more problems in the next lecture, but we will not you will see some of the examples as we proceed the course thing. The thing is that is a mechanical vibration problem.  So, it is also called spring mass dash port system spring mass dash port system that. So, it is a as I said is use absorbers in automobiles it is also barrel heavy guns when you fire a gun you know that it is a it is also comes back to hit you and you have to understand that in a better way how to avoid that one and the main thing is the shock absorber. So, what is a basically a spring mass system? So, you have a spring natural spring attach it with a mass here. So, you have a mass m and you have a spring. This is called this is called the spring mass spring mass you see how does it work? Suppose you pull suppose this length is l right now this is l basically you pull it or push whatever it is l length pulled or pushed l length of delta l then the spring the spring has the thing of the restoring force that is what the spring will do spring will try to restore when you pull it spring will do that one and this delta thing it will exert a force exert a force proportional to delta l and that is we call it k into delta l and that is how the spring constant this k is called the depends on the how strong your spring is this called the spring constant. So, it is an important parameter. So, k positive spring constant. So, you will have vibrations by Newton's second law of first law you have to say that when you have a spring and if there are no external forces nothing else when you give start vibrating it should start vibrating without stopping we should we want to see all that phenomena thing.  So, what you do is that you put this spring mass system in oil whatever it you put it in oil whatever it. So, you want to understand. So, as soon as you put the spring mass system put it in oil the oil will have its own effect on that spring mass system when there is nothing by Newton's law it should start vibrating when you pull it it will keep on oscillating and that is what it may suddenly create, but when you put it there you want to do that one. So, you again want to the Newton's second law of motion what you get it you will have again if the mass is m you will have d square y by d t square and what is y t for you here y t is the distance from the measured distance at time t distance at time t measured in the downward direction measured at distance at time t. So, you have the total force that is what you have to understand what are the total forces will come let me you reserve this one total force. So, you want to understand what are the forces there will be a force due to gravity and what are the other forces there will be a restoring force the spring has an effect I told you the moment you pull it this will have a restoring the spring will try to restore it to its original position and that will act against the motion for example, if you pull it it will go to the position you will push it up it will come back. So, the restoring force will have a play against this is a gravity it is coming down and then what are the other forces available there you will have a drag force you will have a drag force and that also act against it and then some external disturbances that is what more interest. So, you will have some external force. So, this is due to gravity so that is nothing, but your mg and then you have the restoring force how do you compute that one force. So, you have your restoring force you have to write it suppose it is a y t and if you pull a distance of delta l and so the restoring. So, y is the distance at time t and you pull it a distance of delta l the restoring force will be y t plus delta l. So, y t at time you pull it that is a restoring force and drag force as I told you is normally proportional to the velocity. So, you will have c into d y by d t that is the velocity. So, these are the terms you have to apply, but now we are analyzing the situation at equilibrium. At the equilibrium what will happen when it is an equilibrium that one created due to this pulley should be cancelled with your gravity force. So, you are exactly you will have it mg that is nothing, but your w will be e to the power of delta equal to the k into delta l. So, that is what will happen. So, you have to write down the restoring force I should not put sign here. So, basically you will have k into delta l. So, final equation if you rewrite all these equations comparing here you put it here everything what you will happen is that after cancellation you will have an equation of the form you rewrite derive finally, do the a bit of computation finally, m into d square y by d t square plus what you will have is that c into d y by d t plus k y. All these terms will come you see d c into d y by d t will come and I have taken the sign. So, it will come here with a minus sign you will have a sign here that will come here and the other terms will get cancelled only one term is equal to f of t. So, you have a you see this is say. So, you have to understand this terminology m is mass this is called the damping basically you are putting a damping you have to understand why mechanical system you need damping. If you do not have a damping it is exactly due to that you are putting it in the oil you are putting this system in oil and creating a damping on the system. So, whenever you create any mechanical system you have to give enough damping otherwise the it will create oscillation this is about the spring constant you see it is a spring constant. So, all these terms m c k are positive this of course, it is an external force which you do not know. So, you can have an external force. So, you have to analyze this system you know how to solve suppose f t equal to 0 you know this is a second order as I say second order earlier equations for first order. Now, you have a second order easier thing it is in a linear and with constant coefficients. So, you have all simple form with constant coefficient and we know how to solve it we will do this solving later, but I will write down the solution and I want to interpret. Now, from these last two examples you have understood just writing the solutions are not enough you have to write the solutions and you have to interpret the solution what are the things happening in a mechanical system. So, when you design a mechanical system you have to take into account how much damping you have to put into the system what is the minimum thing required. So, that you do not have the vibrations of your mechanical system there are disasters due to lack of damping. So, we will do that in the next lecture, but in the few minutes I am having I just want you to show one more example leading to the same example electrical circuit, simple electrical circuit I want to do this this is an RLC circuit simple RLC. So, you have a some EMF coming from here the true mode if force coming connected to a resistor and you have a inductance and you have the capacitance. So, you have plus I will put I hope the minus sign if you want you can put a key this is a simple RLC circuit. So, you have your resistance here and you have the corresponding inductance here and you have your capacitance and what you do the what are the things you have it you want to understand the current I t at time t and you have the charge suppose Q t is the charge at the capacitor charge. How do you model this one this is a closed circuit simple closed circuit. So, you apply Kirchhoff law I told you the physical laws you have to apply. So, you have the Kirchhoff law.  So, across L what is a voltage drop L into b I by g t that you know it this is from comes from how they design that if you know little bit of electrical circuits and the it means you can see that this is the kind of voltage drop that is nothing, but you have also a relation here I t is I is nothing, but d Q by d t. So, you have that also this relation. So, these are standard things which when you study the basics of this one. So, this is nothing, but L into d square Q by d t square and across R you have these that you know it nothing, but R into I right the voltage drop this R I that is nothing, but equal to R into d Q by d t and across C is nothing, but 1 by C is nothing, but Q by C and you have to write an integral form if you want to write the I. So, it will be Q by C. So, if you add these three add these three your equation is you see equation is L into d square Q by d t square d by d t square plus R into d by d t square plus R into d by d Q by d t plus Q by C 1 by C Q is equal to E t. You see it is exactly the similar equation as in mechanicals absolutely no different only the quantities are different the interpretations are different. So, you have a similar equation. So, quite often the same equation the previous equation is also written in terms of current what you want if you want to write it as a second order equation in terms of the current you differentiate once more if you differentiate once more what you will get is that I into. So, you can write in this format also d square I by d t square plus R into d I by d t. So, you can write this equation in this form plus 1 by C I, but you have to differentiate once more. So, you will have basically E prime of t the derivative of this thing. So, you can see a comparison it is an analogy it is not really a comparison, but you can have an analogy because in the mechanical system I am going to do a detailed analysis a similar things can be done for the electrical system also. The interesting thing is that in the mechanical system you can see that. So, both places they just like you there you use damping in electrical circuits you use resistance. So, an unwanted vibrations what you have seen you are there you are putting the thing to remove the vibrations and so you want to have a stable system, but the use of that in electrical circuit we want to create that amplifications. So, the same phenomena there you have vibrations and removing through damping which you will see is used you do not want unwanted vibrations in the mechanical system. So, the bridges etcetera this exactly have what happened to the tachoma bridge collapse which we will explain later. On the electrical systems the same things are used the frequency model is used to amplify can correctly this is exactly the principle used to match the frequency and to tune your radios and other televisions etcetera. So, how do you get all the signals are coming into your televisions system and you are want to get that. We will explain this one we do the analysis on these systems more and in the next lecture and we will continue to meet the next lecture. Thank you.