Autistic people are nine times more likely to die by suicide, which I think even here and that makes you understand how, you know, urgent it is. The Autism Hive is a mental health suicide awareness charity. It's a service led by autistic young people. They're ages between 16 and 25. This is so important to me because unfortunately my son who was autistic died by suicide February 2021. It was then as a mother I wanted to know how did my son be in this position that I didn't see coming. I had to get up and keep going, so what did I do? I started the Hive. Julia I have found to be very human in her experience and she connects and relates quite quickly to people and has that empathy that people, you know, respond to. She's very genuine in the support that she wants to give and can give. She's got a great attitude in relation to working in partnership with people and that's what makes the Hive special. The Autism Hive is just a small group of young people at the moment that are meeting together once a week on a Thursday morning. Do arts and crafts. We do games, chess. We took them one day to the rage room, so we got to break TVs and do different things, so it was really a way for them to get their frustrations out. As an autistic person turns to adulthood, the services aren't available. The like of what we do it's just bringing them alongside to see where we can show them where to go. My name is Rebecca McCulloch. I am the founder of Eden Consultancy, which is a business that works at equipping those who are working with or raising neurodiverse individuals. And then linking together with Julia, that's been that beautiful collaboration of her lived experience and especially then talking about mental health and autism. I personally speak with my daughter. We have experienced four attempts of suicide within her journey and that's from an earliest 13 years old. Why are our kids nine times more likely to commit suicide if they have autism and three out of ten with autism and ask for just go ahead and attempt suicide? So we're asking the questions of why that is and that's why the autism hive is so key and a key time when there's such a prevalence of suicide within our area of Northern Ireland. The National Lottery were actually the first ones to give us any funding. I think to get the recognition from the lottery of what we are doing and understand in how important our services is is definitely give us the confidence to go further. What we really want for the autism hive is that when you come and you're autistic that as soon as you step through the door you're going to get diagnosed then we're going to be able to send you to the other services that are available. So it's like a one-stop progress but then it's also given back to education and training and learning and prevention. There's hope out there for autistic adults that people are more aware of autism and mental health and suicide. The autism hive is just everything about Luke. Doing anything with the autism hive he's the first person that I think of. Would he have liked it? Would it have been something that he would have found useful? Would it have made his life easier?


Hello, my name is Saad. I'm going to talk to you about mud and Mediterranean. I do strange things. I make coffee machines out of clothes hangers. I make healthy boots. I make dinosaurs that are triggered from the internet. I make healthy boots that are activated by your butt. The world's first and only butt activated is healthy boots. It's the page from IKEA that fell out. But what I'm actually going to talk about is microbial fuel cells and if you get this slide, you're done. You can actually do this presentation. All right. Who's not familiar with Star Wars story line? You're not familiar. So we've got spoilers over here. I'm going to try and sidestep them, but it's in popular culture, so you shouldn't worry too much about it. Anybody have noticed the essential, quintessential difference between Star Trek and Star Wars? I have hacked as a reward. The boss is a good answer, but not the quintessential difference. Okay, maybe the hacks for some other crowd then. One is set in the past, one is set in the future. Anybody want to guess which one is which? Thank you very much. That's how it starts. That's the first thing that you get hacked. That's what it starts off with. This is Star Wars in a galaxy far far away a long time ago. So it's set in the past. So you cannot confuse two, which is this is why the fandom of one side and the fandom on the other side gets really, really annoyed when the time makes the two. But if you're running for a political office in India, it doesn't really matter. You can mix them up with Wolverine even. Anyway, so there was this one little boy in there called Anakin Skywalker and he grew up and went through quite a few phases as you can see from here. And this is basically what my presentation is based on because in the beginning there was this strange guy with long hair who came up and walked up to him and stole some of his blood and then analyzed his blood and found midichlorians in him and these midichlorians are tiny microbial creatures which apparently power the force. Okay, with me so far. Microscopic found in the blood that power the force. So the more midichlorians you have in your blood chances are the more control you have over the force. So Yoda, for example, has a lot of midichlorians. Anakin Skywalker turns out has a lot more and hence the prophesied one. No spoilers. In our world, however, much, much, much, much in the future, which is our present, which is what we're concerned about because the past is boring. It's in the past. The future is much more interesting. These are microbes, these are bacterium. Okay, this is a real thing. It's not a fictional thing. And this is important for us because in the age of Trump, very important to have, these things exist anywhere on the planet including acidic lakes, frozen, arctic polar regions and anywhere in the food in whatever we do. But what's important is that we rely on them. We have more bacterial cells in us than we have human cells. And this is a fact that blew my mind to the point that I was wondering, you know, why are we not talking about this one single thing for the rest of our lives? I mean, this is so amazing. The number of cells that make you you are fewer in comparison with the number of alien bacterial cells that you have inside your body right now. By a magnitude of 10, if you want to know more about it, you can look at it. But yes, once to 10. So every single human cell that I have that makes me me, there are 10 cells that are not human that are microbial. There's some dispute about this number. Some people say it's 1 is to 1.3, but the point I'm trying to make is it's good shit and it there's a lot more often alien DNA than there is human DNA. We see this in foods. We see this in other places. The two microbes that I want to tell you about and show you examples of is this one and this one. Geobacter and chubanella. And what's important about this is that they produce electricity. They're electro-genic. So if you're familiar with electric eels, they're biological creatures that produce electricity and will stun their prey into submission and then eat them. But they produce electricity without having batteries in them. And now our entire lives are revolving around things that are powered by batteries. I'm going to extend by one minute and then we'll do Q and A. So these bacterium, since they produce electricity, they're going to all they need to do is harness this power. So theoretically, if we have lots of these bacteria, which are everywhere, you can't really see them, you'll have an invisible thing or invisible film that will produce electricity. There's a video to show you how that works, but generally this is what a battery looks like. And if you put a bacterium instead of a chemical reaction, you're able to generate power. This is what it looks like in a lab. But if you want to do one of these by yourself, which is what I highly recommend, you can do this at home using mud that you get from a river. This is a good project. They've actually used this. This is a self-powered robot that roams around taking samples of things to see where the pollution is and powers itself using various renewable technologies, renewable sources of energy. So there's solar, there's wind and there's also microbes. So it pulls out microbes from the river and powers itself and keeps it living. Very useful in areas where power is not accessible. You can make your own batteries out of mud and that kind of looks like this. You get a jar, put in some charcoal at the bottom, fill it up with mud, put some charcoal on top. You've got two connectors, charcoal and charcoal, and you create a circuit and that's what you get out of it. That's about 0.1 volts of electricity per cell. I have the examples here later on, you can take a look. That's it. Questions? When did the cells expire? So it's a symbiotic relationship. Microbes, tiny little ones, they create a colony at the bottom because they're anaerobic, so they move away from oxygen and as long as they have food, they will survive. It's a symbiotic relationship. So it's fungus that breaks down complex sugars and bacterium, which is the electrogenic ones, which feed off of the simple sugars and produce electricity as a by-product of their metabolism. So the power that you're getting out of it is a by-product. So to answer your question, as long as there's food in the mud, it should last. The cell that I have here, I made in January, it's still going. It's got this much of mud in it. I should last for about, I don't know, five or six years. The tiny amount of voltage, tiny amount of power, but I mean, so it's impractical in every shape or form.  No. So as long as there's food in there, like a decaying vegetable matter, it will stay alive. So if you want to recharge your battery, you just have to feed it. Just on that, you have a room for this. Yes. I could power my phone. Yes, you could. So if you had a room for these, yes. Actually, we probably wouldn't even need a room for, because theoretically, I can get about half a volt out of each one of these cells. And if you factor the surface area and carefully construct it, instead of just going to your kitchen and finding what you can find and making one of these, then you could probably make it smaller. So I have another example here. That would be your question. So I've been trying this out. It hasn't worked. But these are cells. So it's a tiny little sushi tray, and I've created a layer of exactly the same thing you're seeing in here. And I put them sort of like an array. So it doesn't produce enough voltage, but I'm hoping that when it grows enough to form a layer, it should be able to function as a battery. So yeah, if you do this, you could probably create as much as this table and you'd be able to power your phone. For how long? I don't know. About 60 years. Theoretically, yes. But then the amount of power that it puts out is a factor of the surface area that's in contact with the microbes. And they form like a biofilm. So it's very hard to predict. None that I can detect. It's very cool, literally. How's the erasure of the fish? Not. It's not at all. But from, you can try, I've got a volt multimeter here. You can plug it in and see. This one is relatively stable at 0.3 volts. And it sort of stays that way. But when you start drawing from it, it fluctuates wildly. Mostly because of the way it's been constructed. It's constructed in a way that you could try this at home. So if it was nicely done with maybe like sheets of graphite, it would probably be easier. I haven't been able to figure that out yet. Because the amount of charcoal that I put on top is limited by the container itself and the biofilm that forms underneath. So it's between the mud and the charcoal underneath. And the charcoal itself is sort of crushed. It's activated carbon. So, I mean, you get it from these humidifiers. That's where I got this stuff from. So you can't really tell how the biofilm is in contact with the charcoal and how much of these little tendrils are touching the charcoal. So the more surface area there is for these microbes to, you know, conduct electricity, the more power you'll be able to draw from it. But I haven't found a way to measure it yet. I think you're at time. But if you have any finished questions, can you come up for this?


Tonight we continue our look at the current workforce shortage in the Brainerd Lakes region and find that there are certain industries that are currently trying to get ahead of the problem before it gets out of hand. Our Logan Gay is in our Brainerd studio with more. Logan? Yes, Dennis, well as I researched the workforce shortage I was surprised to find out that it's not only hurting our commercial businesses but also our hospitals. Many hospitals are preparing themselves for a nearby workforce shortage in the future.. Hospitals like Hyuna Regional Medical Center are facing an approaching staff shortage. We're looking at an impending physician shortage. By about 2025, we're gonna start to see a decline in the number of physicians that are working. And so we're gonna have to, you know, step up our game as we plan for that. The shortage of staff is not only physicians. Definitely impacts physicians but also nurse practitioners, nurses, both registered nurses, LPNs, medical assistants all the way through all of our care team to include housekeeping and other support type of positions. Currently CRMC employs over 1000 people between their four facilities. In order to prepare for the shortage of physicians, CRMC starts recruiting early. We're working three and four and five years out, you know, to recruit physicians to come here and have them commit to working here. Having a shortage of doctors means longer periods patients could go without being seen. We don't want to ever lose physicians that we have here because it's going to affect how our patients are seen by our medical staff. If we have shortage of doctors, there is going to be such a long wait for patients to be seen by a physician. Part of BuyMark's job as a physician recruiter is not only to use the hospital as a recruiting tool, but also the community. That's one thing that I've noticed with the next generation is that work-life balance is extremely important to them. You know, this generation is about getting home, getting active. And one of the advantages that we have here specifically in Crosby. One of the ways essential health has been working to improve the shortage is by helping qualified individuals further their education. In the past couple of years, we've supported over 40 of our employees to go back to school to further their education, including we have sponsored over six people to receive their nurse practitioner degree over 22 registered nurses to go on and get a bachelor's degree. And so that's one of the ways that we've been trying to improve the workforce. Holly Swanson, a nurse practitioner at the essential health baxter clinic, recognized the need for workers in the health field and has won the many nurses and physicians who benefited from the scholarships essential health provides. Being able to apply what I'm learning in school in the field and staying up to date on current practices and making those connections was so beneficial to me as I started my new career as a nurse practitioner and having all that clinical knowledge. The scholarships that I was able to receive during school helped me to work part time and go to school full time. And while doing my research, I also found out that essential health also partners up with central east college to support their nursing students. Alright, well, thank you very much Logan for that report tonight. Tomorrow we will finish the three part series on the workforce shortage by discussing the solution to the problem and a reminder if you've missed any portion of the series you can watch them all on our website, Lakeland news.org. If you've enjoyed this segment of Lakeland news, please consider making a tax deductible contribution to Lakeland Public Television.


So under trigonometric ratios and identities, there is a very small thing which is left off which we call as the harmonic forms. Okay. What are harmonic forms? Let me just take a small example to illustrate this. Let us say somebody comes to you with a question. He says, hey, there is a function like this. 3 sin x plus 4 cos x. Can you, number one, sketch the graph of this? Okay. Number two, can you find the range of this function? Okay. That means can you find out the maximum or minimum value that is the max and minimum value of this function? Okay. So how will you solve this? How will you solve this particular problem? Now, sketching the graph is not that easy because here both sine curve and cos curve are involved. And please let me tell you, if you're thinking that you're going to sketch both the curves on the same xy coordinate system, that would be considered as a sum of both the graph. No, that is the wrong notion. Okay. Sketching both the function, sine function, cos function on the same coordinate axis doesn't make the graph of sum of these. Okay. So how do you sketch? That is one issue. Second thing is, how do you know the range of this function? That means how do you find the maximum or minimum value of this particular function? Okay. No issues. Okay. Just let me know that you are going for that. Okay. Okay. Now, let us understand it. Now, in this particular shape, it is difficult to do both the sketching part and finding the range of the function. So what I'm going to do here is, all of you please pay attention. I'm going to convert this. I'm going to convert this to a harmonic form. The word harmonic has come as a combination of the word harmony. Harmony means trying to make this entire function as a single trigonometric function, either a sine function or a cos function. That means I would like to convert this function either as a constant sine X plus minus some angle or you convert it as R.  Here you can see that there has been a harmony established between the two different trigonometric ratios by converting it to a single trigonometric ratio. So if I'm able to convert f of X in either of the two form, in either of the two, I will be able to answer both of these questions very easily. Okay. Now, many people ask me, Sir, why do you want to convert it to a single trigonometric ratio like a sine or a cos? Because my dear students, managing a single trigonometric ratio is very easy. You can always draw the graph of R sine X plus minus alpha very easily. You can always find out the range of such a function very easily and so is true for the second one as well. Okay. So how do I do that first of all? What is my R? What is my alpha? And then how come this particular form will help me to sketch the function and range of the function? Let us try to understand through the very same example. Okay. Now let's see the process. Now you choose which form you want to convert it to. I'm leaving up to you. Which form you want to convert it to? You want to convert it to the first one or the second one? Okay. Say to all the first one to choose. So he said convert it to sine. Okay, fine. So now what I'm going to do, everybody please pay attention. Very, very important. The process I am explaining you. So this three sine X plus four cos X. Okay. This number three. This number four. Okay. Pick it up and make it as a coordinate. Okay. So what did I do? I picked up this number three and I picked up this number four and I made it as a coordinate. Okay. Sir, are we doing coordinate geometry or are we doing trigonometry? We're doing trigonometry only but a small interesting thing I want you to observe. Let's say this is a coordinate of a point P. Okay. So at this point is let's say our units away from the origin. That means this distance is capital R. Okay. And this angle is alpha. Good enough. Now tell me how can you write three and four in terms of R and alpha? You will say sir simple. You have asked a very easy question. This will become your R cos alpha.   Yes or no? Correct. Can you find out R from here? Yes, I can easily find out R. Just square them and add them. Sir, what are you doing and why are you doing all these things? I will explain you. Give me some time. Give me some time. Okay.  If you want, I can write it for the time being. So R here will become a five because R represents the distance. Isn't it? So how will you get alpha here? Alpha is very simple. Take the ratio of these two.  That will give me four upon three.  Okay. Many of you know the answer for this. This is roughly fifty threes degree, right? Roughly fifty three degree. Correct. Even if you don't know it, not going to hamper a lot of things. Right. So once you have done this, now come back to this expression. Okay. So, sir, you made a coordinate out of it. You found the distance of that coordinate from the origin. You found the angle made by that particular vector. So as to say Shalini correct with the X axis. Why are you doing this? What is the reason for this, sir? Okay. Let me explain the reason. Now this three that you have written. Can I write it as R cos alpha like this? Okay. Then sine X, I'll copy it as it is. This four that I have written. Can I write it as R sine alpha? Okay. Into cos X. Okay. If you see this term very, very carefully, it will remind you of your compound angle identity. You will say, are you, sir?  Okay. And this is what actually I wanted. See here. This is what I wanted. Isn't it? I have achieved it. So let's put the nitty gritties in this particular expression. So your R would actually be, or your R was actually five and alpha was actually 53 degree. Okay. Let's say I'm approximately taking as 53. Okay. Now, once I obtained this, is it easy for us to answer these two questions? Yes. Of course it will be easy for you to answer this question. So let us start with sketching part first. Okay. So how do you sketch the graph or five signs? So let's say you have now this function in front of you. How do you sketch this graph? Okay. So very simple. You'll say, sir, just draw the graph of sine X first. Okay. I'm just making it in dotted way, because this is not my final graph. So I'm just making a dotted graph. Okay. So this is your sine X graph. Okay. Of course your top end will be one minus one in the bottom. Okay. Passing through the origin. Okay. Now let's go step by step. This is the graph of sine X. Okay. Let me call this as Y equal to sine X graph. Now, if I want five sign X, what do I do? Let's say next step is five sign X. You'll say sir simple increase the amplitude of the graph by five times. Right. So this, this whole graph will actually become extended along the Y axis, something like this. I mean, I maybe not by scale. I'm not making it. So it gets extended five times like this. Okay. So this is the graph of five sign X. The top end will come at five. Bottom end will come at minus five. In fact, this on UG also don't worry about it. And now finally tell me if I have to make the graph of five sign X. This packet is not required. Five sign X plus 53 degree. What do I do to this graph? What do I do to this graph? Tell me people who are there in the bridge course transformation of graph chapter. You'll say sir shift this by 53 degree left. Absolutely. So when I shift this 53 degree left, your final graph will look like this. Pardon me. If I have done some, you know, graphing error. Okay. This is how the graph is going to look like. Okay. Let me show this exactly. How does it look on? From there we'll be able to appreciate in a much better way. Okay. So graphing became possible. Okay. So from this graph, I'll be able to tell its range also. Isn't it? Won't I be able to tell the range? You'll say yes sir. It has gone to a maximum of five. Okay. In fact, without the graph also you can tell the range. So if I ask you what is the maximum value this function can take, you'll say this maximum value is going to be five. Why? Because sign of any angle, this can become a max of one. So this whole thing will become a max of this whole thing will become a max of five. Isn't it? Because sign of any angle can maximum become one. Okay. Five sign x is just the extension of the sign x graph five times. Its amplitude became five times. Think like that. Right. So it was oscillatory graph. Right. It was basically a sinusoidal graph. Its amplitude became five times. Think as if somebody took it and stretched it along the y axis. Okay. Similarly, what will be the minimum value of this function? You'll say sir, it will be minus five because this fellow can take a minimum value of minus one. That means overall this function will have a minimum value of minus five. So this graph will oscillate from a high value of five to a low value of minus five. That would be the range of the graph. Okay. Now, you may get this question in your mind. Sir, can I use calculus for this if I know it? Of course, if calculus is known to you, then you don't have to rely on these methods. Okay. But sometimes let me tell you for these simple questions, you should not go for calculus. Calculus is like a, you can say it's a heavy weapon. Okay. Don't use to kill.  Okay. So don't use calculus, you know, for simpler questions where you can manage without it also. Now, time to show you this on your, uh, let's go to use you and see whether have I got a correct graph for this function. And does my graph actually have a range of minus five to five. But before that, before I change the screen, anybody has any questions. Okay. Now, if I wanted, I could have converted things in terms of cost also, just like I converted things in terms of sign, I would have converted things in cost also. How other way around, I would have taken three as our sign alpha and four as our cost alpha that that we would come into costs. Okay. But converting it to costs or converting it to sign will not have any implication with respect to the graph. There will not be any change in the graph. There will not be any change in the range. Don't worry about it. So you are free to choose whichever form you want to convert it to. So converting it to cost, you can try it out as your homework. How did you find alpha? Okay. So Noel, what did I do? I divided the, let's say I call this as the first equation. And I call this as a second equation. I did two divided by one. And I got this. RR got canceled and I got tan alpha, tan alpha is four by three. So alpha value, normally four by three is a very well known angle. I don't know whether Deere said has spoken about it ever. So four by three basically corresponds to 53 degree. Okay. So Noel, is it fine? Any questions? Ajat, today I was, I was starting my session and I got a message that some meeting is already going on, on this particular ID. And I realized that one of you, I don't want to name the person had joined some trigonometry session. Hmm. And that person is there in this meeting. Please do not click any old link of zoom send to you. Even my mistake. Because as a message, I will get that there is some other meeting going on. You cannot join the meeting. Okay. So one of you had joined trigonometry meeting of the last class. Please do not do that. Okay. Is it fine? Any questions? Okay. Because I get a mail that so and so has started that meeting. Because I am the license owner of this zoom. So I'll get a mail directly that so and so student has logged in and is trying to have a meeting there. Okay. All right. Anyway, let's go to the, let's go to the, I'll just minimize it. Yeah. So my function was three sign X plus four Cossack's. So three sign X plus four Cossack's. Okay. Please have a look at it. This is the graph that we had actually drawn. Three sign X plus four Cossack's here. So the top end of the graph is a plus five. The bottom end of this graph is at minus five. Okay. And how did I draw the graph also? I will tell you what did I use to make the graph. Just a quick revision of graph and is transformation topic that we had done in our bridge course. out the transformation from there on. I'll just mute this for time being a special focus to say to you are wondering know what will happen when you multiply with 5. So see here. So this was the sign next. Now if you multiply this with 5, see what happens on the x axis, it doesn't displace anywhere. It just becomes higher oscillations. So five times the oscillation okay. And now finally we displace this by, we displace it by some angle. So sign x plus. Let me write 53. I don't know whether it's going to take degrees over here. 53 degrees. Wonderful. Okay. I think it has taken 53 degrees. All right. So this is this is the graph that you will finally get. I think this matches with our original graph. No, which how much you displace it here more than 53 degrees, I believe. Okay. Anyways, let me write it as tan inverse of delete. Yeah. Let me write it as plus plus tan inverse of our tan four by three. Okay. This graph and this graph, as you can see, they both match. I'm switching both of them on together. Yeah. You see that? Right. So both the graphs are same graphs. Okay. So this is how you can actually sketch the graph. And of course, as I told you, you can easily find out the domain and the range. What happens if your x becomes 5x? Okay. Now say to saying, if I make x as 5x, what will happen to the graph? You tell me what will happen to the graph? The graph is going to shrink by five times. You want to see? You want to see what will happen? Okay. This is a sine x graph. Let me make a five over here. You see that? It got shrunk by five times. Okay. Anyways, so here is a generic theory with respect to whatever we have discussed over here. So basically when you have been, I'm just write a general form. Okay. Basically, if you have been given a function like a sine x plus b cos x, okay, you can always convert your function in terms of r sine x plus minus alpha or r cos x plus minus alpha. Okay. Let me not write alpha here. Let me write a beta because there's a difference between alpha and beta values, whatever. And the basis of this, you can sketch the graph. By the way, r value, I can directly tell you r value will always be under root of a square plus b square. Okay. Alpha will depend upon which form you are actually choosing. So as per the form you are trying to convert it to. So any of the two forms you can choose as per your whims and fancies. Okay. And you can get your r will be same for both of them. It will not change. Alpha will vary depending upon which, you know, this angle is going to change depending upon which form you are trying to convert it to. So one important thing comes out from here. Since we already know my r, I can always comment that the maximum value of this function will always be r only. Isn't it? Just like in this case, our max value came out to be 5 and 5 was your r. Isn't it? And your min value will always come out to be negative of under root a square plus b square, which is actually negative r. That is what we got here also as a negative 5. Okay. This is a very interesting theory that you should all note down because directly maximum minimum questions are asked on this particular concept. Okay. Now a couple of things to be noted over here. Many people ask this question, sir. Can I apply this to, you know, any scenario? That means let's say if it is a sin x and b cos 2x, can I apply it? Or let's say a sin 2x and b cos 5x, can I apply it? No. This formula or this direct result that you are using for maximum and minimum can only be applied when these two angles are same. If these two angles are not same, you cannot apply the direct formula. Then you have to break it up and bring it to terms which are having the same angle. We will see it through some questions. Okay. One or two questions we will take up and we'll see how it works. Okay. So please note down whatever I have written on the screen right now because I'm going to switch my screen to the next page. I'll take hardly 10 more minutes and then I'll start with straight lines. Okay. Actually not straight lines. We are going to start with the prerequisites to learning straight lines. Are you, sir? That important a chapter that we need prerequisites? All right. Yes. Of course. Okay. Time to take questions. Let's take questions. Tignometry is here. Let's take this question. I know it's a proof that question, but assume that these values are not given to you. Let's say this value is hidden from you. This also value is hidden for you. Just find out what is the range of this function? What is the range of this function? Find the range. You will automatically get the range as between minus 4 to 10. Okay. Let's do this and if you're done, just write are done on the chat box. Don't get confused. In the earlier slide, I had taken angle as X. Here they've taken angle as theta. It's just the change of the name of the variable involved. Concept remains the same idea. Concept is not going to change. Okay. Okay. Could I write my answer as maximum value is 5 square plus 3 square under root? Can I say this is the max value? Can I say that? Will it be right to say this? Will it be right to say this? And can I say min value is negative of this? Will it be right to say this? You say of course no, else it would have matched with your minus 4 and 10. So this is not going to work. Why is it not going to work? Because as I already told you, this formula works when these two angles are same, but they're not the same. So you cannot apply this as the max and the min value. At the question being just 5 cos theta plus 3 sin theta, then of course I can say maximum value is root 34. Minimum value is minus root 34. But in this case, I cannot say so because these two angles are different. Yes or no? So what do I have to do then? Simple. You need to sit and expand this at least the second term you need to expand and write it as cos theta cos pi by 3 minus sin theta sin pi by 3. So let's expand it even further. So it's 5 cos theta. This will be 3 by 2 cos theta and this will be minus 3 root 3 by 2 sin theta. Am I right? Now club the cos theta terms together. So this is going to give you 13 by 2 cos theta minus 3 root 3 root 3 by 2 sin theta. Now you have this expression. Can I now say the maximum value of this expression? The max value of this expression, I can easily say will be under root of 13 by 2 whole square and 3 root 3 by 2 whole square, which is nothing but 1 by 2. 13 square is 169 and this is 27, which is I think, I think is root 196. So which 1 minus 6 is 14. So max value is 3. But by the way, sorry, max value 7. By the way, there was also a 3 sitting over here. So I should write that 3 also everywhere. And this 3 is going to remain 3. It is not going to be affected. So your max value will be this plus 3, this plus 3, this plus 3, okay. This plus 3, this plus 3, which makes it 10. In other words, your f theta will always be less than equal to 10 because it is the max value of that particular expression. So ideally it will be lesser than equal to that value always. Is it fine? How did it work out in this case? Any questions, any concerns? Anybody? Clear? Or any doubt is there? So can you also now figure out what will be the minimum value of this function theta? You say, sir, now you have already done all the hard work. We just have to change the sign here. So they just let me know when you once you're done so that I can go down and done. Okay, great. So what is going to be the minimum value of this expression? You'll say, sir, simple. All you need to do is take this as a negative of this quantity. And you don't have to redo the whole thing because we have already seen that this value comes out to be 7. So it will be minus 7 plus 3. So minus 7 plus 3 will be a negative 4. So your f of theta will be always be more than negative 4. Okay, so let us combine these two. Let's call this as 1 and 2. So if you combine these two, we can claim that the f of theta lies between your f of theta lies between minus 4 to 10. This is what we wanted to do. Okay. Do you think the maths is asking neat exams? Shalini? No, maths is not in need. You will not be tested on maths if you are a neat aspirant. But if you're asking for CET very much, this question is very much asked in CB. Okay. In need only PCB is tested. PCMB is not tested. Okay. Is it fine? Any questions, any concerns? Please note this down and we'll take one last question and then we will close this particular topic for the time being, not permanently, for the time being. So we'll wait when your school will start again with trigonometry because we have trigonometric equations left to be completed. And one of the most important topics for your KVPY also which is called properties of triangles that will also be taken up. Okay. Can we go to the next page? Done everybody? Okay. One last question we'll take up. Find the maximum and the minimum value of this expression. Okay. Many times you will ask me, sir, maximum value when you're asking, why can't we do this thing? We'll make sine x also one, cos x also one, everything has one. We'll make it maximum. See in the previous example, in the first case which I gave you, if you wanted to make a maximum value out of it, right? Why can't I say, okay, the maximum value of this is three, the maximum value of this is four. So maximum value of this is seven. Why can't I say this? Why did my answer not match with this? My answer came out to be five actually. Do you remember the very first question which we took as an example? Why not seven? Can anybody explain me that? Correct Nikhil? Absolutely. Because sine and cos cannot simultaneously become a one. Right. That is the main reason why we had to do all these drama, right? If sine x and cos x become simultaneously one at some value of x, I would happily choose that to be my, you know, position of maximum value or if they become simultaneously minus one, I could happily make that as my minimum value. But unfortunately, there's a lag between sine and cos. They cannot become simultaneously one or they cannot become a simultaneously minus one. Absolutely right. Correct. All right. So please attempt this question. This is the last question for trigonometric ratios and identities and give me a response in the chat box. Okay, Shalini, anybody else? Very good. Now here you will realize that the expression has a mix of x and two x, but thankfully by knowing my double angle identity, I could convert this term as three into two sine x cos x. Correct. Okay. And two sine x cos x is actually sine two x. Now, just recall what I had said in the previous discussion in like, I think last to last slide. When you have the same angle sitting over here, you can use directly the formula for maximum and the minimum values. So the max value of this is simply going to be under root of three square plus four square. That's a five. Absolutely right. Those who give that answer and minimum value will be minus under root three square plus four square, which is minus five. Is this fine? Any questions? Any questions with respect to this? Okay, Prishan, did you realize a mistake? Clear now? Okay. Now I'll give you, we will talk about that later on when we do calculus. As of now, let's not go into calculus part of it. Well, last question, I would just take this up. Find the maximum and minimum value values of the following function. Let's take two sine square x plus four sine two x plus three. Now, see here, there is a sine square x, there's a sine two x. Okay. Let's see. Again, please don't use calculus even if you know it. So whatever we have done so far is good enough to solve this question. If you're done, you can write it done also. There's no need to actually sit and type out if the figures are ugly. Okay. Don't take, don't bother yourself for typing it out. Just say done. Nikhil is done. Very good. How about this? Nikhil, you're from Kormangala or HSR? Or neither? Okay, Kormangala. Let's wait for one more minute. If anybody is trying hard, please finish it off in the next one minute. Then we'll discuss it out. Okay, Prishan is done. Shardul thinks she's done. Good, good, good, good. How about others? Noel is done. Very good, Noel. Okay, okay, take your time. Okay, let's discuss it without much ado. See the problem here is there is a, you know, sine square sitting over here. Earlier we had us just, you know, without any power, right? And second problem is that there is an x sitting here and there's a two x sitting over here. So what should I do then? Okay. So basically both these problems will cancel out each other. How? Let's see. Can I convert sine square x in terms of cos 2x? If yes, you'll say you'll have to recall your double angle formulas, right? So please recall. I'll just write it down over here. Recall that we had done cos 2a as 1 minus 2 sine square a, isn't it? So I can say 2 sine square a is 1 minus cos 2a, right?  Okay. So overall, this expression simplifies out to a familiar one, which we can actually handle out. Okay, minus cos 2x plus or 4. Don't be scared by this minus sign over here. It doesn't make any impact to the result that we had taken out. So the same a sine x b cos x format will work here also. Okay. It's just that your b is now or a whatever you want to call it is a negative quantity, but that doesn't change our maximum minimum results formula. So if you look at this expression, the max value of this expression will be 4 square minus 1 square under root. Okay. So this will be your maximum value of the given function and that comes out to be if I'm not mistaken, 4 plus root 17. Okay. The minimum value of this expression will come out to be negative of this and plus 4. See this 4 is not going to change. This 4 is a constant, right? It is not dependent on any x. So 4 will remain 4 for the whole of its life. Okay. Only this guy is going to change depending upon the x values. So the maximum that can take is under root of 4 square plus minus 1 square under root, which is root 17. The minimum it can take is negative root 17. So your answer to the minimum value will be this. Okay. So if somebody asks you for the range of the given function, you can say with confidence that it will be 4 minus root 17 to 4 plus root 17. Okay. So those who said done, did you get the same result or did you get something else? Same result. Excellent. Very good. Awesome. So for the time being, my dears, friends, I'm going to give this chapter a pause. Okay.  In fact, we have done almost only around 60% of the chapter trigonometry. 40% is still left. Okay. But we'll come back to it when you do it in the second semester. All right. All set. Everybody's fine. Happy. Okay. So let's start the new chapter.


Hello, my name is Freddy Combe and I play basketball on the NDSU team. Today, we're going to be making a healthy snack called apple banana bites. And first, before we do any type of preparation, we want to wash our hands. You're going to start with hot water, and first you're going to get your hands wet.  Make sure you get your fingertips, your knuckles, and between your nails. Just make sure you get all of them germed. And once you think you have all of them germed, you want to go ahead and rinse off. And before shutting the water off, you want to take a paper towel. So you don't get them germs that back from the faucet. You want to make sure you dry your hands thoroughly. Now we're back here at our workstation, but before we start preparing, I'm going to go over the ingredients. We have peanut butter here, cinnamon sugar, and also the key ingredients, apple and banana. But before we start cutting the apple and banana, we're going to go ahead and rinse them off. We're going to use cold water. We're just going to make sure we get all around the apple and banana. And now we're ready to start cutting. It makes a great snack. Grabbing an apple or a banana after competition is very easy. So now we're all ready to make our apple banana bites. What we're going to do is we're going to cut our apple and cut our banana. And we're going to spread our peanut butter over the apple and sprinkle it with cinnamon sugar. Now make sure you have a parent here to help you cut your fruit. Now what we're going to do is take one apple slice and go dig into our peanut butter here. We're going to spread it over the top of the apple. Then we're going to take our banana slices, go ahead and place a couple of banana slices right on top of that peanut butter there. We're going to take our cinnamon sugar, we're going to sprinkle over the top of the banana. And there's one apple banana bite. Our apple banana bites are all finished. They cost for a really easy snack. But just remember to eat smart and play hard.


Okay, recording is on. Good morning and welcome everybody to this brand new semester. Spring 2023 and welcome to this course on PC214, Developing the Human Spirit. I'm really excited about sharing this course with you and the things we're going to learn. I trust it will be a blessing to all of us. Let's pray together and then we will get started. Could somebody just lead us in prayer and then we will start. Go ahead, Zafina. Dear Heavenly Father, we come to you under the name of Jesus. We thank you for this beautiful day and for the class we are about to have. God, as we learn this course, help us to get each and every word into our heart and help us to translate the truth into action in our lives so that people will know that you're God, so that your light will be shining through our lives and our actions and in everything that we do. I give Pastor Ashishan to your hands. Be with him and guide him. And we pray that this whole semester will be a blessing to us and it will help us to get a lot more deeper in our relationship with you so that we can proclaim this gospel much more boldly for your glory. Lord, be with us and guide us throughout the session. Give us the good Wi-Fi connections that we need and everything else we give into your hands in Jesus' name. Amen. Amen. Thank you. All right, just one quick announcement. We will not be having classes next three days. That is Wednesday, Thursday, Friday because we're going to be having our Christian Leaders conference. We have that once a year in the month of January. So the next three days we're having conference here. The good news is this conference will be live-streamed online and also, of course, it will be recorded and the sessions will be available. So you're welcome to tune in live or to listen to the recording of the conference. This year the team is on intimacy. And so we'll be focusing on that. Just coming, bringing us all, reminding us all about the importance of being in a place of intimacy with God and doing ministry out of that place. So I just want to let us know there won't be classes, but please join or listen to the conference recordings if you are interested, right? So let's introduce this course and get started with this course. I've put both the course introduction and the first lesson in the Classwork section so those of you online can get it. You can get it from the Google Classroom. Let me just go ahead and share the... So this course, developing the human spirit, actually it's a relatively new course. We only introduced it last year. So this is the only the second time we are teaching this course. So it's a new course. And I felt it was important for us to do this as a course, to emphasize this aspect of Christian life and ministry, which is about the spiritual aspect, the human spirit, and how to really develop our human spirit. Because so much of what we do, we are depending on our mind and our body, but really we are spiritual beings. And so we have to live out of our spirit.  And from there we have to live out. So if we don't do that and only limit ourselves to our soul and body, that's what we can do mentally and physically, then we become very limited. And as Paul said, in 1 Corinthians 3, we live like ordinary people or mere men, instead of being living as spiritual people. So I felt this course was important, just to enlighten us on the importance of the human spirit and how we develop our spirit and live out of that, do ministry out of that. So we introduced this course for the first time last year. And so it's still a relatively new course. And hopefully we will enjoy this. We're going to talk about some things we cover in this course. It's about understanding the human spirit, to understand how the human spirit functions and how the place the spirit is supposed to have in our whole existence. And so understand that. Understand the functions of the human spirit and the ways we can develop our human spirit. Just as we develop our mind, we all go through education and we keep learning and all of that. We develop our mind, we take care of our body. You must also develop our spirit and we want to understand the importance of doing it. There's only one lecture every week because it's not like a very vast content, content you have to cover. Nonetheless, it's important content that we will be covering in each of these lectures on developing the human spirit. The rest of the things in terms of assessment, grade, everything's going to be simple as you are familiar with. So we are going to start off our first section in understanding the human spirit. All of you can see the notes here. The first lesson we're going to talk about. The first thing we must understand is what the Bible teaches. I think many of us are familiar with this about spirit, soul, and body. We will look at these three scriptures. Again, these are familiar scriptures for us, but it's good to look at them. Can somebody please read for us? First Thessalonians chapter 5 and verse 23, please. First Thessalonians 5, 23. Somebody could read that for us. So we'll look at these three scriptures. First Thessalonians 5, verse 23. First Thessalonians chapter 5, verse 23. Now, may the God of peace make you holy in every way and may your whole spirit and soul and body be kept blameless until our Lord Jesus Christ comes again. Thank you. Let's also read Hebrews chapter 4 and verse 12. We will read these verses and then we'll all compare it. We'll study it together. Hebrews 4 verse 12. Somebody could read that for us. Hebrews chapter 4 verse 12. For the word of God is alive and powerful. It is sharper than the sharpest to its sword, cutting between soul and spirit, and the point and marrow. It exposes our innermost thoughts and desires. Amen. And one more passage scripture. First Peter chapter 3. And we're going to read verse number 4. First Peter 3 verse number 4, please. First Peter chapter 3 verse 4. You should clothe yourself instead with the beauty that comes from within the unfading beauty and quiet spirit, which is so precious to God. So let's look at these three passages of scripture. So in 1 Thessalonians 5, 23, Paul is saying, you know, may God sanctify you completely. So he's talking about you, meaning as people. May God make you holy completely.  May God sanctify you completely. And then who is you? Your whole spirit, soul and body. So he says, may God make you holy completely. And to explain it further, he says, may your whole spirit, soul and body. So this, from this scripture, we understand that every person is a tripod being. Three parts to us, spirit, soul, body. So if you look into the Greek, the spirit is pneumum. The soul is suke and the body, the physical body, you know, could be just depending on the body. That's the flesh or the physical part of us. So he's talking about three parts. I forget the Greek word now for body, but let me see if I put it here in the notes. Yeah, soma. So the Greek, the word soma. So he's saying your whole spirit, soul and body pre-punch to us. The spirit is that part of us, which is spiritual or connects with the spiritual realm. The suke, the soul is the seed of the mind, the intellect, the emotions, the psychological part of us, the emotional part of us. And the body, of course, we all know it's the outer man, the outer part of us. Now, when we look at Hebrews 412, he's talking about the division of soul and spirit. That means the soul and the spirit are distinct parts because there is the distinction of soul and spirit, division of soul and spirit. So the soul is not the spirit and the spirit is not the soul. They are distinct parts of us. And yet there is so much of overlap. Together the Bible talks about the inner man. So when the Bible talks about the inner man, we are talking many times of the soul and the spirit together or sometimes in the context of where it is written, we can say, well, it's talking only about the spirit or maybe addressing only about the spirit. But generally inner man, we're talking about spirit and soul together. But the spirit and soul are distinct parts of us because he says in Hebrews 412, the word of God divides us under soul and spirit to separate parts of us. But because they are inner parts of us, they overlap and their functions sometimes are parallel. So we can sometimes even get confused. Is that my soul or is that my spirit? Is that coming from my spirit? Is that coming from my soul? But the key here in Hebrews 412 is the more we engage with the word of God, the more we can see the distinction of spirit and soul because it is the word of God that goes deep to the place where it divides or distinguishes spirit and soul. So the key here, which we will come back to later on is as we engage with the word of God, we are able to clearly see the distinction between soul and spirit. Or this is from my spirit. This is actually my soul, my own emotion at work and so I must deal with that a little differently. So from Hebrews 412, two things to take away. One is the spirit and soul are distinct parts of us, even though many times they may seem like the same thing because they're inner parts of us. The second takeaway from Hebrews 412 is it's the word of God that helps us distinguish spirit and soul. What is of the spirit? What is of the soul? And he tells us here it is a disson of the thoughts and intents of the heart. So the word of God can help us clearly distinguish these thoughts and intents. Where is it coming from? Is it from my spirit? Is it from my soul? Two takeaways there from Hebrews 412. And then first Peter chapter 3, very interesting when Peter is writing here. Of course, the context is about conduct and how he talks about the art word adorning and all of that. That's the context. Now, I don't want to emphasize the context, but what I want to emphasize is what he actually says in first Peter 3 verse 4 about the heart. Now, in the New Testament, the word spirit and the word heart are used in a synonymous way. Spirit, heart. So in the New Testament, you use the word heart. You see the word heart. He's talking about the spirit man, the inner person, spirit person. Now, I said it in the New Testament because in the Old Testament, the word heart is used in a more general way. It can be used to talk about what in the New Testament we refer to as the soul, meaning the soulish part, the mind-intellect emotions in the Old Testament. So in the Old Testament, you look closely at the context and say, okay, yeah, that's addressing the soul or it's addressing the spirit. But in the New Testament, the distinction is a little bit more clearer when the New Testament used the word heart. Very often, most likely, it's talking about spirit. So now, in 1 Peter 3, 4, it says, notice what it says, let it be the hidden person of the heart. So a lot of things we can take away from 1 Peter 3, verse 4. The hidden person of the heart. That means the heart is actually the real person. But the heart is the hidden person. That means it's not what we see outside. Outside, yeah, you see me right now. We are seeing the outer person of me. That's what I look in my soma, in my body. This is my appearance, wearing certain clothes now and this, et cetera. That is the outward appearance. But the real person is the hidden person of the heart. So in the context, Peter is saying, don't worry so much of the outer person because the real person is the hidden person. The person of the heart.  I can say like the spirit is the real you. That's the real person. It's the hidden person. The second thing he says is that this hidden person, sorry, has incorruptible beauty. That means the virtues of the inner person, the spirit person carries character. Just as the outer person has its own character, its appearance, et cetera.  His hair is black. He is six feet, whatever at all. He's like this. He's like that. That is the outer person, you know, the characteristics of the outer person. But the characteristics of the outer person can change.  All those things will happen. It is fading away. But Peter is saying the virtues of the hidden person, they're incorruptible. They're incorruptible, right? That means who you are really on the inside in your spirit. And what you carry in your spirit is something that can stay through time. It can even get better through time. Whereas the outer man is fading, right? We're all growing old and older. The outer man is perishing. But the inner man, the spirit is being renewed and the beauty of the inner person is incorruptible. And then he mentions some of the characteristics that make the beauty or the virtue of the inner person. He talks about a gentle and quiet spirit. So gentleness, quietness, that is peacefulness. These are characteristics, you know, just like we mentioned. You look at the outer man, yeah, brown skin, black hair, this, this, this, this. Okay, those are characteristics of the outer person. Now, how do you talk about the characteristics of the inner person? Oh, the characteristics of the inner person are things like gentleness, quietness, peacefulness. And those characteristics, they are incorruptible. So the inner person, so what are we saying? We are saying the hidden person, the heart, the heart, your spirit is the real person. The spirit has characteristics. That is where your real character is. Thirdly, we are saying the characteristics of this spirit person are incorruptible. They endure through time. They could get better even through time. Or of course, if the person is evil, he gets more evil. But we are talking about from a believer's perspective. The characteristics, the hidden person, the characteristics of the hidden person, the heart is enduring, it's incorruptible. And then he also says, in the sight of God, it is very precious. Think about this.  So God is not impressed by my outer person. Of course, God created the body and we take care of the body and all of that. But what is God looking at? Here he says, it is this character of the hidden person, the heart, which is very precious in the sight of God. You know, we know in the Old Testament, Samuel said, Man looks at the outward appearance, but God looks at the heart. So we know that. But Peter is taking it a step forward. He's saying, the character of the spirit is very precious in the sight of God. That means you can imagine it like this. God looks at your spirit. He sees gentleness. He sees those characteristics of maybe love, maybe compassion, maybe patience, maybe gentleness, quietness, humility. You know, those attributes of those characteristics of your heart and God says that is very precious. The heart is the real person. The heart has character or characteristics. These characteristics are enduring through time. And these characteristics are what is precious in the sight of God. So if you and I, we want to put on our best before God, so to speak, it is the character of the heart that we must focus on. And so we want to learn about that. And you know, one of the things God says, I resist the proud, but I give more grace to the humble. That means these characteristics of the heart, they actually draw the grace of God on our lives. They draw the grace of God upon our lives. Why? He says, I resist the proud. What is the pride? That is the characteristics of the heart. The characteristics of the heart. He says, okay, there's pride. I resist it. But there's humility. I'm giving more grace. It draws God. It draws. He says, you draw near to God. He'll draw near to you. But what is it that draws God near to us? The heart. Blessed are the pure in heart. They will see God. So what is going on in my heart? It draws the grace of God that attracts the very presence of God. So the heart of man, and talking from a perspective of us believers, our heart, the condition of our heart, or our spirit is so important. And then we can take this further. Let me look at a few more scriptures here. I'll share this PDF now at this point. So like I mentioned a little earlier in the New Testament, when we say the inner word inner man, it's the spirit and soul together. So when you read about the inner man or the inward man, and this is a term the Apostle Paul uses often. For example, in 2 Corinthians 4.16 he says, though our outward man is perishing the inner man, the inward man, is being renewed. In Ephesians 3.16 he says, you be strengthened with mind by his spirit in the inner man. So he's talking about the inside person being strengthened. And what happens at death? At death the soma or the body decays. But the inner man, which is spirit and soul, they go either to heaven or to hell.  But that doesn't mean we seize having feelings. Because when you look into the scripture, a simple example is the story of Lazarus. The rich man in Lazarus in Luke 16, Jesus said, the rich man went to hell. Lazarus was in Abraham's bosom.  Now he said, oh, may Lazarus dip his finger in water and come and touch the tip of my tongue. So that means though these people are dead and their inner person is gone to heaven or hell, in that this was the Old Testament. So Lazarus was in Abraham's bosom.  He could feel. He could even remember there was consciousness. He said, Lord, please send somebody to go and speak to my brothers. I don't want them to end up here. So there was that consciousness and there was that emotion. So what we're saying is at death, the body decays, the soma decays, but the inner man, the spirit and soul, they go to heaven or hell and there is consciousness, there is awareness and so on. That's this little background here. Let's continue talking about the importance of the heart. In John chapter four, let's go now to John four and we look at these scriptures here. In John four, 21 to 24, Jesus teaches us something very important. Again, we are familiar with John four, but it's to look at it from the context of the human spirit. So John chapter four, verses 21 to 24, Jesus is... He's talking to this woman at the well of Samaria and he says, she's asking, which mountain must we go to worship? And Jesus says, look, you're not going to worship. It doesn't matter which mountain you go. It's not this mountain, that mountain. But then the key verse here, verse 24, he says, God is spirit and those who worship him must worship in spirit and truth. God is spirit. God is a spiritual being. God is spirit. He's a being in the spiritual realm. God is spirit. So therefore, our primary interactions with God is spirit to spirit. We interact with God's spirit to spirit. God is spirit. We worship him in spirit. We interact with him in spirit. He interacts with us primarily in the spirit. And that doesn't mean God cannot touch our soul or God cannot touch our body. Of course he does. But our primary interactions are spirit to spirit. And that's important for us to understand because when we want a touch of God, many times, okay, we're waiting for something to happen in the natural, something happening here. But when we want a touch of God, we should first look at spirit to spirit, that God will touch us in our spirit. And through our spirit, he will impact, touch our soul and body. That's primary way. He can circumvent that, of course. He can go straight to the soul and the body, of course. But in our interactions with God, primary interactions, spirit to spirit. Paul reinforces this or he reiterates this in Philippians chapter 3 verse 3. Somebody could read that for us. For us, Philippians chapter 3 and verse 3. Philippians 3 verse 3. We will also read Romans 1-9. We look at both these scriptures together. Philippians 3-3 and Romans 1-9. Somebody could read that for us, please. Philippians 3 verse 3. For we are the circumcision who worship God in the spirit, rejoice in Christ Jesus and have no confidence in the flesh. And Romans chapter 1. We look at these two together. Romans 1 and verse 9, please. Romans 1-9. For God is my witness whom I serve with my spirit in the gospel of his Son that without ceasing I may mention of you always in my prayers. Thank you. So Jesus said, when you worship God, worship in the spirit because God is spirit. Paul is writing, Philippians 3, we worship God in the spirit. He says we have no confidence in the flesh. That means I am not trying to impress God or trying to connect with God through my flesh. Now, of course, the flesh, the body is important. We have to keep it in subjection. We have to keep it, you know, honorable before God. It is important. But we worship God in the spirit and we are not trying to impress with the flesh. Do we worship God in the spirit? But over in Romans 1-9, he says, I serve God with my spirit. That means our ministry starts in the spirit. I serve with my spirit or out of my spirit. It's starting there, not in the flesh. So example, I'll just give a simple example. Suppose I'm going to go to preach. Okay, I think about what clothes to wear. I'm going to be on stage. I have to wear a nice shirt. It has to be nicely ironed, clean, a nice trouser. Yeah, that is good. I'm not saying we shouldn't. You dress properly. You respectfully, because you're going to do something very important. So of course, you want to dress well now. But the ministry that's going to happen, it's not going to happen because I wear some nice clothes. It's going to happen because of what is in my spirit. I serve Romans 1-9. How do we serve God? I serve with my spirit. So the ministry that's going to happen, it's going to happen out of what is going on in my spirit. Example, I want to worship God. Of course, we will tune all our instruments and make sure our music is good. Okay, that's important. I'm not saying it's not important. Yeah, you do all that, do it well. But when we worship God, we worship God in the spirit. So my spirit has to connect with God. If I have great music, all of that, but if my spirit is not connecting with God, then I really haven't worshiped God. I have everything outside. But I don't serve God with my flesh. Or with these things, we worship God with our spirit. It has to be a spirit-to-spirit connection. So our worship of God and our service to God or for God both come out of our spirit. So the condition of our spirit is so important. So important. So in the ministry, we are all interested. We are all preparing. We are all involved in Christian ministry. And it's okay. I'm going to serve God. But how do we serve God? It's not the outside. Outside to a certain extent. Yeah, we have to, you know, walk properly and so on. But more important than that is we serve God with my spirit. It's a spiritual service. And therefore the condition of my spirit is so important. And that's what we want to focus on. How can I develop my human spirit? How can I, you know, keep my spirit in the place where it should be so that I can serve God? Well, it's what we will journey into in this course. And how do I connect with God in my spirit so that out of my spirit we can minister to God. And many of us may have experienced this. You know, you go into a situation, maybe a counseling situation. And sometimes, you know, when people, I'm about to talk to people. So I say, God, I have no idea how to handle the situation. It's so complex. It's so difficult, you know. And I don't know what to do, God. But then you just go in, boldly in the situation. And then out of your spirit comes the wisdom of God. Out of your spirit comes. And you're, you know, you're like, okay, where did that thought come? Where did that idea come? How did that solution come? How did it even happen? And it's coming out of from God, the wisdom of God. It's coming from God, but it's coming through your spirit. And it's going into that situation. So although in the, in our soul, in our body, we had no capacity to handle the situation, to, to solve the problem. But because we are serving in the spirit, God, who is the source of wisdom, releases that wisdom to our spirit. And from there, we are able to serve the people. And we're able to bless the people, right? So the condition of our human spirit is so important, both in our relating to God and also in our serving people, serving God by serving people. It's both sides. It's very, very important. Okay. So we will pause here for today. I just want to quickly recap what we said. So we started by saying, first of students, 523, we had tripod beings, spirit, soul, body. We understood that. And then we said, the spirit and soul are distinct parts of us. Okay. Don't, we don't, we shouldn't mix the two. Sometimes, you know, people just use the word soul without talking about the spirit, but there is the human spirit. Okay. So there is these two are distinct parts of us. And what we also said was the more we engage with the word of God, the more clearer the distinction becomes and we are able to discern thoughts and intents. What thoughts and intents come from the soul? What thoughts and intents are from the spirit? We are able to discern that. And then we said, based on spirit 3, 4, that this spirit, the spirit or the heart, that's the real person. The spirit or heart has characteristics, traits, and those characteristics, those traits are enduring. They're incorruptible. And the good, we talk, you know, the assumption here is it's good, the good characteristics and traits, which is the example, gentleness and quietness. In the sight of God, they're very precious. So who you are in the spirit, the character, God looks at that and it is very precious in his eyes, the good, the good character traits. So that is where real beauty is it's in the spirit. And then we said, God is spirit. So our primary way of interacting with God is going to be spirit to spirit. Our spirit connects with God, God goes spirit. And when we worship, it is an expression of our spirit coming up to God. Yes, we sing songs in our language and we lift up our hands, all that is good, but really it is the heart that is being expressed through the soul and the body, through the music and the words and all that. It's the heart that matters. So we worship in the spirit and we also said, we serve God in the spirit. So our ministry is flowing out of our spirit. So the condition of our spirit is so important. That is where ministry comes from. Okay. So with this, I will pause here.  Any questions? Any thoughts before we close today? Any questions? Any questions? Anyone else in class? So I think this introduction was clear and simple. So let us close in prayer please. May I request somebody to pray with us and we close. And we will take this further. I'm very excited about just delving into this further next week. Somebody could pray with us and we close please. Lord we thank you for this time of learning. Lord we thank you for this beautiful subject that we have ahead of us to learn. Lord we pray that you would teach us from your word and help us to develop our spirit and to walk in alignment with your word and to see what you have installed for us manifested in the days to come Lord. We thank you for each one of us and for your pastor to deliver your word God. We thank you Lord. In Jesus' name we pray. Amen. Thank you everyone. Thanks for being on the class today. We'll see you again next week. Thank you. Bye.


Everybody forced here ripping 2022 honors first off the line. I'm act first off the line. I'm sitting a hobby and prism football hobby six box mixer number one A random team, so it's one honors one. I'm act to obsidian to prism There's the random results. You can find them anytime elite sports cards calm here. We go y'all. All right. I'll start with these prism boxes here These are the good ones Sex is looking good Just another 10 minutes hyper Hutchinson nice one lions rookie to 175 156 to 175 Ballinger and Pierce If you get a chance to go against it any of them even if it's not your team I highly suggest going the winter classic was awesome fireworks over Cali Murray Cardinals So the hyper AJ Terrell Falcons to 175 The Darian Mathis Sam Howell I will for sure try to attend another one at some point Silver Donovan people's Jones Browns with a Kenny picket Greenscope rookie auto Kp That right now Ryan L. That is nice 23 out of 75 That is gorgeous big time. That's for the lowest number picket auto. I've pulled so far out of this Greenscope so sick Blue ice JJ watt Cardinals to 99 nice JJ 26 to 99 Chaco rookie Taylor and Tolbert. Yeah, no glove. Is that even him? Is it a clone? Is it a wax figure? Hey a flashback prison mohawk to the chiefs Redway Volante Taylor to 149 Ricky Saints Dobbs and Anderson Mr. Anderson He's over McBride I was hoping you I'm glad we don't know Green Scope Shaquille entered Colts to 75 And we can make David just is like on another a different level It's like there's like make David is a big gap There's a bunch of other people that are like maybe second best Make David's build different He may end up going down as the goat one one day eventually Then if anyone can pass Gretzier get on Gretzky's level it's him 36 to 149 Eli Mitchell Niners Maybe he can be the LeBron to Jordan basically to Gretzky's Jordan Silver rookie emergent James and Williams Lyons with a purple to 125 Trayvon digs cowboys 39 to 125 Bailey's happy rookie. Oh, we J has Sunday take it on us for the Giants and get it. Oh, that's pretty cool Blue wave rookie Andrew Booth junior Vikings number 21 on that You mean that did Penini has that checklist out already Vaughan is out. You're saying I guess contenders photos are you out? Sometimes photo comes out way earlier. That is that's that's that's what I took away from what you just said Orange Derwent James jr. The 249 chargers Jermaine Johnson feel as Jones Is that Wednesday? Silver Dexter Lawrence for the Giants with a Well, 25 a hundred points. All right, that's no that's no slouch of a points card right there Sam Williams Kenneth Walker the third. Okay, so photo photos already out there and gotcha. That's early for a photo Silver KJ Osborne Vikings purple ice Vince Young to T25 Titans Any cool Patriots on that on that one Vaughan? Do Marcus and Jack both have autos? I would assume they do contenders is like the one with if they didn't contenders They probably don't have rookie autos. They probably don't exist All out Trevor Lawrence Jags purple Devon according Pats to 125 Hutchinson Sliver rookie at the Ketsey a Falcons blue ice to 99 Darrell Henderson Rams So on Haskins Jalen Petrie Mack has that autos Usually second-year guys still have autos in it purple ice rookie Pierre Strong jr. Pats to 225 Olavé and Charles Cross fireworks silver rookie George Pickens Steelers orange wave to 60 Mark Andrews Ravens 52 of 60 the Drake London base rookie and Ekka McClone. Yeah, prison basketball is not not far off Green Scope to 75 or Sean Gary Packers number 2475 optic football. I think I saw May. I looked it up earlier actually sometime in May Our prisms should be in April sometime. It's coming up orange Mike Williams Chargers number to 249 Got Datsun and Stingley Even Evanderate Kane got a hat trick Silver chase young commanders Mark Brunel auto to 149 for the Jags Drake Jackson Skyler Thompson Silver LT Chargers purple ice at 225 Shaquille Barrett bucks Orange rookie Skyler Thompson dolphins at 249 Evan Neil Pierre Strong Prison break silver Kyle Pitts Falcons Blue wave to 199 J. Alexander Packers. Well, they go Packers Abner Garrett Wilson.  Silver DJ more Panthers They jet silver rookie out of Breeze Hall nice breeze bad centering top to bottom unfortunately tippadoe McBride Conor Bedard Conor Bedard is the name Bedard sake one to 175 hyper for the Giants Chikir and Berks. Okay, let's do some obsidian Let's go down down the list here Big amount of points to make sure you get copy Leo Chenal rookie chiefs to 25 God Stafford Rams orange to 75 Met your rookie base Texans 75 Kenny pick a trifecta material triple patch Steelers rookie Christian Harris to 199 rookie auto Texans Cowboys the Marcus wear auto to 75 nice galaxy ink and the 175 rookie Jersey auto George Pickens alive George Pickens These are the stickers are gonna look like Black Hank just says G kind of with the P Steelers It is just look like that That's been nice hit for the Steelers still alive George Pickens is his good stuff right now He hadn't been live in a long time He was he was redemption and origins, I think Green rookie Pascal Lyons were Pashaal to 50 and orange to 75 Pashaal Lyons Marcus Jones rookie for the Pats 225 Cortland Sutton Broncos Jersey card 600 pointer and everybody at the end Unbreakable Jersey Alec Pierce cults to 125 and to 175 rookie Jersey auto James Williams Lyons Nice Jamo Maybe maybe not my tough to say with a receiver I Mac photo Looking for a green RPA usually at a green base parallel as well I think he knows it's just more of like a I get paid the same whether I have whether I sign it nice or not Honestly, if someone made me sign like 10,000 stickers, I'd probably do the same Not gonna lie on auto so you know on a graph machine though to 23 Antonio Gibson commanders Rookie jumbo patch Desmond writer six to ten nice card Falcons Jersey chiefs tonight to 49 Travis Kelsey dual patch Cowboys DeMarcus where Micah Parsons That's cool 11 of 99 Parsons Jersey number on that.  Oh My god green color match to first off the line parallel Goodness gracious I'm a pass fan. That's filth That's ridiculous Jets William M. That is just ridiculous, dude And it's his jersey number. Oh my god. Oh my god. Oh the humanity Get the camera Color match green jersey number in the R.  What will he do next? That's right. That's exactly what he said, dude Whatever I want whatever I would like Nick Chubb 23 of 99 silver and a purple Derek Henry Titans 12 10 of 12 National first football probably over the summer. I would think Nick Chubb purple lotto Browns combo spot hit 10 of 10 There you go Browns a Kurt Warner one-of-one extravagance patch auto 19 impeccable design on this one recollection collection Nice hit of rams both encased autos and honors combo spots Congrats to you both. Let's do a really quick recap here. I actually let's do points first Okay, pointern of this actually pretty big points random 2,500 is a is a chunk of points That's for sure. That's a chunk and then 600 for the second spot of this random 2,500 top 600 second Good luck. This is actually this is legit for sure for sure. I mean if you want to sell that It'll move it'll move good price 12 top 2 1 2 3 4 5 6 7 8 9 10 11 and 12 Seahawks get the 2,500 congrats on that and the Bengals are getting the 600 relics of wear and parsons. That's still a really cool one I'm Travis Kelsey, Desmond Ritter, Corlyn Sutton, Alec Pierce, Kenny Pickett, autos of Trey McBride Jameson Williams, George Pickens, DeMarcus Ware, Christian Harris, Breece Hall, Mark Brinell Pickett rookie greenscope autos stealers to 75 a Nick Chubb purple auto to 10 from honors photo and a one-of-one Kurt Warner recollection collection rams from honors photo and This ridiculous jersey numbered color matched first off the line parallel prime Patrick Iota with the ARP from New York Garrett Wilson Jets to 18. That'll do it. Thanks again everybody all to the next one


Good day everybody. Today I shall talk about the internal capsule of the brain, how it is structured, what is its orientation, and what are the various nerve fiber tracks inside the internal capsule. My name is Dr. Sanjay Sanyal. I'm a professor and course director of neuroscience and I'm a surgeon and medical informatician by profession. Let's take a look at an axial section for the brain. When we take an axial section for the brain, we see first a thin rim of gray matter which is referred to as the cortex, the cerebral cortex. But let's focus on this white matter here. This is referred to as the subcautical white matter which becomes confluent with the central white matter and which merges with the periventricular white matter. This whole thing is composed of nerve fibers which are malenated and that's why it's referred to as the white matter. For the ease of understanding this white matter has been divided into three broad groups, the so-called commissural fibers, the projection fibers and association fibers. Let's take a look at how these fibers are disposed. This is a very special type of investigation which is referred to as diffusion tensor imaging with white matter tractography. It's a very sophisticated investigation which gives a three-dimensional representation of the white matter inside the brain. So this is a coronal view of the brain and you can see that this is one hemisphere here, this is another hemisphere, this is the longitudinal fissure, this is a commissural fiber here. These colors have been coded by the computer. This band of fibers that are running down here on either side, this is an example of a projection fiber and these fibers that you see here these are some association fibers. The thrust of our discussion today will be on the projection fibers. Let's take a look at another example of a projection fiber. This is a distinction of a brain and we can see this radiating fan shaped structure here. This is a projection fiber which has been given a specific name called the corona radiata radiating like a crown. So this is a projection fiber. Another example of a projection fiber is this. As you can see this is a more diagrammatic representation. The fibers are radiating like a crown that's why it's called the corona radiata. We shall see subsequently that this corona radiata has got many components which are all labeled here. I would like you to take a look at this fact that this corona radiata has been indented from the lateral aspect by one nucleus here which is referred to as the lentiform nucleus and another important point is this corona radiata which is located just inside the brain inside the white gray matter of the brain. As these fibers converge cordially they become more tightly packed and in the region of the basal ganglia they come to be known as the internal capsule which is going to be the main topic for today. This is another picture a DTI division tensor imaging with white matter tractography of the projection fibers. More specifically one component of the projection fibers inside the internal capsule which we shall describe which is referred to as the corticospinal tract. So this is one side corticospinal tract descending through the ponds into the medullary pyramids and this is the other corticospinal tract. So this is a DTI division tensor imaging with white matter tractography. Let's come straight to the internal capsule itself which is the most important component of the projection fibers. During the fifth week of intrauterine life a swelling appears on the lateral wall of the steel and catholic vesicle and this is referred to as the striatal eminence. When the internal capsule fibers are descending down developing they split the striatal eminence into two components a medial part and a lateral part. So this is the descending internal capsule fibers and this medial part of the striatal eminence comes to be known as the caudate nucleus and the lateral part of the striatal eminence comes to be known as the lentiform nucleus or more specifically the putamen and the two together is referred to as the striatum. And finally the descending internal capsule fibers they descend down to the sub cortical structures lateral to the thalamus. So this is a quick overview of the development of the internal capsule. As the internal capsule fibers are descending down this picture shows how it splits the caudate nucleus from the putamen through these striated structures here and this is the reason why these two structures together are referred to as the striatum. So in simple terms the word striatum refers to the caudate nucleus and putamen together and this striated appearance is the place where the fibers of the internal capsule are descending down. This is another picture to show you how the coronary data fibers they converge in the region of the basal ganglia to form the internal capsule and this structure that we see here this is the putamen or the lentiform nucleus and this structure is the caudate nucleus. Now what we shall do we shall take an axial section through the brain to understand exactly the structure and the orientation of the internal capsule and for that we will take an imaginary line an axial or transverse section through the brain at this level which I shall show you in the next slide. So this red line represents roughly the level of the axial section and this picture also shows you a diagrammatic representation of the brain the same picture which I have shown earlier and the axial section has gone approximately at this level and this is yet another picture to show you the level of section. Once we take an axial section and we look at the brain from the top this is what is referred to as the axial view of the internal capsule and what do we see? So we see this cut section of the brain an axial section has been taken as demonstrated in the previous slide. So this is the right cerebral hemisphere this is the left cerebral hemisphere this also shows the same thing this is actually an MRI image and this is a diagrammatic representation of a section of the brain. Let us focus straight on the most important part of our discussion that is the internal capsule. We see this Y shaped or V shaped structure on this side and this V shaped structure on this side these are the two internal capsule mind you these fibers are projection fibers because they are descending down or ascending up in a vertical axis what we are seeing here is basically the cut section the axial section just to bring us up to speed the relationships of the internal capsule are here we see the structure here this is the caudate nucleus which I mentioned earlier this whole composite structure that we see here this is the lentiform nucleus it is called the lentiform because it is roughly shaped like a lens a convex lens and this structure that we see here this is the thalamus so this is the right side internal capsule as we can see that the lentiform nucleus has indented the internal capsule from the lateral aspect and therefore the internal capsule which should have been a straight vertical sheet of white matter has become roughly V shaped and that is what gives us the parts of the internal capsule namely this portion of the internal capsule is referred to as the anterior limb of the internal capsule which is located between the caudate nucleus mediately and the lentiform nucleus laterally this portion of the internal capsule is referred to as the posterior limb of the internal capsule which is situated between the thalamus mediately and the lentiform nucleus laterally and this curved portion of the internal capsule which joins the two limbs is referred to as the genu of the internal capsule the genu in latin means a knee or a bend so this is the internal capsule as seen in an axial section just a quick word before why is this called the word capsule in the initial stages of learning when the anatomists dissected an axial section of the brain they saw this sheet of white matter here and they saw a thin sheet of white matter on the lateral aspect of the lentiform nucleus so they said that the lentiform nucleus is enclosed in a sheet of white matter on the medial side and a sheet of white matter on the lateral side and they called it a capsule so therefore they named this the internal capsule and they named this sheet of white thin sheet of white matter on the lateral aspect as the external capsule but that is just a matter of historical interest now in the next slide what i'm going to demonstrate is what are the various fiber tracks which are running in the anterior limb the genu and the posterior limb of the internal capsule and for that i've made a diagrammatic representation of the internal capsule the right side so to bring us up to speed this is the anterior limb of the internal capsule this whole thing is the posterior limb of the internal capsule and the portion which is joining the two is the genu of the internal capsule and as we have already mentioned on the medial side of the anterior limb we have the chordate nucleus shown diagrammatically here on the lateral side we have the lentiform nucleus which actually is indenting the internal capsule and giving it this V shape open laterally and on the posterior medial aspect of the posterior limb we have this thalamus here let's take a quick look at the posterior limb of the internal capsule because that is clinically more important the posterior limb of the internal capsule we can divide it then the fibers into two broad groups as shown by this artificial color coding this lateral bundle of fibers here this is the corticospina tract which i had shown earlier and i'm going to show it again in another dti image this band of fibers that we see here this is the thalamocortical fibers which carry all the general sensations from the body to the somatosensory cortex of the parietal lobe so let's take a look at the breakup of the fibers in the corticospina tract first because clinically this is very important first this is the anterior portion the fibers in the anterior part of the lateral portion of the posterior limb of the internal capsule are the corticospinal fibers to the upper limb here the fibers are the corticospinal tract fibers to the trunk and it also carries the corticorubril fibers that is from the cortex to the red nucleus of the midbrain going further posteriorly these are the fibers the corticospinal fibers tract fibers which go to the lower motor neurons of the lower limb and finally at the posterior most tip we have certain special type of fibers which come from the temporal lobe to the pontine nuclei they are part of the frontal pontine tract in this case they refer to as the temporal pontine fibers we shall not bother about them in detail anymore so this whole segment is the corticospinal tract corticospinal tract fibers to the upper limb to the trunk to the lower limb remember that these are all fibers which are descending down and we are seeing the cut section in an axial view let's take a look at these fibers here this arrow represents the fact that the fibers descending the impulses are traveling up they are the thalamocortical fibers they go from all the sensory thalamic nuclei to the somatosensory cortex in the parietal lobe and they carry the general sensation from the body so this is the thalamocortical fibers carry now let's take a look at this portion here in circle in yellow this is the genu of the internal capsule now what do the genu carry the genu carries the corticoneuclear or the corticobulbar tracts and what are the corticoneuclear the corticobulbar tracts they are the counterpart of the corticospinal tracts the only difference being they start from the face area of the primary motor cortex and they end in the motor nuclei of the cranial nerves three four five six seven nine ten eleven and twelve so these are the corticobulbar tracts and they supply the motor nuclei of the cranial nerves supplying the head and face so this is the genu one final word about this genu in the posterior limb the whole genu in the posterior limb are supplied by some very special arteries which are branches of the middle cerebral artery and these arteries are known as the lenticulostriate arteries or the arteries of cerebral hemorrhage of sharko and these are the ones which are responsible for the vast majority of strokes involving the genu and the posterior limb of the internal capsule now let's take a look at the anterior limb of the internal capsule the anterior limb of the internal capsule the fibers are divided into for the sake of understanding into two groups the ones labeled green are the fibers which are coming from the frontal lobe to the pontine nuclei they are referred to as the frontopontine fibers or the frontopontine tracts now this is not just one fiber set of fibers they have a whole bundle of fibers and they are part of the corticopontine tract just for the ease of understanding I mentioned a few quick functions of these frontopontine fibers one of them is what is known as emotional smile the mimetic smile they carry fibers from the frontal lobe to the pontine nuclei to the seventh nerve motor nucleus smile emotional smile then we have the fibers for the horizontal conjugate gaze which goes from the frontal eye field to the paramedic pontine nucleus reticular formation nucleus in the pons for horizontal gaze then we have fibers for accommodation which do not go to the pons but they go to the nucleus in the midbrain and finally we have the fibers for mixturation voluntary control and coordinated mixturation which go from the mixturation center in the frontal lobe to the pontine mixturation center in the pons and therefore the m stands for mixturation so emotional smile horizontal gaze accommodation mixturation these are some of the just a few of the functions which are performed by these frontopontine tract fibers of course there are many more and there are many other functions this is just a few this central portion of the anterior limb the one marked in red here the fibers are going up they are also thalamocortical fibers like these but there's a considerable difference between these thalamocortical fibers and these thalamocortical fibers while these thalamocortical fibers carry general sensation these thalamocortical fibers they do not go to the parietal lobe instead they go to the frontal lobe and one example of these thalamocortical fibers are that which is part of the papae circuit which goes from the anterior nucleus of the thalamus to the cingulate chyrus it is a part of the papae circuit so this is just one example of course there are many such thalamocortical fibers which are traveling in the anterior limb of the internal capsule so this is a diagrammatic representation of the internal capsule so in the anterior limb the genome and the posterior limb with the various types of fibers traveling which have been given color coding and the direction of travel of the impulses are also mentioned by arrows and finally the blood supply to the anterior limb of the internal capsule is the anterior central branches of the anterior cerebral artery so this is in a nutshell the various fiber tracts which are located in the internal capsule and this is again a diffusion tensor imaging and white mitrotractography showing the disposition in a three-dimensional view of the corticost spinal tract as we can see it is coming from the frontal lobe it's coming from motor cortex and it is descending down and here it is the corona radiator here it becomes the internal capsule and it descends further down so this is the and incidentally in this picture also we can see some fibers of another type of group of fibers which are referred to as the commissure fibers in this case it is the corpus callosum that is just by the way so this is the importance of the projection fibers which become the internal capsule and the very important component of these projection fibers namely the corticost spinal tract why are we so bothered about the internal capsule and the corticost spinal tract again this is just the same picture which I had shown earlier and I have put a quick tabular representation of some lacuna stroke syndromes involving the posterior capsule involving the internal capsule we have something called pure motor stroke or pure motor hemiparesis where the location of lesion can either be in the corona radiator which I had shown earlier it can be in the internal capsule or it can be the basilar part of pons or it can be the medial medulla all of them produce opposite side face arm and leg paralysis pure motor then we have another syndrome mind you this is just a few of them there are some 20 25 different lacuna stroke syndromes described another one is called the dysarthria clumsy hand syndrome where the location of lesion is in the genome and the anterior part of the posterior limb so therefore the patient presents with one sided C at 7 9 10 12 upper motor neuron cranial palsy and weakness of the arm because we remember we had said that the corticost spinal tract fibers to the upper limb are located here so the dysarthria clumsy hand syndrome the location of stroke is here then we have another entity called the ataxic hemiparesis where the location of lesion is in the posterior part of the posterior limb of the internal capsule and here the patient presents with again opposite side weakness where the lower limbs are more weak than the upper limbs and that's why it is referred to as ataxic hemiparesis there these are just a few of the stroke syndromes involving the posterior limb of the internal capsule so this more or less concludes our discussion of the projection fibers the coronary the internal capsule and the clinical correlations of the posterior limb of the internal capsule specifically pertaining to the corticobulbar and the corticospinal tracts however remember that there are many other fibers also which are present in the brain just to give you a quick overview there's something called the commissure of fibers the largest commissure fiber is the corpus callosum which connects the neocortex of both the hemispheres and there's also something called association fibers which run in an anterior posterior axis and connect different regions of the brain in each hemisphere so this concludes our presentation on the projection fibers namely the internal capsule in the coronary radiator and the various tracts which are located thank you for watching and if you have any questions or comments please put them in the section below have a nice day