Today we gather to remember the crew of Extortion 17. Although it's been close to two years since that tragic day in August, the memories are still fresh in the minds of many Colorado National Guard members. Close friends and senior leadership from the Colorado Guard paid their respects to two of their own at the Arlington National Cemetery grave marker bearing the name Extortion 17, the call sign for the Chinook piloted by CW-5 David Carter and crewed by Staff Sergeant Patrick Hamburger, where some of their remains are co-mingled with others from that fateful flight. It's just really an honor and a privilege to be here at Arlington today to remember Dave, to remember the crew of Extortion 17 and those Navy SEALs and the PJs and even the working dog and our Afghan allies, that loss of life that day, again the most significant loss we've suffered in Afghanistan and it caught the nation's memory. Even though Hamburger did not live in Colorado, he was still considered one of their own. Now of the two, Mr. Carter was personally known to us as a member and as resident of the great state of Colorado, Sergeant Hamburger, attached, assigned to our unit was from the great state of Nebraska, our neighbor, so we include them both today. As for Carter, some knew him all too well. We called him Twitchy because he was always drinking coffee and as the true American, he changes both the times and goes to the energy drink so we place a picture of Dave as we remember him and his favorite drink.  He was always the guy you'd look for both professionally and personally just to say hi. Your day always got a little better. Colorado's Adjutant General and Senior Command Staff were in the nation's capital for their state of the state visit which afforded them the opportunity to visit Arlington Cemetery and the Group Burial Marker 4 extortion one set. There's not a day that goes by but I don't think about Dave Carter and his family. Laura, Kyle and Caitlin and Elsie are in my prayers every day because I worry about it and I think about it and I know how much we miss Dave. I can only imagine how much they do. And while both Carter and Hamburger are interred in their home states, a small portion of their remains lie here at Arlington with the men they fought and died with.  I think it's the right and proper area to be honored. At Arlington National Cemetery, this is Sergeant First Class Robert Stevenson reporting.


What's up guys? EvilD here and today I'm going to speak to you about this new website I've found and it's called Chatterplot. And basically the idea behind the website is that you can find speakers of the language that you're interested in or you're learning within your local area just based off of a map of where you are. Now obviously not just speakers but you can also find maybe language meetups or teachers and the whole idea is it's kind of like a very informal way of finding people and meeting up with them at your local cafe or stuff like that. If you've used the Meetup website that's very structured and you need to have pre-designed meetup groups and stuff like that. It's like that concept where you can form meetups but there's none of this whole structure. It's just you find someone in your area you contact them and boom you can meet up with them and do whatever language wise you want to do. So let's just look at the website before I ramble on too much. Now as you can see the basic setup you've got here it's already picked up where I am. I'm in Rockdown in New South Wales so if you want to come and get me come on I'll take you. I'll take you. No I'm not that brutal. So yeah or you can search by languages stuff like that. Now obviously you would first go to sign up and then you'd select whatever your language is that you're interested in what languages you're learning stuff like that. But you know I've already done that and it's pretty self explanatory. Now I'm going to log in my email address will be blurred out just so you guys can't send me random spam. Because I know you're never going to send me anything helpful. So I'm just going to log in. Log in. Log in. Okay so I'm in. Now as you can see apparently my name is Evil Deer. Deo de Lakatoi which just translates as Evil Deer God of the Cats because that's who I am. Now before I just go a little bit too far into it I just want to say this website's in its beta stage. So basically that means that there's still a lot of issues with it. Don't try and use it on IE at the moment because it just breaks. And they've acknowledged that they're working on that because I've actually been speaking with some of the people who are programming this website. There's also it doesn't work on the iPad it works partially on the iPhone. So basically at the moment just try to stick with Google or one of those types of browsers and using your computer. Just give it a few weeks and they reckon they'll have most of these bugs all ironed out because it's in beta stage at the moment. But there's already a lot of people signed up funnily enough. So it looks like it's going to be pretty impressive.  You probably want to change the website's language. So what you want to do is you want to go up to Evil Deer or whatever your name is. Go to settings. Okay and now once you're in settings you want to go down just pretty much right down to the bottom. And it's got display language and you'll notice the language is our German, English, Esperanto, French and Russian. Now how cool is that? Obviously I run an Esperanto channel and having Esperanto as one of the first available languages is pretty sick in my mind. I'm pretty happy with that. I'm assuming later on there's going to be a lot more languages but at the moment that's your choices. So go learn Esperanto so you can be, you know, ahead of the curve type of thing. So we're going to select Esperanto because that's what we care about. We don't care about all those other random languages. Well maybe you do but I don't. I don't. I only care about Esperanto. So now it's changed over. The interface is all pre-translated. Awesome. So now we can go back to my actual profile. Now obviously you've got things like up here like my events and stuff but I haven't signed up for anything. You can see it's picked up. I'm here in Sydney. I'm just going to close this stuff off. You can write some random information about yourself there but we don't care about that. Now as you can see there's already like a marker on the map here to say there's actually something here in Sydney. So I'm just going to zoom in on that. Let's have a look what that is. That's me. Okay that's what that marker is. But I did see another marker earlier. I thought it was over here somewhere. Now I'm going to zoom out now. Let me go right back to the map. Oh whoa okay there we go. So we've just changed over to the US. Now this website is as I said very new so there's not much in Australia at this stage. It looks like there's a few people that have signed up to do some stuff. But let's go to the heart of where this is all from. I believe this website was actually designed by a German group. So obviously there's going to be a lot of groups there at the moment. And if you're in like a random location and you see that there's no one there. I'm assuming you just have to wait a bit until people start signing up. Or just get your friends involved type of thing. Okay so nice big hot patch right here. Let's go zoom in on Berlin. That's where it's all happening by the looks of it. And as you can see the further you zoom in the more names and stuff that appear down the side. You can see these different profiles. I'm not sure what these people really like. You know what look there's Chuck. You know what I'm going to use him as an example. So apparently he speaks English, Esperanto and German. I'm not sure about his English. He seems like a pretty poor English speaker to me. I wouldn't believe that and I'm just messing with you. So we're looking at Chuck's profile here. You can see there's some information about him. This is his preferred meeting location. And you can just send him a message just like that. Just send the message away. And I'm assuming if he comes to my profile looks at me and goes clearly this is evil deal. I'm going to contact him. Then you can just reply and then you guys can meet up and do whatever. And that's basically the concept of the website. Just find people wherever you are. Contact them, meet up, start practicing. How cool is that? There's no subscription fees or anything like that. That's a problem with meetup. With meetup if you want to actually set up meetups. You've got to pay like a subscription service in order to do that. Which is real pain. But this is pretty cool because you don't need any of that. You don't need to be really formalizing your meetups. Just drop pins type of thing. So anyway, that's sort of what we've got going there. I'm pretty much done with that. Now as I said, this website is in the beta stage. So there's a lot of issues with it. Every now and then things just won't load. You'll just have to refresh the page and stuff like that. Just give it a bit. They've been working massively on this. Like I actually checked this website out about a week and a bit ago. And since then I've actually seen a fair few improvements. So yeah, that's pretty much it. I just thought you guys might like that. Because us Esperanists, this is going to be very handy. And as you can see, look down the right hand side here. Esperano. Esperano. German. What? You got no Esperano? Jesus Christ, what's going on there? But as you can see, this guy's apparently a ninja. There's a fair few Esperanists on this website. And I reckon once obviously this goes out on my channel, there'll be a fair few more. And this might help you guys actually find other Esperanists in your area.  Check it out. Play around with it. Tell me how it goes in the comments below. And that is pretty much it. So if you've liked this video, give it a like. Share it around with your friends. Subscribe to my channel if you haven't already. And I'll see you in the next video. And if you're not there, I'll find you on chatablot. And we will meet. But you won't like it. And now, a massive shout out to my Patreon sponsors. And I'm going to totally butch this name. So I'm so sorry. Please fix my pronunciation. I don't know how to say that. Sarah SC and Shane Power. They are donating through Patreon so that this channel can grow and get better and become more awesome. And you can too if you want down below. Just check out the description.


Welcome to this second lecture. In the first lecture, we have explained various aspect of differential equations including the importance of studying ODE as a topic of analysis. That is what we concentrated in the last lecture and that is what we are going to do it throughout the lecture. What we have especially emphasized is that the methods available to study ordinary differential equations is very limited and there are very handful of examples where you can actually develop methods. In fact, most of the physical problems and the corresponding differential equations cannot be solved in the sense that of implicit explicit that means that your solution y as a function of x and a implicit relation between y and t which is in general not possible in most of the interesting differential equations. It is in this respect only we explain the concept the enlarge the concept of solutions to differential equations we the solution does not it is no longer means that when there is a solution the solution can be explained or given in an implicit or explicit form. There are also other concept of the x solutions which we may not come into that, but it is always important especially when you study control theory and other physical problems. We will not come to that one, but for us when you there is a solution exists and that is in the this is the scenario where you need to understand study the solutions and the qualitative study begins there especially the qualitative existence uniqueness and then of course, more qualitative analysis about differential equations. In the next two to three lectures including this lecture we are going to present few real life examples. These examples are not new, but it is a important examples it is available in the literature and we will give some details about some of the examples in this first two three lectures and other details of some other examples you will see when we proceed the course in other lectures we will explain to it. So, you will see also in the through these examples just producing even solutions explicitly or implicitly is not enough because the solutions may not reveal its features. So, the idea if you want to understand you have to even after getting the solution you will see that you have to study the solutions in the sense of analysis, but before coming to the example I would like to explain one or two issues which I learned from experience by going and teaching students of BSE students especially. There are certain issues which are not clear not only to the students and is also not explained to the students by the teachers properly and we want to spend some time maybe 10 minutes on that and if those who are already thinking that that is trivial they can just get out just bypass this part of the thing and they can get into the examples directly. So, let me start with an example what you want to do it this is an example from integration. So, I am going to from the integration theory as you know that the we started from the integration theory. So, I want to start with a very simple example which you do it in your plus two time and that is where our all trouble quite often start certain steps are not clear to look at the integral you want to do it y cube d y you want to integrate the there are two ways of doing it you immediately know the what this integral is. So, you immediately write y power 4 by 4 that is fine that is no problem that is good, but you do not know this thing the another way is which is important here you are able to do it because you know the antiderivative you are you can do that one, but then when you do not know antiderivative the integration is done via substitution. So, what do you do with you will substitution you will do substitution what you do is that suppose you I put to y square equal to t one substitution need not be unique or equivalently y equal to root t. The immediate step you write is you will immediately say the next step you never think of that you will immediately write 1 by 2 root t d t and the next step in the solution you write is therefore, this is what the steps you are write in your standard exactly I am going to write and I want to know that y cube d y is equal to y square is your t and your y d y y square is t. So, d y is equal to otherwise we will write here 2 y d y is equal to d t. So, let me use that one. So, one of this both ways you can write it. So, 2 y d y is equal to d t and you immediately say that. So, y d y y square is substitute as t y d y is half d t you write half d t and you write t square by 4 this is the procedure you follow which is nothing, but y 4 by 4 hence. So, what is not clear which I never got an answer from the BSE or other students when you ask what do you mean by this? This is where the first difficulty in understanding coming to you. What do you mean by what is the meaning of d y d t? If you do not know the meaning of that is a first step and we never most of the time we never get a satisfactory answer to that. In fact, we do not understand this we do not know it we do not know at this level that is important why I say that at this level when you study advanced different advanced topics in mathematics like differential geometry etcetera. Then you do interpret this in a different way, but that is not a thing we have to understand at this stage. So, when you do not know d y and d t how do you how so the question is that what is this what is 2 y d y is equal to d t. So, I want to spend a bit of time here 2 minutes here. So, here is the what is your trouble you are to what you know really is. So, you have to understand that when you treat y as a function of y t that is what we are doing it. We know what is d y by d t together this you as a function of t you know what is this you do not know what is d y probably you do not know what is d t. This is a symbolic representation this is a notation to understand the meaning of this limit delta t tends to 0 y of t plus delta t minus y of t by delta t. So, you have the meaning for as a whole of these thing, but you do not have the individual meaning to it. So, that is what you have to so that is what we are similar I will come to that example together. So, similarly let me start with one more example where a similar lack of understanding this I want to do it because differential equation similar thing how you proceed here you have d y by d t equal to a of y in a similar way what you write is that the next step you write is that all of you will write d y by d t. So, d y by y is equal to a d t this you do it immediately and then say that on integration on integration you immediately write integral of d y by d y is equal to integral of a d t plus some constant integrate you get your log y these are the steps written quite often a d plus c naught and finally, with one more step you write y t is equal to c e power a t good the answer is fine. See the whole thing is that in the previous example the answer is right even the answer is correct here. So, again the issue is that what do you mean by d y by y is equal to y and this is whatever c is an arbitrary constants here. So, what is the meaning again what is d y is equal to a d t d y by y is equal to a d t to do that because to explain this one if you want to understand this one if you want to understand this you have to understand d y and here is a important result we quite often bypass, but that is one of the important aspect when you want to study the not only the integration theory many other things whenever you develop an integration theory you have to understand a one of the important result what is called the change of variable formula. So, we will introduce in our preliminary change of variable is what is the underlined principle behind all these things to explain to use that. So, what I am trying to say is that all these are all. So, when you recall the first example when you have. So, when you when you writing this one this is only a symbolic representation of this fact that is what I am saying that. So, as I said this has no meaning. So, you have an expression here say one you have an expression here two you have an expression here three what I am saying that one and three have meanings two is only a representation of the fact three what you really need to prove derive three from one and this is the part here the part d y by d i equal to y you have to view it as a step to represent three and this is where is given from the what is called from the the change of variable formula. How does a change of variable formula looks like which is what we are going to explain, but you will see it in the preliminaries. Suppose you want to integrate integral of suppose you want to integrate f of y d y and you are making a change of variable that means when you are change of variable here y you view it as the variable here the view y is the independent variable as far as this is concerned and then you are making a y going to equal to as a making a change of variable as a function of g t you have t you see you are making. So, you are having the independent variable y you are making to a new variable t via this relation. So, in that case f of y will be f of g of t you see and thus this can be viewed as a function of t you see you have a function of t and hence we can integrate h with respect to t. So, the question is that what is the relation what is the relation this is given by the change of variable formula this is what is given by change of variable formula which thing that mean you if you integrate this one f of y d y is equal to nothing, but integral f of g of t g prime of t d t this is non trivial. So, it is not immediate need a proof need a proof of course, need a proof and this is what you will be seeing in the need a proof is not trivial this is what I want to say that. So, whenever you making an integration is introduced you have to always prove certain types of change of variable formula unless we do that one we will not be able to proceed further we will not be able to integrate quite often many interesting functions. So, the change of variable formula is very very important when you study any integration whenever you that is you might have study on just not just one integration many other types of you integration we will come across with that each time you have to do a change of variable formula this also important when you have a multi valued function suppose if is a function of different variable y 1 etcetera y n how do you change it then the change of variable formula is much more complicated you will have in terms of here certain Jacobians etcetera there and when. So, when you whenever you make a substitution y equal to g of t the normal procedure you immediately write d y is equal to g prime of t d t what I am trying to convey to you is that this is only a symbolic representation of this fact. So, whenever I am telling that you can integrate whenever you have function f n whatever if f equal to 1 you will have integral of d of y is equal to integral of g of t this is the fact used here. So, as such this has no meaning if at all you are going to give meaning is that you have to give this meaning to this fact this one with this change of variable you will they may in the preliminaries we may say few more words about it there will be of course, it has a function of y you will get a function of t, but you have to resubstitute t in terms of y all that facts are there essentially that one. So, on the or you will have the limits for this integration then there is no problem it is not limits you have to resubstitute back that is what. Now, let us recall the facts now recall our example recall example 1 and I do not want to use it because I do not have anything meaning to that I want to see prove everything just using my integral recall example 1, 2 examples we had an integration theory example. What is the first example you will have f of y is equal to y cube and then you have substitute y square is equal to t or y is equal to root t and then I want to understand the integration now with this relation to that one. So, I am not going to write d y equal to something because that is such a I am not going to use d y equal to d whatever 1 by root 2 d d t at all because that has no meaning. So, I want to understand the integral of that one. So, what is your y cube d y here is equal to change of variable here is a change of variable this is the change of variable what you want to string instead of the change of variable I want to substitute y square equal to t. So, f of that when I put y is equal to root t I will get root t power cube and then what is my g of t here this is my g of t you see. So, I want g prime of t. So, I want root t prime d t. So, when I write this one. So, I have not used anything I have used the change of change of variable formula I if I substitute that one I will get it t power 3 by 2 1 by 2 root t d t is nothing but. So, I have arrived that half of t half cos t t d t. So, you see you arrived that formula integral of y cube I approved this third equation without bypassing that a thing you apply just that and then you proceed it. So, this is your first example which here so whenever you do it we keep we will also write this thing now onwards. So, whenever we write something like this d y equal to something like g prime of v keep it in your mind all the time that there is something relation to this one some sort of that is the meaning of it. So, you need to prove it you need to require a change of variable formula at all point of time to conclude that one you see. Now, we will come to the other example as also differential the example 2 which we have done example what is the example 2 you have your d y by d t is equal to a of y you see I do not want to write d y equal to d y by y equal to a d t eventually we will do it as a, but we have it in mind. So, I want to write this is d y by d t is meaningful I told you because it is a function of t. So, there is no problem. So, I can write y is meaningful. So, I will write 1 over y d y by d t and is equal to this all function of t. So, y is a function of t d y by d t is a function of t you will have a is a constant which is a function of t. So, I can integrate when I integrate with respect to t what do I get it I get 1 over y of t d y by d t which is a function of t d t is equal to integral of a of t a of d t a of d t some constant constant of integration. Now, change of variable what is the change of variable here again change of variable here t to y you can make change of variable anywhere you like it I want here the change are not at earlier it was y of t. So, I want a t going to y I want to view instead of t as my independent variable I want to see y as my independent variable and I want to see as you know very well 1 over y is the function coming into picture. So, I want to integrate 1 over y now I am viewing y as independent variable and I am differentiating. So, my f of y is 1 over y here here f of y is 1 over y and my g of t is equal to the. So, here f of y is equal to 1 over y and my g t is nothing but y of t this is what you are doing it. So, if I do that one by change of variable again change of variable formula again here I have my thing I need view this as a function of t and I want to differentiate this y differentiating is that is nothing but my d y by d t that is it y prime of t I want it and I can integrate d t I have t into d t you see and this is nothing but this is nothing but this left hand side of this one. So, hence that implies if I substitute this for this term I will write integral over 1 over y d y is equal to integral of a d t plus a naught you see. So, you arrived at this formula with a change of variable and this again symbolically represented by d y by y is equal to a d t you see I want to say that this is it this cannot be derived from here this formula cannot be derived from here it is not directly derived it is the fact of integration parts. So, this is the one important thing I would like explain and one more fact which may be looks simple, but I have seen lot of students making mistakes another issue probably trivial to many of you, but I feel that I want to clarify this one because we are going to do this again and again. The other issue which you are again with three this examples let me explain to you this is equal to a y. So, now symbolically let me write it because the meaning of this is understood now I can write this with when I write this one I have something else in my mind right the thing is that there is an integration for a change of variable formula. So, symbolically we are going to do this again and again, but and then you the next step most of the time we write log y or log natural you can use it log y is equal to a t plus c naught and then that you will write eventually y of t is equal to some arbitrary constant into e power a t. Fortunately you get the correct solution correct solution no problem correct solution, but this is not entirely correct while you are writing it though you have a solution here when you integrate here when you integrate this one what you get is really log mod y is equal to a t plus c naught this is what you will get it and then from there you will get modulus of y t is equal to c e power a t naught that is what you will get it. So, how do I arrive mod y is you may not be able to differentiate. So, how do you get how do I how do I get my correct solution from here. So, that is a how do I get my correct solution. So, here is something which I want to tell you may be able to follow that write this write this may be I use a different color write this as modulus of y t into e power minus a t these are simple things, but the moment you understand the simple things and the difficulty the difficult things are the combination of simple and easy things it is nothing like difficulty per se all your simple and easy things if you put it together things looks very difficult and you want to change it. So, it is a your job any student's job or any teacher's job is to understand things the easiest way possible. So, here you have a constant here is again one need to use one of the important thing what are called the continuity of the function. So, this function being differentiable is a continuous function and another thing since this is a modulus this formula is valid c is greater than c equal to 0.  So, it is greater than or equal to 0. So, you will immediately see that this is not for any constant for negative thing, but this is a continuous function. Here is a first small exercise for you exercise which you should do it. So, whenever we are giving this course we will be leaving small lot of gaps in the proofs we will be leaving small small exercises for you and that you have to work out before going for the next lecture. So, study the entire course by lecture by lecture solve the problems solve more problems get into the books try to understand more examples we may present only one or two example, but you try to get more and more examples and then you present it. The example let f from r to r continuous and modulus of f is a constant is a constant this is a very simple example the moment you learn continuity you will be learning, but if you know it you follow that f is a constant then f itself is a constant that is the thing if the modulus if you have a continuous function whose modulus is constant then the function this is not true if f is not continuous this is not true if f is not continuous find the example not continuous find examples trivial examples are available, but we can find that one with this observation this is a continuous function this is a continuous function you see and whose modulus is constant hence this continuous function y t into e power minus a t itself is a constant. So, you will have so that implies the example the exercise implies y t e power minus a t equal to c is a constant what is the difference from earlier this constant can be negative where c can be negative as well can be negative as well. So, that is why I call it very arbitrary arbitrary. So, these two important small observations which you have to one has to be very clear and you have the correct solution which you we see this kind of small facts in your study not only in ordinary differential equation with other equations as well. And for now we are going to give few examples in the as I said in the next few lectures two to three lectures and we will start with some physical models. So, we are starting with the physical models. So, today now to complete this I mean just to one example one you have the population model this is what we are going to do it and our it is easy for you to solve those who are studied any differential equation we will able to solve it immediately, but the purpose is not that we want to see how we use the analysis to derive more about the knowledge of the trajectory population model. So, there are two things one is the linear model. So, we will start with the linear model and then we will see that linear model is not always correct not always be the good model then we will go to the one of the famous non-linear model given one by the biologist will come to that. So, we will go to that one. So, we will have the linear model. So, suppose my y t represents the population represents the population at time t. So, let me population at time t. So, how do you suppose is a population is growing just based on the population no influence from anywhere else you have enough space no computation no natural disasters nothing it depends only on the population of the number of people available. So, it is a natural way to think that suppose you have two cities or two systems in which one system you have n number of population n is the population other one is the 2 n is the population then after an year if there is a growth if it is a normal procedure the extra population in the first system and if you compare the extra population in the second system the second system will have the double the extra population than the first population you see. So, the simplest and easiest model is that your rate of change will depending on the population how much it will grow is what is called the population rate. So, there will be a be the rate then a simpler model will be d y by d t the rate of change of population with this phenomena with there is no other things will be proportional to y itself that is easiest model and that gives you your linear model linear model d y by d t is equal to d y by d t. So, this is equal to some r into y and you have seen you already solved instead of r with a you already solved this equation. So, suppose so you will get the solution you see solution y t is equal to some constant into e power r t you see you have e power r t. So, if at t naught your initial time wherever you can put your initial time you know the population say suppose the population y t naught is equal to y naught then that will imply if you substitute at t naught you will get y naught. So, your population will be y at t will be y at t naught e power r into t minus t naught you can evaluate and do that these are the small steps, but I always suggest to the students that you better work out you may looks trivial but just substitute t naught and do that that is a way you have to learn the mathematics. So, you have your solution is easy way you have the solution completely. Now, can immediately see observation that is what I said you got the solution do not stop there, but always analyze the solution what happens and especially when you create a model of a physical phenomena based on observations data and all kinds of thing you have to see that your model is actually true whether you are actually you are able to predict your thing whether your model goes wrong at some point of time and it does not really give you the does not really represent your physical phenomena you have to that is what is after the analysis which I represent the schematic diagram last week you have to after doing the analysis you have to go back to the modeling once more and you may have to you may need more data it is what I explained you know. So, you see that an immediate observation here this you can prove mathematically of course, is easy as t tends to infinity as t tends to infinity your population y t increases to infinity. But this is not a desired not a desired state of affairs no worry in the universe you can have a population as time goes the population will goes to infinity what will happen is that when the population increases to infinity when the population becomes bigger and bigger there will be much more competition between the species we are analyzing here only about one species there will be if there are systems which we may explain at least one example later more than one species where even with just one species we are analyzing this problem. So, within the system the two species two persons or two bacteria can be a bacteria whatever it is there will be computation between four food space everything all kinds of computations here. So, we are looking into a model where there is only a competition between still we are not taking into account other aspects like natural disasters and things like that and that can also and also the population can come from other places to this one all kinds of things can happen we do not take. So, we are going to give you a non-linear model now as this model is not suitable when this model is not suitable when the population is not the population this model is reasonably ok when you are population is not too big and it is a known fact, but so we are going to give a non-linear model. So, going to introduce a non-linear model with just one fact that you are taking into account the competition between the species within them not the competition with the species with another species. So, the competition and this is given by one of the famous by Dutch mathematician mathematical biologist Dutch mathematical biologist it is a word list is called what is a spelling I think this is given probably in 18 something like 30s or something approximately. So, how do you take into account? So, let us say anything to understand anything to model you have to have an intuitive feeling about that suppose you have a population with n people what are the possible number of competitions a person can meet all other people. So, a person can meet that number of encounters this is called basically I am trying to give a statistical average what are the number of encounters a simple thing we will get it can the number of encounters is that the first person can meet n minus 1 person may be the next person can meet n minus 2 like that. So, the number of encounters will be if everyone meets everybody that would not when that is where you have to understand the population and then you have to put a factor this is something like equal to n minus 1 into n by 2 that is in the order of n square. So, the number this is a property. So, if n is the number of people in a population the number of all encounters between each person meets one is order of n square. So, it is the message is that it is of order square, but not that everybody will meet. So, you have to understand when you are modeling it you have to understand on what fraction and this you have to understand from a particular thing and what wordless given is a model then d y by d t you have already you have the factor r let me use it a now that r is the same as a here a y, but then due to this encounter you are saying that 2 patients meets encounter they get killed may be 2 bacterias meet they attack because both of them will be trying for the same space or same food. So, they one of them they do the fighting and one of them will survive. So, it will reduce the population it will be in the order of y square, but not that everyone will meet. So, there will be a factor. So, as I said for a particular problem whether it is a bacteria growth human population growth study how to choose n b depends on the particular population which we are not going to give it here it has to do a statistical analysis you have to collect the data how over a long period of time and you have to evaluate n b for a particular population even for a particular population it may work for a certain period of time. So, you have to do an update may be will make a remark again later of that one. So, you have a non-linear model you see this is a non-linear model given by d y by d t is equal to a of y minus b of y square. And suppose you are at initial time y naught is equal to y naught. So, you have a very nice initial value problem you see. So, two steps we want to do it here. So, as I said we are not going to give you all the details about the problem I would request the student to go through it and fill up the gaps whichever is missing there. So, first you want to solve it if possible always that is the thing solve it if possible that is the first thing then do the interpretation just solving is not enough after that I want to understand just like in the previous example which you have seen which like previous example your population is growing I want to understand a mathematical study of that equation after getting the solution. The solution may not reveal this one and analyze it and this is what you are quickly going to do that one.  This all of you know it you can use my change of variable concept or now you are know that what does that mean you can do the same thing you can write down your one of a of y minus b of y square d y this is form n, but I can still write formally if you do not like now after seeing that writing this is you have to be you have to see this with pinch of salt whenever I say that there is an integration formula you can divide with a d y by d t equal to 1 and do the same procedure to do that one. So, you will after that you integrate you integrate and put a constant no problem this is fine how to integrate is all right now how do you integrate this one in the of course, you would have studied how to integrate this one this integration is done by a partial fractions partial fractions you can write down. So, you you do go into this you have to do it b y square you can write it as probably you can write it as I do not do the computation, but I you should do the computation when you study this course 1 over y with a minus b of y do the computation is an exercise whatever I am leaving a part of the exercise which you should do it instead of writing the exercise at the end of it will write the exercises here. So, do the computation do that one once you do this one. So, these are in the 1 by y 1 by a minus b 5 form now you write it everything 1 minute we will continue do the computation. So, this is not minus and this is plus do this one. So, this is in the log form this is in the log form make sure that everything is writing in the modulus form do not make the mistakes like writing 1 by log y 1 by log of a minus b y what you have to do is that.  How do you get an implicit representation of the solution 1 over a log mod y by mod y naught y naught is positive because that is given to you y naught is a positive quantity which is given to you or can be 0 also now, but here it is greater than 0 into modulus of a minus b y naught by a minus b y to get that one is equal to t minus t naught. So, you have a solution representation you see quite often you stop at this stage I want do not want you to do that this is for t greater than t naught this does not say anything about you do not understand how your y behaves though you may complete that I have a solution to your problem I have an implicit relation connecting between y and t, but you have to do much more in this analysis and that is what we are going to do a bit more thing we have to see few things about it quickly you will learn these facts later d y b I am telling you few facts, but you write it properly to complete it d y by d t is equal to a y minus b y square look at this expression now when y equal to 0 when y equal to 0 r h s r h s is equal to 0 that mean this such points are called equilibrium points equilibrium points and whenever you have y equal to 0 and if you so if you have solution y at t naught starts at 0 then d y by d t will be 0 and it remains to be 0. So, you get y equal to 0 as an identical solution it does not move. So, it is an equilibrium points or the solution starts at the origin at 0 at t naught if the solution starts from 0 the solution will remain to be 0 all the time. The interesting thing is that there is another equilibrium point there is another equilibrium points equilibrium points what is that equilibrium point this can be a y minus b y square can be written as y into a minus b y. So, when b equal to y equal to a by b one more point here normally b is very small compared to a that is again a thing a fact is equal to tell. Then again this is 0. So, again you have a second equilibrium point when y equal to a by b. So, if you have if you try to draw this thing here. So, if your population. So, the a by b will play going to play an important role here. So, if you have your population if you have population starts at t naught this is the t naught and if this is your y equal to 0 graph that is nothing but y equal to 0 graph. So, if your y t naught is equal to 0 your y t will remain to be 0 all the time is the same thing when you have a curve this is the curve y t equal to a by b y equal to a by b curve. So, this is also an equilibrium point. So, at t naught if your solution is there the solution will remain to be there and then it is an interesting fact that two trajectories all that you will be learning here in a two trajectories the two trajectories will not meet. So, whenever your initial population is somewhere between 0 and a by b the entire trajectory will be somewhere here we do not know we are going to understand more of this graph. Similarly, if your trajectory is somewhere here the trajectory will be here. So, what it shows that what I am trying to say that if your trajectory why not starting between the population 0 and a by b 0 why not less than a by b the exercise is that you have to explain these things whatever I have explain do it and write it properly and this trajectory. So, if you have a proper thing that trajectory will not come here this you will be learning you cannot cross that trajectory because the moment you come here it will remain there you cannot come there you cannot cross this trajectory. Similarly, cannot even go here such trajectories will not exist you take here the trajectories will not cross here if you start from initial point here. So, that immediately shows even though intuitively it is correct. So, the eventually what I am trying to convey to you is that your trajectory the solution y t will always remain to be positive between. So, you see even the intuitively clear yes the population goes, but if you have a non trivial population to start with the such why not you start your population will always be positive that is the fact you are using it. So, from your solution so, what I want you to prove eventually is that use these facts whatever I have explained use the fact explained use these facts to show that y t you already seen y t is always positive one thing the second part is more important a minus b y not by a minus b y is also positive this is a important thing you want you to prove this is what I explained from the earlier graph this graph what I say that if this is one fact there is more information because this is y t equal to a by b is also a equilibrium point if y not is between a by b y t will not only positive y t will be remaining in a by b here. Similarly, y t is greater than a by b y not is greater than a by b y t will also remain greater than a by b hence the solution which you see it the solution you see here the solution which we get it this will and this will retain the sign and hence the whole thing will have the same positive sign it will retain the sign because it will and this is what you have to prove it to prove this one. So, prove this this is an exercise for you once this is positive the entire modulus can be removed from the solution if you look at here the entire this is positive this is positive the entire modulus can be removed and you can write your solution. So, that is where next exercise thing for you the exercise. So, it is a one by one exercise write the solution now in explicit form earlier you got it an implicit form write the solution write the solution as y of t equal to a y not by b y not plus a minus b minus b minus b minus b minus b minus b minus b minus b minus b y not into e power minus a into t minus t not prove this write down this thing for t greater than t not you see. So, you have an explicit representation and still this is not enough for us we want to understand it a little more about it and probably we will do that in the next lecture we will little more time another five minutes I will spend on this equation in the next lecture. And one thing you can immediately see is that y t as t tends to infinity this fact goes to 0 once this goes to 0 a y not and y not will get cancel y not and y not this will go to 0 and y not and y not will cancel and you see that limiting behavior. So, that limit goes to y t goes to a by b you see that is what is wherever you even if it is a very small population the population will go to infinity. We will see these facts in the next lecture and we will do further examples. Thank you.


In this video I want to talk about the graphs of secant and cosecant. In previous videos we talked extensively about the graphs of sine and cosine as well as tangent and cotangent. It turns out because secant and cosecant are the reciprocals of cosine and sine, our knowledge of graphing sine and cosine will help us graph secant and cosecant. So I would say that graphing secant and cosecant is a lot easier than graphing tangent and cotangent because we are more familiar with graphing sine and cosine. So I'll explain that in just a second. So you see the graph of secant presently on the screen illustrated here in yellow. Now cosecant for the most part its graph looks like these buckets. Every once in a while you have a bucket that goes up, every once in a while you have a bucket that goes down. The proper word we'd say is that this portion of the graph is concave upward and this portion of the graph is concave downward. Cosine is a two pi periodic function and secant, which is of course the reciprocal of cosine, it'll inherit that same period. So the period for secant is going to always be two pi as well. And so that will be important for the standard graph. It'll also be important as we repeat the graph. Now you'll notice that when you look at a bucket this bucket goes from negative pi to negative pi halves to pi halves right there. And then the next bucket goes from pi halves to three pi halves. So it's tempting to be like well wouldn't the period be pi because the bucket repeats itself every pi. That's not true. You have an up bucket and a down bucket, right? And so you don't get back an up bucket until you've done a two pi interval. So two pi is in fact the correct period for this function. Another thing to point out is like tangent and cotangent, the graph of secant is, it has vertical asymptotes. That is, there are places in the domain of secant that you're undefined. And the location of the vertical asymptotes of secant are identical to the location of the vertical asymptotes for tangent. And that's because tangent with sine over cosine, secant is one over cosine. Both of these functions have cosine as their denominator. That's actually why their BFFs right here best spends forever because they're the same common denominator. One consequence of that is that secant and tangent have the exact same vertical asymptotes. So secant will be undefined whenever cosine is equal to zero, which happens at pi halves, three pi halves, five pi halves, negative pi halves, negative three pi halves. So any odd multiple of pi halves, that will be the vertical asymptotes of secant because that's when cosine is equal to zero. All right? When it comes to graphing trigonometric functions, I've always mentioned there's like five special points you want to use. You can always use more than that. The more refined you make your graph, the better. But when it comes to cosine, the standard point you would use is you'd use x equals zero, x equals pi halves, x equals pi, x equals three pi halves, and x equals two pi, which would be over here. I've moved things a little bit. So instead of using the last point of pi, I'm actually going to use negative pi halves. And that way it gives us two complete buckets of the graph. But you could also go from zero to two pi like we did before. That's fine. Now you'll notice on the screen, this green curve is actually cosine right here. And I wanted to include this to show you the relationship between secant and cosine given that the reciprocals of each other. So we're pretty good hopefully by now of graphing cosine and sine waves. You can see the standard cosine wave right here. Because secant is the reciprocal of cosine, their graphs are in some essence opposites of each other. When cosine is small, secant will be big. And if cosine ever got big, secant would then get small. Now, cosine's bounded between one and negative one, which actually means secant avoids one and negative one. It turns out that the absolute value of secant is always greater than or equal to one. An up bucket means you're going to be greater than or equal to one. A down bucket means you're less than or equal to negative one. But the absolute value is always greater than or equal to one because you're avoiding the range of cosine right there. Okay. And so if you draw your standard cosine curve, then it turns out that the secant function will actually wrap away from where you see cosine. So in particular, cosine has x intercepts at negative pi halves, at pi halves, and at three pi halves amongst other points, of course. These are locations of vertical asymptotes because cosine is zero at these points. Secant should be one over zero, which essentially is an explosion. It goes off towards infinity and negative infinity. That's the idea of a vertical asymptote. You're trying to divide by zero and it causes this rip in the space-time continuum or just the function, I guess. Maybe it's not as traumatic there. But then also when you look at the graph here, when you see that this portion of the cosine function where it's concave downward, right, it has this maximum value, this is the point where secant and cosine are going to kiss each other, where you're going to have this point of intersection where you have this point zero common one is common to both secant and cosine. You'll have another kissing point right here at this point right here where you're going to have pi common negative one. So where cosine is negative one, secant will also be negative one. They're going to touch each other, just going to kiss each other. But other than these kissing points, the functions wrap away from each other. So while cosine over here between negative pi halves and pi halves is concave down and curves downward, secant is going to curve upward, forming this up bucket that we talked about before. And likewise, as when you're on the down bucket here, when cosine is concave upward, it curves upward, secant will have this down bucket going on like this. And so using the graph of cosine, you can actually graph secant as well. You're just going to graph it so it wraps away from the cosine function. We can see this if we move over to Desmos, of course. You now currently see on the screen the graph of secant like we saw before. Let me add the asymptotes. These are going to be the places where secant is undefined. You see this up bucket shape that we saw earlier and this down bucket shape as well. So it repeats itself up, down, up, down in this alternating fashion. If I put the graph of cosine on the screen, you see the behavior we talked about before, they kiss whenever cosine has a maximum or a minimum. So it kisses at 0, 1, at pi negative 1, at 2 pi 1, and negative pi negative 1, at negative 2 pi comma 1, you get it. Whenever there is an x intercept of cosine, that's where you're going to have a vertical asymptote for secant. And so the behavior is exactly reciprocal of each other. Like so, whenever cosine is bending downward, secant will bend upward. Whenever cosine is bending upward, secant will bend downward. And so with that knowledge, we can very easily graph a secant function by graphing the cosine function that corresponds to it, and then we just reciprocate. We can have a similar discussion about cosecant because the thing about cosecant is that cosecant of x is the reciprocal of sine. And so because of this, there's this reciprocity relationship between cosecant and sine. If we could graph sine, then cosecant will look the same as secant in so much that we're going to wrap away from sine. So some things to note, sine is undefined at 0, at pi, at 2 pi, at negative pi, at negative 2 pi, and at any multiple of pi, sine is 0. This is going to exactly be the vertical asymptotes of cosecant, which are also the vertical asymptotes of cotangent. Cotangent and cosecant are BFFs because they have the same denominator of sine. So we get vertical asymptotes whenever sine goes to 0. Whenever sine has a maximum, cosecant is going to kiss it at that location. So we have this point right here where the sine's at its maximum. This is going to be pi halves comma 1. You're also going to have kissing occurring whenever sine has a minimum, like for example, at 3 pi halves comma negative 1. So whenever sine has its max or min, you're going to have a kissing relationship between cosecant and sine. Also, when you see curvature with sine, cosecant will have the opposite curvature. So for sine here, we see that it's concave down, it's bending down, the bowl goes down. Therefore, cosecant will have an upward bucket when sine is wrapping down. On the other hand, when sine is curving upward, you have this concave upward shape that you'll get a down bucket for cosecant right here. Some other things to note about cosecant, it's its period is going to equal to 2 pi just like sine. It doesn't have any x-intercepts. In fact, if you look at the range of cosecant, the cosecant gets all real numbers, other than the interval from negative 1 to 1. So in particular, the absolute value of cosecant is greater than equal to 1. Up buckets are going to be greater than equal to 1, and the down bucket is going to be less than or equal to 1. So with these graphs down in mind, we could start graphing modified secants and cosecants. Let's look at a secant graph right here. You have y equals 1 third secant of 2x. We can start graphing this by transformations. There's a vertical compression of 3 and a horizontal compression of 2 when we graph that. But instead, when it comes to graphing secant and cosecant, my suggestion is actually we're going to graph first the function y equals 1 third cosine of 2x. We're more comfortable graphing sine and cosine, so let's do that. If we graph cosine, we're going to have an amplitude of 1 third, and we're going to have a period of 2 pi over 2. That is a period of pi. And so using that, we can then graph our five points that we would normally want to do. So we can go from 0 to pi if we wanted to. I'm going to take one step to the left and actually start at negative pi force. So negative pi fourth is right here. Zero, we're going to take pi fourth, pi halves, three pi halves, excuse me, three pi fourths like so. And so when it comes to graphing a trigonometric function, apparently every picture looks the same. It just comes up to labeling. If you relabel the graph, or I should say if you leave the grid lines blank, all the pictures look the same. So really the hardest part about graphing a trigonometric function is making sure you have the right intervals, all right? Since the amplitude is going to be one third, I'm actually going to put this right here as one third. So this is two thirds, and then this is going to be one. And then it's going to be negative one third, negative two thirds, and one and below as well. So we're going to put the start and ending of a single period here. So we're going to go from negative pi fourths to three pi fourths. That is a length of pi. Like I said before, we could have gone from zero to two pi. That would be acceptable. But because of the bucket shape of secant, it's going to be a little bit better if we start at negative pi halves, negative pi fourths, excuse me, because if we were to draw the cosine function, we're going to get something like the following, right? So that's one complete cycle of cosine. It kind of looks like a sign because we started to the left, and that's okay. So the thing to note now is that when it comes to our secant function, we have vertical asymptotes occurring at the x intercepts of cosine. So we're going to have a vertical asymptote at negative pi fourths. So this is why we graph cosine first, because from the cosine function, we can very easily construct our secant function. So we have a vertical asymptote at negative pi fourths at pi fourths and at three pi fourths, like so. And so now we're going to draw our function so it wraps away from the cosine.  So this should be maximum at zero and a minimum at pi halves. Otherwise, we're going to wrap away going towards the vertical asymptotes, like so. There's our up bucket. And then we got our down bucket as well, right here. And so then we can graph our function y equals one third secant of 2x. And so that's going to be my strategy for you. If you have to graph secant or cosecant, first graph sine or cosine as a helper function and then reciprocate in order to get the graph of secant or cosecant. And so that's going to end lecture 12 here about the graphs of tangent, cotangent, and cosecant, and cosecant. It also really ends our discussion of graphing trigonometric functions. We do have one more unit in chapter four about graphing trigonometric functions. That's going to be applications in particular. We're going to talk about simple harmonic motion. Check the link you can see on the screen right now to watch that video. It's going to be a good one. Thanks for watching, everyone. If you want to see more videos like this, of course, subscribe. And always, if you have questions, post them in the comments below, and I'll be happy to answer them. Bye, everyone.


As a Japanese-American, I am the descendant of a people that crossed oceans as exploited plantation laborers only to be abused and lynched by white peers, only to be subject to mass incarceration during the Second World War. People of every cultural background need to affirm now more than ever that black lives matter.


Hi everyone and welcome back to another vlog so today's vlog is all about applying for your very first job as a newly qualified nurse. Well any job really is a nurse so yeah hopefully you're going to find it useful and I can give you some tips and advice to help you on your way and hopefully you're going to smash it. In this vlog I'm also going to talk mainly about GP interviews because that is where my main love is but I am going to give some overall advice for standard interviews hopefully that's going to help you out as well if you're not applying to GP. I also just need to add that I have already done a community nursing interview vlog which I will post the link below so have a look at that if you want more district nursing specifically go and check that one out. My first tip on interviews to this one is probably the biggest tip I think is how to ease those nerves because I'm the sort of person probably like you where I get really nervous my mind goes blank they'll ask me questions that I know the answer to every day in everyday life but at the interview under the pressure your mind goes blank you're like I have no idea what colour the grass is outside it's one of those and it's terrible why do we do it to ourselves but this tip is exactly for you and hopefully it's going to help you calm those nerves a bit. So go in and look around contact the place or area that you're applying to ask can you go in meet the team see what they do have a look around at the clinic rooms things like that this is what I did that I was very very fortunate that the practice said to me you're new to the area do you want to come in and have a look around meet the team and if you are still interested you like the look of the place come and apply and it was amazing I'm so glad I did this because it honestly put my nerves ease I spent an hour in that place that day and it wasn't even the interview it was just looking around chatting to all the staff it was lovely and it honestly on the day of my interview I was so relaxed I was still a bit nervous because I really wanted it but it really it just yeah it really benefited me and hopefully that's going to help you out. However there are obviously other techniques that you can use breathing techniques a bit of meditation calm yourself down listening to music on the way little things like that that you can do whatever you know and works best for you use that. My second point is as well dressed to impress everyone sort of seeing comments about asking what shall I wear to an interview first impressions is everything to me I went in a full-blown suit let me show you so my full-blown suit was this jacket not the blue shirt underneath ignore that but this was my suit jacket beautiful colour green is fashionable at the minute apparently and these were my suit trousers and I wore a white shirt underneath and it just it looks professional and I wanted them to look at me and think wow we could employ this girl and that's the way you should think as well so yeah OTT is the way I see it so let's move on to the specific questions of interviews because that's what you really really want to know you want to know the questions answers all of that jazz so I'm gonna move along into that and have to apologise I've got little dog in the background who might jump on on the bed jump off the bed so I'm really sorry if that's a distraction throughout this video but it is what it is he's cute so the first question that they always ask I've been asked this in every single interview I've ever had whether it's very HCA role might both my nursing roles even when I worked in like sales and hospitality it's something that everyone has always asked so you're guaranteed you're more than likely 99% gonna be asked this question why do you want this job why do you want to work in this particular area so mine was GP why do you want to be a GP nurse you have to share your passion if it's just a job to you and you're just applying for the sake of applying because you really need the money think of something to say don't say that just say come from the heart think about all the positives of the role think about the area you're gonna be working in what do you love about that area what has made that stand out compared to all of the other nursing jobs that you could apply for because there's thousands on NHS jobs why is that one in particular stood out to you and why do you can you see yourself working in that area just answer it honestly and openly but please don't say I just need the money because I don't think I'll go down too well the next question that you usually get asked but not always is your experience and quality so what can you bring to the team what qualities do you have this is where you have to sell yourself and I know people really struggle I really struggle with selling myself but the way I see it is it's me or somebody else so if you're not selling yourself enough that can literally just be a tiny little point that they pick upon to not give you the job I failed a couple of times previously at interviews purely on selling myself and I rang up and I got the feedback because I was getting to the point where I was like why am I getting this job so I rang up feedback on two occasions both times they said you need to sell yourself more and you need more confidence so it just goes to show that is a big thing because if everyone's got the same experience if everyone's got same qualifications which we all have all nurses you really really need to sell yourself make you stand out from everybody else another question you might get asked on is the person spec on the job so I would massive tip look around the person spec and the job requirement slash description for the particular area that you're working at whether it's GP or another area make sure you know those look through the essential criteria because they might say to you okay what experience do you have in this you've said that you meet the criteria talk to me about it so just do that go through the list and think on your head okay what am I gonna say to answer these questions if they ask me about it and my experiences but you already know that anyway because you obviously meet the criteria you wouldn't have an interview so that's just gonna come naturally off the top of your head they usually ask things like team working like what makes a good team how would you be a good team player those sort of questions as well and just think about good teams that you've worked in so if you've had a placement somewhere or if you've worked in an area as a HCA or a qualified nurse if you're qualified nurse already think about the sort of do the good teams that you've worked in what was good about that team what what worked what didn't work and just to say that in the interview just go through the lists of and show examples as well another tip sorry always if you're gonna give an answer always give examples they love if you give loads of examples of how you do it it just shows that you're understanding the question and you'll understand what's expected of you in the role as well if that makes sense so always give examples you're also more than likely not everywhere does this but nine times out of ten I think most places always ask a scenario based question so they want to see what your responses in this sort of question so they might give you the angry patient scenario what you're gonna do with an angry patient if they come into your room you're the only one there how you're gonna handle that situation are you a calm person are you patient can you sort of distract the patient and sort of settle them they just want to see your reaction and how you handle the stress basically and that's all about your communication skills it's all about you know listening to the patient not overpowering the patient telling them that you understand their concerns and all of that and just making them comfortable and yeah and seeking help and advice if you need it so if a patient's getting really aggressive to the point where they're punching you or something you want to call security and so yeah it's about being safe but sensible at the same time so if you are applying for GP it's a lot of lone working questions as well so how are you at being autonomous you need to show that you're autonomous because if you want to work in primary care community district nursing GP that sort of area you need to be confident in your own skills you need to be confident as a nurse obviously you'll have the support and you'll have the training and all of that but it is a lone working type of role you're not gonna have a ward to fall back on all these people and to be honest I love that this is why GP's perfect for me I love being on my own and being in control of my own clinic my own patients I love it I thrive in that sort of environment so you need to show that you need to show that you can do that give an example again of when you've been autonomous and when you've handled that sort of situation how you work in that situation do you cope well under the pressure all those sort of little things is exactly what they're looking for a few other things that I've heard I don't know I wasn't asked these sort of questions but I have seen on other Facebook pages and things like that is people have been asked about safeguarding and mental health when in GP in particular because that's quite big as well about recognising those signs and symptoms and who you would refer to your appropriate services so if you are applying to GP look around the area at what's about like have they got mind have they got healthy minds have they got mental health teams community mental health teams what are the local safeguarding is the multi-agency safeguarding involved have a look at all those sort of things just to be prepared just in case they do ask you that question always better to be over prepared for an interview I think and lastly just be yourself just if you can't be yourself who can you be so be yourself try and relax show that passion in the area that you want to work in and they will absolutely love you I'm sure on one last note sorry guys take your folder take a portfolio if you've got a portfolio this is mine with all of my certificates all of my achievements in at the back I've got some previous mental feedback slips that I've put in there that they can get out and they can read if they want and just ID and things like that in the back just in case they need to photocopy that sort of thing but take a portfolio with you take if you're a student nurse newly qualified nurse take all of your mentors feedback any patient feedback anything you've got that's going to make you shine take and just yeah sell yourself like I said so just one last little summary of applying for any sort of nurse job out there just one look up the area you're working at know it inside out know what they do services they preside ride everything because they might ask you that to if you are applying to GP make sure you know the local prevalence of the area what sort conditions are out there age ranges things like that have a look on the government and council websites the GP practice website itself might give you that information and the values and visions look them up as well the job description and the person spec you want to know inside out just in case they ask you anything and they ask you to give you examples make sure you know those because they're more than likely going to ask you the essential stuff in the interview and the rest we'll just follow the rest of just come naturally the scenario questions teamwork and you know it guys you do it out there already you've done it on placements you've done it as a nurse whatever you know we just relax calm your mind and just answer as you would and lastly give examples I've said it already give examples make sure you example everything so you show you understand what they're saying so thank you as always for tuning in don't forget to subscribe you haven't subscribed yet and I just wanted to say if I haven't covered anything if there's something extra that you'd like to know give me an inbox and I'm more than happy to answer any questions that you've got for me so thank you so so much and I shall see you next time


dedicated to the strength of the nation. Proudly, we hail, hail, starring Bill Williams in Time Out, United States Army, United States Air Force Presentation. And our here is our producer, the well-known Hollywood showman, C.P. McGregor. Thank you, thank you, and greetings from Hollywood, ladies and gentlemen. Welcome to your Theater of Stars, where foremost names of the motion picture world join us for your entertainment and plays we know that you'll enjoy. Our star is Bill Williams, the title of our play, Time Out. This is a gripping story of the price-fight game about a fighter with a heart of a champion. Our story takes us all to ringside at the battle for the crown. We'll have the curtain for act one of Time Out immediately after this important message from Wendell Niles. Young men and women, the U.S. Air Force offers you the finest aviation training in the world and you earn while you learn. Under a new Air Force program, every effort is made to place you in the job for which you are best suited and have the best chance for success. You can become an aviation specialist with steady increase in pay, with job security and a carefully planned program for promotions. For details, visit your U.S. Army and U.S. Air Force Recruiting Station right away. And all once again, our producer. It's curtain time and here's act one of Time Out starring Bill Williams as Bob Howard. This is about a fighter, a young, up-and-coming boxer. It was the night of his most important bout. He was resting on the rubbing table in his locker room. His manager had stepped out to talk to the newspaper man, leaving him alone with his girl.  Yes, it's a, it's a soothing sound. It loves me. Of course, having soon nearby helps too. And on this, the biggest hour of my career. Waiting for the championship fight with battling Pabian. All my long years of training and rigorous living were to be finally called into action for the greatest prize in fighting, the championship crown. I'm ready for this one, believe me. Sue, isn't that the buzzer for me? No, Bob. I'll let you know when we're ready. Okay, okay. Are you all right? Oh, you bet. You sure? Every time the same thing.  I do not flutter. But you sure worry. Well, I just can't help it, I guess. All those fans around the ring, thousands more listening in on the radios, television, newsreels. Oh, you make it sound real exciting. Keep talking. Everybody doesn't have ice water running through their veins. How can you keep so cool? Hidden in my gloves. Two little men with fans. Even at a time like this, you can keep it. Oh, come on. Sue, relax. All right, I'll relax, if you will. If I were any more relaxed, I'd fall apart. Hey, what time is it getting to be anyway? There's lots of time, dear. Just take it easy. Take it easy. My thoughts went to other hours like this. Back to my first fight in Gary, Indiana. Then farther back. All the way back to my father. I remember the day Dad bought me the greatest gift of all.  Gee, what is it, Dad? Well, open it and see. I'll bet it's a punching bag. Yes, again. Open it, will you? All right. What is it? I wonder what it is. Holy smokes. Gosh, Dad. Boxing gloves.  Thanks, Dad. Thanks a million. Never mind that. Feel that leather. You wanted to be a box roughly bad, didn't you, Dad? Yeah, I would have made it, too, if it hadn't been... I'll put you sure to get around for a fella who's got a... game leg. I do all right, kid. I didn't mean that, Dad. I know, Bob. Here, try these mitts on for size. Let me help you here. Oh, okay, boy. Boy, do they feel good. Wait a minute. Wait a minute, son. Let me lace them. These laces can mean a lot of trouble. There you are. Gee, they sure fit me swell. I got them exactly your size, the champ size. Let me slip on the other pair of my own dukes here. Okay. Okay, fella, what up, you dukes? Now, look how I'm gonna throw on your way. Well, let it go. Careful now.  Strike one. Okay, now, you try to tag me. Well, I don't wanna, Dad. Don't be scared. Nobody was ever able to lay a glove on me. Come on, swing. But I don't think I... Come on. Well, all right, here it is. Dad. Dad, did I hurt you? No, no. You sure? This is all part of my battle plan.  Good old Dad. He never lost sight of the goal he had set for me. I was to be the champion of the world. He even went so far as to get a trainer for me while I was still in high school. Franey was just like Dad, all wrapped up in the fight game. Hi, kid. Oh, hi, Franey. Where's your pop? Oh, he had to go to town. Well, that won't hold us up none from our practice, will it? Oh, I'm sure of that. I know all this rope skipping and exercising gets kinda tiresome, but there's no shortcut. But why can't we just put the gloves on and box? I'm getting to be an old man already. Oh, yeah. Seventeen is getting along, but I don't see no gray hairs in your head yet. Well, I never argue with you over training. I don't chase after girls or anything like that. Oh, see, by the way, I've got a favor to ask you. A favor? Yeah. See, kid, I figure you're getting to the point where you ought to have a nice girlfriend. But just any old girl won't do, see? Franey, I don't... You better have a girl who's interested in the same things you are. You know, boxing and stuff like that. Not out, tell me. You see, her dad used to be a pretty good scrapper himself. So the minute I seen this girl, I knew she was meant for you. Franey, you're just wasting time. But I thought... No, it's no soap. But you... No! And okay, okay. Can't shoot a guy for trying. She's outside. I'll tell her to go on home. Sue, would you mind running on home now? I thought I needed you to help out on some things here, but there's no hurry. All right, Franey. Any time you need me, just call. Yeah. Oh, Sue, this is Bob Howard. Oh, hello. Hello. Well, I'll be running along now, Franey. It's been nice meeting you, Bob. Oh, wait a minute. Oh, Franey, I've been thinking it over. And you know what? I think you're absolutely right about what you said before. Absolutely. Sue, sweet Sue. I remember how clever I thought I was when I first called her there. It was at a school party, and I had walked in late. Thank you, Doris. Hi, Sue. Bob, I didn't know you were coming here tonight. I didn't know it either. But aren't you supposed to fight at the Civic Center tomorrow night? That's right. That's why I came over. You know to the victor belong the spoils. You're the spoils of your pardon expression. I'm very flattered, of course. But how can you be the victor when you haven't fought them at you? Oh, I'm psychic. Already I can see the ref holding my hand up and talking of sweet victory. I lose more boyfriends that way. Not this time. Uh, step this way, please. Wait a minute. Where are we going? Out in the garden. May I ask why? I want to count the stars. Come here a second. Bob, please. You said you were going to count stars. Oh, yes, sir. Well, now there's the big dipper. Seven stars. One, two, three, four, five, six, seven. Now there's the little dipper. And right above is the north star. Where? There. Look up. Is that? I love you, Sue. Sweet Sue. May I bust in a second? Franey, what the heck are you doing here? Counting stars. Now don't try to be funny. What's the big idea? You know the idea, kid. You've got a scrap in your hands tomorrow night. Look, Franey, you're just my second-in-trainer. See, you're not my mother.  I'm in top shape. I can beat that peluga tomorrow night with no sleep for a month. Okay, okay, Superman, let's go. Nothing doing. I'm not a baby. I'm a man. I've got a mind of my own. Good night, Bob. Be seeing you. What's this? That was that mind of your own. Come on. Let's go. Nice fight tonight, Bob. Thanks, Sue. Well, you've just about cleaned up this whole region now. Yeah. And that's what I've got to, uh... Well, leave. Leave? For where? Chicago. That's where the big timers are. And if I make good, then I... I might even get the fight battling Fabian. I think you ought to give this a lot of thought. You know how I feel about fighting? I love the game. And boxing is my road. You mean it's the road your father chose? Maybe so. But I've got to get to the top. You understand, don't you, Sue? I understand. You'll wait for me. Yes, Bob. I'll wait. I went to the windy city and started on the long road. I began to make the headlines, and I also began to make money. And Dad passed away. I guess it wasn't in the cards for him to be there. I began to notice that I wasn't having much trouble making my weight limit. I ate well, but for some reason I was losing poundage. I had an appointment with Dr. Tolson. The same afternoon, I was expecting Sue in town. Sue, sweet Sue. Oh, it's so wonderful seeing you again. Oh, Bob, are you all right? You look thinner. Oh, nothing to worry about. Been training a little too hard lately, that's all. You're overdoing that will to win, Bob. I'm going to be the next champion. I think you are too. Only if by any chance something prevents you from making it, we're not going to let it spoil things for us, are we? You know we won't. If I ever lose, I promise I'll quit. Only I got a hunch you're going to be the next Mrs. Champ. Say, where are your bags? There, at the checking counter. Well, look, I got a very important appointment that'll only take a few minutes. Would you mind waiting for me here in the coffee shop? Of course not. I hate to leave you like this, but it can't be helped. I'll be back in a jiffy. Hello, Dr. Tolson. Hello, Mr. Howard. Take a seat, please. Thanks. How do you feel? Just fine, Doc. Just fine. Mr. Howard, we've taken many tests, as you know. You certainly have. The tests have brought out one basic weakness in your makeup. Weakness? I don't like that word, Doctor. But that's what it is.  I know, Doctor. That's why I'm here. And they're not good when you're engaged in strenuous activity. You mean like fighting? That's it. Well, what am I supposed to do about it? You'd quit boxing if you want to live long. We cross briefly from our story time-out starring Bill Williams to bring you an important message from our government. Ladies and gentlemen, our Army and our Air Force are critically short of physicians and dentists. Over 2,000 volunteers from these two professions are urgently needed today to safeguard and care for the health of the men and women who as members of the United States Army and United States Air Force are serving you and me at home and overseas. Young physicians and dentists, particularly those who did not serve in the armed services during World War II, have been asked by their government to act now to volunteer for duty at once. If you are one of these young physicians or dentists, please write or wire either the Surgeon General of the United States Army or the Air Surgeon of the United States Air Force at once and volunteer your services. If you know of one of these young physicians or dentists, please call his attention to this urgent message. Thank you. The curtain rises on Act 2 of time-out starring Bill Williams as Bob Howard. Bob was nearing the ambition of his father, which was to see him crown boxing champion of the world. Bob's father had passed away before he could witness this achievement. Sue, his girl, was as interested in the fight game as he was, but even she didn't know of Bob's mysterious attacks, which caused him to black out temporarily. Bob didn't let this hold him back, however. That was a fine thing to tell a fighter, wasn't it? Quit fighting or you won't live long. But the attacks didn't repeat, so I went right on toward my goal. The big shot at the crown, worn by battling Fabian. My path took me from Chicago and I moved on to the big city of New York, where I was to meet a real obstacle in the form of red Metcalf. Sue was with me during all this time. She sat right behind my corner where I could turn around and look at that streamlined figure of hers. Oh, look, kid, you're going to watch that left of Metcalf. You've been walking into it all night. Okay, okay, so I'm feeling him out. You have to do it with your chin. Stay away. Stay away. That guy's got arms like an octopus. You better figure him out fast. This is the eighth round. It's going to be awful close if you don't tag him while he's ahead on... Get down, Sue. You're not supposed to be in this ring. Neither are you the way you're going. Bob, listen to me. I've been watching Metcalf. Weakness. Weakness for what? Blondes? No, no. Now, every time he throws that left of his in lamps, he lowers his right for a split second. Cross your left over when he does and you'll cool him off. Are you sure of that? Absolutely. I've been checking and rechecking him. It happened so fast you can hardly catch it. I'm going to think of it. You might have something there. I was trying to figure out what he was doing wrong. Except he was so busy beating your ears off, he didn't have time to notice nothing. Well, watch me this round, kiddies. We're going a straight and quite half. I'll... get this little package and tie it with a blue ribbon. Get going! Red Metcalf was beginning to feel his oats a bit. He knew he was ahead on points and so far I hadn't done much more than the muscles' hair. He came out cautiously and jabbed a left to my face. It didn't hurt, but it was the same left he'd been poking into my open confidence all evening. I tried to maneuver him into a nice, cozy corner, but in fact, the booing of the crowd got under red skin and he came out of his shell for a few seconds. He stepped forward and we exchanged hard rights to the body. Test the same. I wasn't winning the fight. I had to get red soon or it'll be too late. I remembered what Sue had said about him dropping his right when he connected with the left. I figured this was as good a time to test the theory. I shot at a right that was purposely short. Red's left flicked out and caught me squarely on the face. The punch hurt, but it was worth it. Now I knew Sue was right. Metcalf had lowered his right for a fraction of a second when his left foot landed. At the moment on, I knew what to do. I pretended to be a little dazed by the blow and stopped short. Red gained confidence. Again, I threw out a right that fell short. Once more, Metcalf's long left jabbed out and caught me in the face again, but now my left was whistling over toward the spot where his right glove should have been and wasn't. Now we're ready for the championship. Championship crown is sure going to look good on your head. I sure you and Sue a lot. I don't think I'd ever gotten this far without you two. Aw, kid, you'd have gotten there all right. I'll just take you a little longer, that's all. Okay, so now let's get to work, huh? I've got to celebrate tonight's win with Sue. She's waiting for me now. Don't get in an uproar here, boy. Lay back on this rubbing table, will you? Add up, boy, add up, boy. Now we put this hot oil on and we'll just rub it in here. Now, you feel better? Oh, that's swell. Massage that right shoulder muscle a little, will you, Franky? Okay. I sort of gave it a twist when I tagged Red with my left. There. Yeah. Hey, you got a little cut over your left cheek here. I better patch it up so you look real pretty for Sue, huh? Here, a little of this alcohol just infected. Go ahead. Okay. Here you are. Now just hold on. It'll burn. There, there. Hey, doesn't that sting? Hey, Bob, doesn't that hurt? Bob, what's the matter? Oh, kid. Kid, do you hear me?  Snap out of it. Huh? Hey, what's the matter with you? Nothing's the matter with me. What's wrong with you? It's the idea of slapping my face. You were out.  My gosh, can a guy even relax a minute without you getting all worked up about it? Say, you're pretty light on your toes, too. Oh, but it's easy to be light on the dance floor, Mr. Howard. One's partner is another Arthur Murray. What is this, a mutual flattery deal? It is a little rich, isn't it? Uh, just a moment, Bob. Where are you steering us now? Out to this balcony here. Thought we could count the stars. You can remove your arm now, as long as we're not dancing. Do you really want me to? No. But it seemed like the proper thing to say. I'll bet even after we're married you'll be worried about the proper thing to say. Never mind that. You brought me out to count stars. Now that's the big differ. And that, Bob, what's wrong with you? Oh. Oh, Bob, what is it here? Lean against the railing. There. What's wrong? Bob, can you hear me? Huh? Bob, you've just blacked out. Did I? Yes, you almost fell over. Bob, you better see a doctor right away. No, no, that's no good. But you have to do this something wrong. It's nothing to worry about, Sue. Take it easy. Nothing to worry about? You know better than that. I mean it, Sue. I've had these little attacks before. In fact, I've already gone to see a doctor. The best in the business. He said it was just a family trait. Nothing to it at all. A little temporary amnesia. It passes away like that. Oh, but when you're boxing, what then? It wouldn't matter. It wouldn't matter. Not much it wouldn't. I've never seen you coming in the ring, not knowing what was going on. I've never had one of these spells in the ring yet. They always seem to come when I'm nice and relaxed. Are you sure, Bob? Certainly. And another thing, they only come along once in a blue moon. Oh, I wish I could believe that. Look, Sue, I've never lied to you and I'm not going to start now. Everything I've said is true. All I can do is give you my word. Isn't that enough? I'm sorry. I do believe you, Bob. I don't? Okay. I see I'll have to prove it. Now you must look up in that sky and start counting stars. I'll show you whether I believe you or not.  Nothing was going to stop me now, no, sir. I had aimed at this championship too long and I had the memory of my dad's ambition to help me on my last lap. And now that I was all steamed up and ready to go, it was just like Franey to suddenly disappear. Hiya, Ken. How are things? Well, well. And just where have you been keeping yourself the last few days? I took me a little trip. I didn't have time to tell him.  The trip was a complete surprise. It's a surprise, all right. I'll be surprised if Sue ever talks to you again, leaving us right when we're close to a championship. Yeah, I'll be right back. Now where are you going? Over to Sue. I've got something awful important to talk to her about. Okay. But before you go, I want you to do something for me. Take this money and bet every cent on me against the champ. Here I am tonight at the climax of my career, waiting for the championship fight with battle and failure. All the long years of training are finally to be called into action for the greatest prize in fighting. I'm ready for this one. Sue, there's the buzzer for me. It must be. Seems awful late to me. I've been on the scrubbing table a long time. Let me see you watch. Hey, it's 10.30. I got to get in the ring. The fight's going to start. Bob, please. The fight isn't going to start. It isn't? Why not? Because the fight's over. You were knocked out. Huh? That's right. I... I was knocked out? Yes. Half an hour ago. I'm sorry, Bob. Come here soon. Oh, Bob, dear. Sweet Sue. Well, I promised I'd quit if I lost. But now I don't even know if we can even afford to get married for a while. You see, I bet every cent I had on myself. Don't you worry. You'll always make good. Come on in, Fanny, and help celebrate my ring retirement. Oh, you're smart to do it, kid. And look here. Here's a nice king-sized nest egg to start hatching. Wait a minute. What's this money for? It's the winning from the dough. You gave me the bet. But I told you to bet it all on me. I know, kid. I know. There's something else I know, too. I know all about your visit to Dr. Tolson. I went back to Chicago to check up on you after you passed out on the rubbing table that time. Well, how do you like that? I knew I couldn't talk you out of this championship fight. So now, may I leave you with your money and wish you both a happy good night? Wait a second. What now? You're not through seconding me yet, brother. Tomorrow you're going to be in my corner as our best man. The curtain falls in the final act of time out. Our star, Bill Williams, will return for a curtain call after this timely message from Wendell Niles. This is important. This is urgent. Over 2,000 young physicians and dentists are needed as volunteers at once for service in the United States Army or United States Air Force. These physicians and dentists are required to safeguard the health of the men and women who are serving our country in the armed services. If you are a physician or a dentist, you are needed now. Right or wire, the Surgeon General of the United States Army or the Air Surgeon of the United States Air Force at once volunteering for active duty. Let me repeat that. Right or wire, the Surgeon General of the United States Army or the Air Surgeon of the United States Air Force today or see your local U.S. Army and U.S. Air Force recruiting station. And I'll back at the microphone our star, Bill Williams and our producer. Bill, it seems sometimes since you've been our star on Proudly We Hail, so don't you think we should bring our audience up to date? Sure, but what do we talk about? What's your favorite subject? Barbara Hail, my wife and little Jody. Now wait a minute. We'll talk about Barbara sometime when she's on the show. This is Pappy's Day to Howl. Remember? We're going to talk about you. Can't talk about Barbara and Jody?  We all love Barbara and we think she's beautiful and little Jody is precious. No? I want to hear about your pictures. Well, I worked with Jimmy Stewart and June Ellison at MGM on the Stratton story. I played the catcher Eddie White. I know that Jimmy Stewart and all of you did a wonderful job in the Stratton story, but I hear some of those big league pictures really fixed you. Fixed me. CP, they tried to kill me. There was no substituting a big lead catcher to backstop them. Among the pictures were Bob Gillespie from the White Sox and Gene Bearden from Cleveland. Gene Bearden was the here-of-the-world series last year. And what a picture. But those guys don't know what it means to throw an easy ball. When I got home that first night, my hand looked like a piece of raw ham. And the same size. They precooked it, believe me. Oh yes, I asked them about batting and about hitting their fastball. And when do I start swinging? Well, I stood up at the plate and got all set and watched the wind up. Boom! The ball was in the catch's mitt before I even got the bat off my shoulders. Well, how do you hit those pictures? CP, I never did find out. Well, I gotta get going and I've had a swell time. But before I leave, who's your star next week? Next week, Bill, and ladies and gentlemen, that well-known and popular actor Brian Donlevy will be our star in the title of our play, The High Timber. This is a dramatic story of a lumber camp foreman who races time in an important cutting contract with a promotion as his reward but finds a deadly series of obstacles confronting him which require his skill, courage, and fist to surmount. That should be a good show. And we'll all be listening at home. So long, CP. Goodbye, Bill. We should have joined us next week, ladies and gentlemen, when Brian Donlevy joins us to star in a dramatic story, The High Timber. Until then, thanks for listening and cheerio from Hollywood. Bill Williams appears for the third seat of the Hollywood Court in the committee with the outrageous public appearance of all stars in this program. Script was by Bill Vance, music by Eddie Dunn Center. This program is transcribed in Hollywood for release at this time. Wendell Niles speaking.