hello friends welcome to another session on polynomials and we were discussing graphs of different types of polynomial and today we are going to take up graphs of our cubic polynomial and see in our graphing tool that is geojibra that we use how does a cubic polynomial behave if we change the values of the coefficients now here is the cubic polynomial which is given right so it's ax cubed ax cubed bx square plus cx plus d this is the coefficient the polynomial in degree 3 right hence it is called a cubic polynomial you know this right and a b c d belongs to the set of real numbers that's how we represented and a obviously cannot be 0 why because if a is 0 then the the polynomial loses its identity of being a cubic polynomial now let us go take an example and then see how to plot a graph so let us say px is equal to x cube plus 3x square plus x plus 1 is the given polynomial okay now if I have to plot this polynomial that means if different values of x what is the corresponding response in y right how do I do that so we take random values of x and corresponding value of y's are found so x let us take this first one x is equal to 0 so if you put x equals to 0 you will get if you put 0 everywhere wherever you see x you will get y as 1 right so hence my first point to be plot is 0 comma 1 right we'll see how to plot this later now so when you take x equals to 1 you will get y is equal to 1 cube plus 3 1 square 3 times 1 square now don't get confused by this dot over here this is not a decimal this is to represent multiplication so multiplication is also represented by a decimal as in dot right so don't don't treat it as to be a decimal now so the value will be you can see it is 5 so hence the next point is 1 comma 5 or rather it will be 1 plus 3 4 plus 1 6 it's not be 5 it will be 6 actually so this one is 6 okay so this value is 6 right 1 plus 3 4 plus 1 5 plus 1 6 now if x is equal to minus 1 then what will happen so if you see x equals to minus 1 will give you minus 1 cube plus 3 times minus 1 square plus minus 1 plus 1 and this value will be minus 1 plus 1 goes this these two will cancel each other out now minus 1 cube is minus 1 and plus 3 here so that is 2 so this is the second point so hence third point rather so it is minus 1 comma 2 now if you take x equals to minus 3 then it is minus 2 right so now let us plot these points on the graph so let us say this this is x and y I have shown here x and y now let us plot the points so 0 comma 1 is the first point so 0 comma 1 would be this point so I'm encircling it 0 comma 1 then 1 comma 6 1 comma 6 will be 1 2 3 4 5 6 this is 1 comma 6 correct so this is 1 comma 6 and minus 1 comma 2 would be somewhere here right and minus 3 comma minus 2 will be minus 3 comma minus 2 is somewhere here let me zoom it a bit yeah so clearly these points do not look like they are you know straight line so if you join them free hand so this is how you'll have to join them something like this so this is what our cubic curve look like okay now if you see in this case the curve is cutting the x axis exactly at one point okay one point and it is if you see there are two turns of the curve two turns so curve is turning two times so one is this type first time and then this is the second time so if you see there is a local maxima here local maximum why local maximum because it's not the maximum value throughout the curve but in this region this is the maximum right in this surrounding area this is the maximum and if you also see this this point is local minimum or minimum we say okay so the curve is having two turns so you can see cubic equation will have two turns at max it need not be having two turns all the time but at max it can have two turns it will never have three turns that means what do I mean this will not cubic curve will never be like this okay so there are three turns in it isn't it this is a bi-quadratic curve actually so cubic curve will be either this or this like that or it will simply be like that or like that these are the different types of cubic curve and we'll go to geojibra tool you will see what are the different varieties of cubic curve but you can rest assured that it will never be of this shape never why because this is a three turns curve right and so on and so forth so it will also be not like this never only three turns at max is allowed or possible rather right so hence and it is cutting x-axis at one point but it can it can cut at three points all also for example another another type of cubic curve not three points other two points only so a cubic curve can cut x-axis at max at two points so like that if it is i'm sorry at max at three points right so one two and three this is one variety another variety could be this something like that now let us examine the same cubic curve in the geojibra tool so what I have shown here is a curve and you know you can see here y is equal to one x cube plus one x square plus one x plus four point three seven it says on the left hand side now what we are going to do is we have to see you know we're going to analyze this curve by changing the values of let us say a b c and d so in the first case let me just drag this d value back to one so you can see how does the curve look like if you can see exactly at one point it is cutting the x-axis now let me change the value of a so as you know the value of a is changing can you see now a is growing up and now it is coming down down down and you can see the entire you know the two limbs of the curve flip over the moment it becomes a becomes negative right so it just gets flipped over so this is how if a changes it behaves like this so let me put it back a as one let me take a to b one now let me see what happens with b is change now b is increasing so only one limb of the curve you know grows up and goes down and then secondly so at one time only one one limb one side of the curve only changes right most max the most of the changes happening only on the one side of the limb this is how b behaves or the curve behaves when the b value keeps on changing now let me stop it and then we'll change the value of c and c what happens to the curve okay so this is now c is changing now i'm changing the c value and now if you see it is appearing as if the curve is being stretched up and compressed the two sides of the curves right it's like stretched and compressed it becomes almost like a straight line or at one point right so the two peaks and the valley which is there one peak and one valley is there it is you know made more steep now that is what happens when the c value changes but you can see that at max at any given given moment or the curve doesn't intersect x-axis more than thrice it and the least number of cut is one also so hence number of intersection with x-axis is either one or three it cannot have two cuts and only two cuts that is yeah so either one or three so only odd number of times it is intersecting now i am changing the value to one okay so one now let us see what happens and b changes so like quadratic equation this time also the curve just simply gets translated up and down nothing else so if you change the value of d the curve simply gets translated up and down that's how the curve behaves so hence you can now understand what happens if different values of a and b all the coefficients are changed then how the curve behaves is it so what did we learn in this session we learned that a cubic curve or polynomial can have at max three cuts to the x-axis right and the minimum number of cut is definitely one so hence either it will be one cut or three cuts those points where the cubic curve intersects the x-axis are called the zeros of the polynomial there are two turns at max the curve can have so turns means thus the change in direction of the growth of the curve so it goes up becomes maximum then turns down goes down to minimum and then again turns up and goes towards maximum so this is how that is what i was trying to tell you so if you see yeah so as i change the value of a can you see yeah so this is what i was trying to talk about so as x increases y increases hit some maximum value then with increase in x y goes down and then again at some point after some point as x increases y increases and the vice versa the other way could also be possible this is what i was saying so as x is increasing y comes down becomes minimum then there is a phase when x increases y also increases and then after that as x increases y again starts decreasing so that's how a cubic curve will behave i hope you know you understood most of the properties of a cubic curve how to plot them and how to see or what are the behavior of the curve when different values of the coefficients are there you can also try downloading this app geojibra and write your own equation and try to understand different varieties of cubic curves thank you


We're now going to solve an example problem involving the conservation of energy or the first law of thermodynamics in control volume formulation and what we'll be doing is we'll be looking at the example of an air compressor. Okay, so there we have what our air compressor looks like in terms of the input and the exit properties. What I'm going to do now is I'm going to draw the control volume around the air compressor and I've carefully drawn this so that the flow coming in is normal to the control volume itself as well as the flow leaving. So our compressor goes from 14 psi up to 50 psi, not that much of a pressure rise. We're told it's 20 pound mass per second and 600 horsepower and the thing that they want us to find in this problem is they want us to find the rate of heat transfer. So given that they're asking for the rate of heat transfer, that's a pretty big hint right off the start that this is going to involve using the first law of thermodynamics. So let's set the problem up. We'll start with the assumptions that we're going to make and then we'll start working with the basic equations. So the assumptions, okay, so those are the assumptions that we'll be making in this problem. Steady flow, so it's not changing with time. Uniform properties over the inlet and exit, so that would be temperature as well as the velocity. We'll apply and use the ideal gas equation in this. We're assuming, I mentioned the control surface at one and two is perpendicular to the velocity vector and therefore the shear component disappears. There is no change in potential energy and the inlet kinetic energy is small. If you recall, I think I had v1 was approximately zero. That doesn't mean the mass flow rate is zero, but what that does mean is that the kinetic energy can be neglected on the inlet. So with those assumptions, what we're going to do, we're going to start with the first basic equation and that will be continuity and we will use that in control volume formulation. So that is the continuity equation. We're dealing with the steady flow, so that term disappears. And what we're left with is just the mass flux across the control boundaries, so your input and the exit have to be a little careful with the sign of that. So on inlet control surface one, we had a velocity coming like that, but our area vector would be out in that direction, so that's control surface one. And then for two on exit, the velocity vector was in that direction and our area vector would be there. So the dot product here is a negative and the dot product here is a positive. Okay, so those are equal to the mass flow rate. That's what we get out of continuity. Now the thing to make a comment here, one of the assumptions we made was that v1 was approximately equal to zero. But be careful, that doesn't mean mass flux is zero. All that means is that kinetic energy at one is approximately equal to zero. So that can sometimes be a point of confusion for students. Okay, so continuity next equation that we go to, we're going to go to the energy equation. Our first law of thermodynamics. So let's take a look at that. Okay, so that's the conservation of energy. To begin with, we had mentioned that the velocity coming into and leaving was normal to the control surface. And consequently, the shear work term disappears. We're dealing with the steady flow. And so the time rate of change term disappears. So those two, we can remove right off the bat. Let's rewrite our first law equation. And one thing that I'm going to do here, I mentioned this earlier, the u, u plus p over rho, recall that's u plus pv, specific volume. And that from thermodynamics we know is just enthalpy. So I'll make that substitution as well. Okay, so that's where we get our first law equation, too. Now what we need to do, we need to look at this here. This is the mass flux term. And remember with momentum, we have to be careful with that as well, because the sign depends upon which control surface we're looking at. And so what we'll do now is we will expand that out. Okay, so that's what we get for our conservation of energy. A couple of things that we can do here. First off, we said that the kinetic energy on the inlet was negligible. So that term disappears. Another thing that we can do, we have here rho 1 v1 a1. And then here we have rho 2 v2 a2. We know from continuity that that was just what we called the mass flow rate. And so we can replace that. And recall the minus sign here, that was because we had on control surface one, the vector of velocity coming that way, but the area was actually in that direction. And that's why that's negative. And here we have velocity leaving and we have dA going in that direction. So the dot product is positive. And that's why we have positive in the second term. But with that, let's plug in m dot and we'll rearrange the equations and take a look at what we get. So it looks a lot like what you get in thermodynamics. It is the system formulation or the expression, not for a fixed mass, but for a controlled volume of the first law where you have mass crossing the boundaries. We did say that the potential energy did not change. So that term disappears. We have H2 minus H1. How do we deal with that? Well, if you recall back to thermodynamics, dH is equal to Cp dt. And if we assume constant specific heats, which we probably can because our temperature rise here, we're going from 70 Fahrenheit to 100 Fahrenheit, very, very little change. So with that, we then get H2 minus H1 is equal to Cp times T2 minus T1. So we can make that substitution as well. And with that, we can rewrite the first law or our conservation of energy equation to look something like this. Okay. So looking at our problem, what do we need to get? We have to get a few things here. We have to figure out what the velocity is at two and the temperature difference was given to us. Once we get the velocity at two, we can get the mass flow rate. We know the work coming in. We were told that that was 600 horsepower and then we can get the heat transfer. The biggest trick from here on is the fact that we're using British units. If you're comfortable with British units, it's going to be easy. If you're not, I'm going to slog through and use British units. But another way that you can do it at this point, you convert to SI and go through and solve it that way, which is probably what I would do. But I'm not going to because I'm going to show you how to go through with British units. So here we go. Beginning with continuity, we want to get V2. That will be the mass flow rate divided by rho 2 A2. And the density at two, we can get from the ideal gas equation. So rho is P over RT or P2 is rho RT2, R being the gas constant for air. Okay, so there we got a lot of stuff. We're doing unit conversion in here. That's why it's a little messy. But when you go through and you put in the values, you get the velocity at two is 82.9 feet per second. So that's what we get out of continuity. Now that we know that, what we can do is go back to our first law. Let's look at it here. So this was the formulation. We know velocity. And we have pretty much everything else. We know the mass flow rate. CCP, we can look that up for air. We know the temperature change. We know the work. We can calculate everything. Again, the biggest challenge is going to be dealing with the units. So let's go through and see what we get. Okay, so we have the value of CCP. We have a conversion between horsepower and foot pound for second. So let's go through and plug everything in. So with all of that, we plug it in. We have to do a conversion between foot pound force and BTU here. But what we get is we get Q dot is minus 277 BTU per second.  If you recall, we said that heat transfer into the system and work done on the system are positive. And so in this case, given that it's a negative, that means that it is a heat loss term or heat is losing or leaving our system. And so that would be a case where we have heat loss or heat rejection from our system. So with that, that concludes the example problem of looking at applying the control volume to the first law of thermodynamics or the energy equation.


Yeah, actually the phone calls started coming in about 3-3-30 this morning. We got word that the company and the union met late last night and worked up into the night trying to work hash some things out and basically they have resolved the unfair labor practice charge that was filed at the table. Supposedly they have someone now that can make some judgment and maybe get us some moving forward in the direction we need to be headed. That's really all we were asking for is just some respect at that bargaining table and as of now they're saying that it seems to have turned the tide some and we just hope for some progress and move forward and be able to get a contract and keep our jobs. Yeah, we actually got the message last night to everyone to come back in at one. I think that was they were holding out last minute. We were all nervous, a lot of calls coming in, hey, what do we do? Because originally we heard 10 in the morning and then finally they sent one so I think that was something else that maybe was agreed upon by the company and the union so we could go back in and organize time and not have so much confusion with contractors that were brought in and all that sort of thing. That sounds like something else that they've worked out at the table so maybe a little ray of hope on what else they're working out at the table. But we are glad to be back and get out here and try to get some of these lines repaired or what's the things that's happened over the weekend with some rain and things so we're going to jump back out there and get at it and give the bargaining team another chance to move forward.


Where do we start you to team keep it clean more big news For the Ravens and we gotta cover a wide spread of things in a short amount of time So let's get straight into it first and foremost Rookie David a job boat who boy on Twitter a lot of back-and-forth Conversation of mugs Ravens fans about David a job bow and George Pickens and whatnot and I just been in the background Scoping but anyway David a job O Hardball said that uh, he swears he's gonna be back by mid-season at the latest at the latest and Hey, that would be nice. That would be great, but hardball did say he's a we got to get rid of them beach legs Oh, okay, I know you could be petty hardball sometime But we got a little low blow today with a job boat and I know it was a joke So nobody's taking it seriously cuz I know it's always gonna be somebody. Oh, I mean great He was just joking man. You take we know it was a joke anyway So with David a job, oh, we'll see what happens with him if he can return and sort of help the Ravens out for a little playoff Which we'll see we'll see I'm not counting on him this year I'm not gonna expect him this year So if he does end up making his words count and he does end up coming back by mid-season Oh awesome that it that'll be great and it but anything we get out of him in my opinion this year is a bonus It's a bonus now Ronnie Stanley and Tyus Bowser John Hobo say Ronnie's looking good. I think he's got a shot for the first game But of course you want those guys to practice the next two to three weeks and with Tyus Bowser. It's the same thing so Ronnie had a shot at the first game last year too, and then we saw what happened He didn't have a shot for the rest of the season So again with with all these guys. It's the same thing. Please don't rush them back now Speaking of Ronnie Stanley Ronnie Stanley kind of you know, we they know us Ravens fans We got a lot of Detectives Ravens fans if they see something on social media, they will be like they will break it down They will tell you why this player put that they will tell you what it means give you the full breakdown in detail I've done it myself seen a lot of other people do it too, but Ronnie Stanley on his Instagram He put a little a little emoji of the little what are the little yoga pose or whatever that is somebody meditating or something Then he says soon and then it was a ninja after that So that would give us an indication that he feels like he's gonna be back Soon and with hardball saying what he said about Ronnie Stanley. I mean a we can hope right we can hope Because again Ronnie Stanley would just make life Easier for everybody His impact would be so huge even if he's not the same Ronnie Stanley from before Well, when he even if he's not the same right saying that it was when he was healthy If he can just start to work his way back to that and it just starts by playing it starts by playing so We'll see Ronnie Stanley. I know you know what you're doing with with that Instagram thing So hey, don't don't be messing with our heads man, even though he is But hey, you all right now. We're gonna see we're gonna see and with tightest Bowser. Yeah Same thing. We'll see we'll see now. Um, John hardball and Gus Edwards now This isn't a little bit man. We ain't really been hearing anything positive on Gus Edwards The only thing that I heard is that it's not looking like he gonna be back anytime soon That's what I heard but what a John hardball said Gus is doing really well He's kind of he's kind of a patient rehab guy. I don't know that he'll be There the first week, but before the season's over. I know he's gonna be roaring and ready to go so before So before the season's over he's gonna be roaring and ready to go before the season's over He's gonna be roaring and ready to go Then if our regular season has 17 games 18 weeks So before the season's over Gus Edwards is going to be roaring and ready to go Now how about I'm gonna take your word on that. I'm taking word on it even though that word covers 18 weeks I'm gonna still take your word on that. I'ma trust you on that one But yeah, like I said, I just I haven't heard anything good with when it comes to Gus Edwards We haven't even like seen him even out on the field or nothing like night We haven't even seen him on the sidelines. I mean, of course, we ain't seen him out on the field We ain't even seen him on the sidelines or nothing But yeah, I I ain't heard nothing good on that now as far as somebody who did return not somebody who's return We waiting on somebody who is actually back JK Dobbins Hardball said how he does in the next week to two weeks is gonna tell the story He's got to get in shape his leg got real tired yesterday just going through the individual period just because he's been Rehabbing And he said the range of motion quickness extending it when when he strives those are the kind of things that will tell the Story and that's pretty obvious. I mean with JK Dobbins, we don't expect them to throw everything on him at once We expect it to be a gradual process. That's why the um One of my guys DMV. Oh yesterday. He made such a great point because we were talking and the Ravens we were talking about the Mike Davis signing and Just the timing of it and he brought up the point He was like man, he thinks that the Raven signed Mike Davis when they got an update on Gus Edwards That wasn't looking so good and I was thinking man that makes sense because they signed Mike Davis on May 10th So that was after the draft. They already had JK Dobbins and Gus Edwards on the roster They had Nate McCrary signed to a future reserve deal already. They still had Justice Hill They had drafted Tyler Beatty as well, but they still signed Mike Davis on May 10th, so I was like, ah, yeah, that that makes a lot of sense not saying that is what happened But what my guy DMV brought out it just made too much sense with the timing of it and now they signed Corey Clement too So we'll see but again stay ready so you ain't got to get ready You know, Jake JK is iffy right now, but he is on the way Gus Edwards is iffy and probably gonna be iffy for a while Overcompensate get more than enough running backs So you can be ready for when when those guys are out and then when they come back a For the fin, it'll be a gradual process for both of them So we'll see how everything plays itself out With Lamar Jackson and and these these reports and updates from because John Hubba was on serious serious radio So these updates and reports some came from Ryan mink as far as the updates on What John Hubba was saying on a serious XM radio and then we got to switch it over before we switch it over Mink also talked about how Lamar Jackson said he's making more suggestions to Greg Roman on plays and there was a play yesterday During practice where Lamar made a suggestion and G-Roll is like alright go ahead and they went for it and they scored And that I mean that makes sense. It should be that way Lamar obviously has has input and he should have input He should have a say so And you know Lamar like any chance he get we all we all know the famous go for it. We all remember that But it's it's a lot deeper than that and it should be a lot deeper than that With him calling plays him changing stuff up him doing stuff the way he wants to do it That's how a lot of it should be done Um, of course, you still got the coaching staff in place for a reason and they're gonna implement their things But you you want to make sure that your quarterback your franchise quarterback that is he's doing things that he wants to do and He's doing things that he's happy doing Because you want to make your franchise quarterback happy happy quarterback happy receivers happy tight end happy offense Happy touchdowns, too So, yeah, anyway, and then last but certainly not least Jeff Zeribic Reported that the Ravens had some workouts. They worked out a linebacker's Chris Smith and Brandon Copeland Who have both been with the Ravens before and they also worked out Trent Harris Who also is a linebacker and they worked out a defensive end named Ronald Blair and the defensive tackle Dondri Tillman. So the Ravens have been extremely busy Over the during this whole week, they've been extremely busy and then tomorrow night It gets that much busier Because the Baltimore Ravens they play in their very first preseason game against the Tennessee Titans So that should be a lot of fun. It should be a lot of fun I know they we know the starters ain't gonna be playing but it's still gonna be a lot of fun Just to give y'all heads up. We will be live streaming the game. Well, it's been a long time since we live stream the game, huh? Since I guess week 17 or week 18 when Ravens played the Steelers. Yeah That's the last time we live stream the game. That was the last Ravens game Whoo, it's been a minute. So yeah, that should be fun. That should be different Should be refreshing too, but I'm looking forward to it because this it's been a long time coming And again as we head into tomorrow official preseason game I got to thank you all for making this offseason what it's been and really making it fly by Thank you all for 56,000 subscribers Channel steel very very small, but I appreciate all of you. I appreciate it a lot I appreciate you subscribing Supporting the videos commenting telling people about the channel and whatnot and just staying active The the questions from subs do everything from top to bottom. I appreciate y'all a lot. I love y'all I hope y'all have a really really great day. I'll see y'all later on we out


You are obviously in 13 Reasons Why, which we are very much looking forward to seeing the second season. Is there something in particular you are very excited for fans to see from season two? I'm really excited because the show touches on very important topics and it sheds lights on issues that I think needs to be addressed in today's society, especially with social media everything. So I'm excited because for people to be able to see the different sides and perspectives from other characters that were involved in the situation that happened with Hannah Baker. And I think it's important that it's like, it sucks that that happened, but it's like think about other people and the moment after there's just so much more to something in a whole situation. It's not just her and so you get to see the other perspectives and point of views from everybody else and what they're going through. So I think that's going to work and be helpful in many ways. What has been the most sort of memorable response you've had from a fan of the show? Is there like one that sticks in your mind? I have people cry and they say you saved my life and I'm like, you know, that like for me, I don't know, I want, I always want my career to be something amazing and if my career can save somebody's life, a role I do can save your life, what's, what's, you know what I mean? What's better than that?  Oh, it's just like, but you have to understand the bigger issues and what it's actually doing for people. So it's important the roles that I take and how it impacts people because film, industry, music, everything, it touches the world and it changes it in so many ways. I always want to make sure whatever project I'm doing or the music I'm singing is for the good. And I think about everybody else and how it'll affect them and inspire them in ways. And you guys have such a great ensemble cost, but if you were going to have anyone that make a cameo in the next season, who would it be?  I'll do stuff like that before I know. I think that'll be cool.


I seek salvation from shaitan the accursed. Dearest viewers from all over the world, as-salamu alaikum, jami'an wa rahmatullahi wabarakatuh. Welcome to another episode of the Ramadan show with me, your host, Dr. Shabia Tijani. In this episode, we will be recounting the events and recounting the martyrdom of Amirul Mu'mineen alaihi salam. It's going to be a very saddening show as we remember this great individual and the martyrdom that took place. Before proceeding on to the show, I just want to remind you once again to join us on social media and send in your videos. Before proceeding, I would like to firstly ask you to please not forget us in your du'as in this very special of nights. Also I want to leave you with a hadith or a saying before proceeding on to the show and that is that Allah SWT in Hadith al-Qudsi says that if a person runs between Safa and Marwa countless times, so much so that they become like a dried sack but in their hearts they do not have the willaya of Amirul Mu'mineen, I shall not accept their worship. In this episode, as we remember and commemorate the martyrdom of Amirul Mu'mineen alaihi salam, we learn from his life many, many qualities but above them all his steadfastness when he came to Salah. I've spoken in previous episodes about how he would always stop in the middle of battle just to pray and with that we continue with our topic from yesterday which is how to prepare yourself practically, spiritually for Salah and we got up to strategy two, now we will continue with strategy three. Strategy three for preparing for Salah is to understand what you recite, focus on the meanings of what you're reciting in order to keep your mind busy, in order to keep your mind active. Imam Sa'diq alaihi salam has said, one who offers two units of prayer with the knowledge of what he said, he does not finish them without God forgiving him every sin that there is between God and him. Understanding what you're reciting in prayer is helpful in developing a more peaceful state of mind and allowing you to control your thoughts and feelings that would distract you from prayer. If you understand the words, appreciate the words, even if you're translating in your own language, recite what you are, think about what you're reciting and understand it so that your mind doesn't wander away. It's also important to focus on the quality of your prayers, not only just the quantity, the holy prophet peace and blessings be upon him has courted to have said to Abadar, two light units of prayer offered with contemplation are better than a whole night spent in worship. The next strategy, strategy four, to help you to prepare yourself for prayer is to have a relaxed and alert state of mind. An alert state of mind is one of the very vital ingredients of prayer. If you're tired and exhausted, it is better to rest or to meditate in order to get you to a state where you're ready for prayer.  Verily the reward a devotee derives from prayer is equal to the extent of it that he offers with an attentive heart.  At this point when you're totally mentally focused in your prayer, you achieve the greatest benefit from it. And that is that there is unlimited rewards. You stay away from the point where you become mentally exhausted and fatigued when you're in that state of mind. Upon completion of your prayer, if you do it in the right way, you'll feel completely relaxed. You'll feel a sense of satisfaction and reward. You'll be alert and even more focused. Your senses will be heightened and you will generally feel more confident and secure and you'll have a positive state of mind. In this state you'll feel more happier. The next strategy in order to try and get ready for prayer or during prayer is to have confidence in his book called Self-Building. Amini suggests that you start praying, you pick a secluded place, removable of all obstacles. Remember death and readiness as four main ways to develop and maintain one's attention in prayer. But most importantly, he focuses on one vital strategy and that is confidence in yourself, confidence that you can achieve the ultimate concentration during prayer, the confidence in yourself that you can achieve enlightenment through your prayers. If you do not succeed immediately, do not get disappointed.  When you're in that state, you'll feel cleansed in your mind and your mind will be rid of any thoughts which should not belong there during the state of prayer. When you have firm intention and firm intention of belief specifically, you won't be misled during prayer. You'll become more confident and you'll accept the prayer. You will forget about shaitan's forces and shaitan's forces will not be able to enter into your mind and slowly over time the good forces will become stronger and stronger and the whispers of shaitan will diminish smaller and smaller. Building self-confidence and defeating, distracting thoughts aren't something that happen overnight. It is something that takes time, something that takes persistence and something that takes effort. We look at many strategies trying to achieve this and one of them is goal setting. When you start by setting yourself goals over a prolonged period of time you don't achieve it straight away but you try and set yourself measurable goals and as you do that, as you pray more and more whilst you've got these goals in your mind you will find that initially you will start to feel much better about yourself and your prayer but also you'll realize that your focus during this prayer is getting better and better and the negative thoughts are diminishing more and more. The next strategy is cleanliness. An important part of Islamic teaching is related to cleanliness. You have to be ritually pure to perform your Salat so that's doing your Wudu' and Ghusl whenever necessary. The Ghusl of Jama'a of Friday has been specifically stressed as it cleanses your soul from many sins. When you keep yourself clean and pure it becomes difficult for shaitan to penetrate into your mind and into your soul. Cleanliness is a barrier to preventing any negative thoughts in one tradition of the Holy Prophet peace and blessings be upon him. He has said an everlasting proverb cleanliness is part of faith and faith leads a person to paradise so here the Holy Prophet peace be upon him has said cleanliness is a vital part of your being in order for you to attain paradise.   When you create a clean environment and you make yourself clean that will have a positive impact upon your prayer. As we move on to the next segment I just want you to once again remember Amirul Mo'minin many of these strategies that we've compiled have come through his teachings and through his life and as you remember him and you remember your Amal and you use these strategies in your own prayers tonight please do not forget us in your du'as and inshallah tomorrow we'll continue with our strategies in order for you to get the most out of your prayers. Imam al-Sadiq made the peace and blessings of the lobby upon him and said if the month of Ramadan remains safe and sound with respect to sins then the entire year shall also remain so. The month of Ramadan is the beginning of the year. As we've gone through the nights of Ramadan we've been trying to explore different parts of the world how you in different countries across the globe prepare for the month of Ramadan how you change your day-to-day lives in order to try and accommodate for this holy month. Today I want to talk about a place which is in Saudi Arabia which is known as Qatif. A lot of you know that this is one of the largest populations or largest Shia population within Saudi Arabia and again it's another community because of its isolation because of the Shia faith they're quite isolated in Saudi Arabia so they prepare in a very unique way and there's a lot of strong bonds that are built within the community within this month. In the city of Qatif obviously as it's a predominantly Shia and a Muslim area the working hours change people tend to work shorter hours during the day so instead of starting very early in the morning and finishing very late at night they start later in the mornings and they finish much earlier during the day so that they can use the rest of the day for rest and also to try and prepare themselves spiritually for the nights that lie ahead. The preparations for the month of Ramadan start from Shahaban where people will gather ingredients for their foods not necessarily the foods themselves but gather the ingredients freeze them or prepare them just before the month of Ramadan so that when the month comes around they are ready and they can start making their food. The day-to-day life of the people of Qatif when it comes to the time of Maghrib families will get together they will have their Iftar usually Iftar is a very light meal for them they would usually start off with dates and yoghurt and then they would have some soup which contains oats this is just to replenish their stores in order to give them a bit of energy some long-term energy and also it's very light so that they can keep themselves ready for the night that lies ahead. Obviously after that the whole community comes together within the Hussainiyah obviously it's a Shia city and there's a lot of strong bonds brotherhood and sisterhood because of the isolation of this community that are built during this month everybody comes together and becomes really strong and galvanized during this month they get together children men, women, adults, everyone, elders they come together within the Hussainiyah they prepare themselves spiritually so that they are ready for the nights that lie ahead they join in the Majalis Dua'a and Amal for those very special nights and then after that they all go home after going home extended families come together for sahur because sahur is the biggest meal of their day so they have a large meal for sahur before they go to sleep and then the next day starts once again obviously like I've mentioned a lot of the people from Qatif they like to prepare themselves for the month ahead from Shah Abaan this is not only true of the physical preparation of the food but also they decorate their houses they prepare themselves spiritually by fasting on some days of the month of Shah Abaan and also they like to prepare themselves in a mental state as well as we've gone through these nights of the month of Ramadan we've talked about how different countries around the world they prepare themselves like I've said every night it would be great if you yourself from wherever you are in the world could send us your preparation for the month of Ramadan how you prepare your day-to-day lives how you prepare yourself for work what your working hours are like how you prepare yourself for if-bar what you have for if-bar what your daily routine is like and in shah-la if you can send that to us we'll be very grateful so that we can air it and show it to the rest of the brothers and sisters across the ummah across the muslim nation and across the world Bismillahirrahmanirrahim dearest Imam Hussain TV viewers Assalamu alaikum warahmatullahi wabarakatuh may peace and blessings of Allah be upon each and every one of you in yesterday's report we showed you Rakhna Sultan restaurant this restaurant is so special the chiefs that they have here have come from different variety of cultures they have Iranian chiefs they have Syrian, Lebanese and Turkish as well so stay tuned as we go inside and show you how these different cultures being brought in one restaurant to satisfy the needs of the visitors here In the name of Rakhna Sultan, we have Turkish, Iranian and Lebanese in the name of Turkish we have Turkish kebab, chicken, chicken, chicken, meat and all the famous dishes in Turkey in the Syrian section and the Lebanese section too The Syrian grill that you can see behind me is from different two types they have meat and chicken they add some specific spices to this meat which give it a specific taste that the customers who come to this restaurant know this taste very well For this episode when we talk about health tips and advice I want to just take your minds to a different place I want you to think about your tears when you cry what benefit does crying actually have on your human body on your physical form and how do tears actually correlate with what we taught from the Ahlul Bayt, alayhi salam I want to take a study that has been conducted an article has been written by my brother, Dr. Abbas Tajani where he talks about why we cry from a scientific perspective when we talk about tears what I'll talk about is the different types of tears what those tears contain and essentially what impact those tears actually have on our bodies tears exist in three different types, three different forms we have basal tears irritation tears and emotional tears when we break these three down basal tears are the tears that are produced when we blink every single time and these tears help to lubricate the surface of the eye they contain specific substances that help us to keep our eyes fresh and replenished such as enzymes and antibodies that defend against bugs and stop diseases getting into the eye stop microbes and pathogens getting into the eye basal tears also have mucus which allows them to adhere to the surface of the eye without causing any harm but the main part of tears obviously is water and salts such as sodium chloride and potassium chloride the ratio of salt to water and tears is similar to that of the rest of the body if the body's salt concentration climbs too high it will take advantage of these tears to excrete the salt concentration or to excrete the salt through the tears so basal tears are what we produce on an ongoing basis through the course of the day next we have irritant tears or irritation tears these actually protect the eye and get secreted when the eye comes into contact with irritants such as dust or things like wind or any other foreign body that may enter the eye irritant or reflex tears have the same constituents as basal tears and the main aim or the goal of these tears is to protect the eye to stop harm coming to the eye to stop any foreign body that may have bugs or bacteria on it to affect the eye so you may stop any infections getting into the eye itself just like basal tears the irritation tears produce salt in great quantities salt is known also to help fight against any bugs or any bacteria and it also contains mucus so that the tears can actually slide on the surface of the eye without causing irritation finally we get to the emotional tears now scientists have done a lot of research into tears themselves and what happens when we secret or when we cry emotional tears and what's within the constituents of these tears aside from the things I've already mentioned such as salts mucus enzymes antibodies there's also other things that are released when you cry emotional tears and those are certain hormones these hormones include things like prolactin or adrenal corticotrophic hormone ACTH you see these hormones are actually in the body and when they are in the body for a prolonged period of time without being excreted or if they become at two high levels in the human body they build up to cause stress and they weaken the body's immune system as well but when we cry and these hormones are excreted what happens? science has shown that it's actually very healthy to cry emotional tears but sometimes people find it when they are crying in public it becomes socially awkward and they become embarrassed when going through a time of bereavement people often say that they feel better after they've had a cry and it's because that this crying process these emotional tears actually allow one person to rid themselves of the hormones that cause stress if the hormones are excreted or secreted even after physical pain those emotional tears will help to reduce the stress that is being built up due to that pain talking a little bit about prolactin which is one of the hormones which is produced in the human body it is found more in women than in men and that's why often scientists or generally we see that women tend to be more emotionally charged they tend to be more prone to be able to cry and it doesn't take much to make them cry it is thought that prolactin often becomes heightened just before someone cries emotional tears the level of prolactin in one system provides a threshold effect so the more prolactin you have in your system the easier it is for you to cry but that in term excretes the prolactin and allows you to get back to a state of equilibrium also scientists have found that men's tear ducts are actually smaller than women's and this may be an evolutionary change due to the fact that women over prolonged periods of time over many many thousands of years because of their hormonal balance have cried more Dr. William Frey who is a biochemist in Minnesota has researched the chemical content of human tears one of the substances that are mentioned that's found in tears is the stress hormone ACTH shedding tears helps to reduce excessive amounts of ACTH built up in one system Dr. Frey has suggested the purpose of emotional crying may be to actually remove waste products from the human body similar to the excretory processes that we have of human waste this may be another form of excreting toxic compounds in the human body Dr. Frey's conclusion is we may increase our susceptibility to a variety of physical and psychological problems when we suppress our tears crying not only removes toxins from the body but also reduces tension studies that have been conducted in adult psychotherapy have found people who have cried for a prolonged period of time during certain therapy sessions often leave the room with lower blood pressure lower heart rates lower body temperatures and also psychologically they seem more at ease than those who do not cry a study that was performed in Germany in Heidelberg from 1973 to 1986 showed the effects of suppressing one's grief and crying on long-term physical health this study was carried out on 7000 patients and the results are astounding they show that cancer and heart disease were more prevalent in people who had suppressed emotional grief completely over a period of two years or longer and people who had actually grieved and had openly been emotional had lower levels of cancer and heart disease this showed that crying emotional tears actually has a protective effect on the human body as a whole so let's bring this in context with what we taught from the Ahlul Bayt alayhi salam and from Allah SWT we are told in the Holy Quran indeed Allah SWT loves those who repent when we connect this with what we've just learnt about emotional tears when Allah SWT says you are close to me when you repent and cry through the periods of night and now we're approaching the nights of Qadr it is very important that we remember Allah SWT remember these verses and ask for forgiveness not only through lip service but also cry, open up your hearts after all they say the eyes are the window to the heart so if you cry Allah SWT will become ever closer to you then we look at the messages that we've got from the Ahlul Bayt alayhi salam we're told about the stories of the Ahlul Bayt the pain that they went through we're approaching the night of the martyrdom of Amir al-Mu'mineen and we learn about the the martyrdom of Amir al-Mu'mineen and the reason why we recount these events continuously is because we've been taught that in order to replenish our souls we must continuously remember the Ahlul Bayt and the sacrifices that they've given for us after all Imam Hussain meant in his final farewell to Imam Sajjad when he said when you return to Medina and meet Mashi'a let them know that on the plains of Karbala Yomulah was remembering tremendously Imam al-Hussain is trying to remind us tell us about his sacrifice so that we may remember it not only so that we may shed tears which will be beneficial for our bodies but also that we may shed tears which will also allow us to get close to him I want to leave you with this final saying from Imam Ja'far al-Sadik which talks about the link between grief and the remembrance of Aba Abdullah he says surely there is a burning heat in the hearts of the believers with respect to the killing of Hussain that will never cool down those people who remember Imam al-Hussain al-Salam and his sacrifice remember the sacrifices of all the Ahl al-Bayt al-Salam when they cry and they remember those stories not only do they physically become better not only do they physically become in a more superior state also psychologically they improve the stress and spiritually they get close to the Ahl al-Bayt and in turn to Allah subhanahu wa ta'ala during the ruling of Imam Ali ibn Abi Talib he was counting the revenues and expenses of the state just then Talha al-Zubair appeared they inspired some positions of authority Imam Ali ibn Abi Talib's ruling and they come to strike a deal with Ali ibn Abi Talib when Imam Ali saw Talha al-Zubair he extinguished one candle and lit the other Talha al-Zubair were very surprised at this they said we have come to you on some personal business an important business but why did you extinguished one candle and lit the other Imam Ali ibn Abi Talib says the first candle that I extinguished was from the treasury was bought from the treasury's money and the candle that I lit was bought from my own pocket and since now you have come to me with personal matters I lit the candle that was bought from my own treasury when Talha al-Zubair saw this they left and they excused themselves about saying any other word on this saddest of nights we remember the martyrdom of Amir al-Mu'mineen there's a short poem I want to recite dedicated to his life to his martyrdom in fact it was written by myself and my brother Abbas and it's called The O-Line of Allah struck by a poisoned soul his blood flowed like a river so badly was he manned has been the victim of a deed so inhumane a deed so inhumane then skies lament that Haider has just been slain to tragedy such was the force of that strike a pod gushed out from the wound the skies lament has been slain every day depend the one who fed the bear sat with the after today they wouldn't have a deed so Haider has just been slain he showed love to the young and elderly he wiped away the tears gave comfort to the has been slain as the sole Prestimon Zainab Hasan Hussein has been the victim Haider has just been slain Imam al-Sadiq made the peace and blessings of Allah upon him if the month of Ramadan remains safe and sound with respect to sins then the entire year shall also remain so the month of Ramadan is the beginning of the year as we end another episode of the Ramadan show I would like to leave you with a final thought we're in the very crux of the most important nights the nights of Qadr so it's very very important to start contemplating thinking, reassessing our lives and if we're heading in the wrong direction to take a new direction towards Allah SWT the thought I want to leave you with is don't perform any act because you're lured by success, material success and don't do anything because of fear of failure do things because you want to become the best person you can be and you want to be fulfilled the people that are most happiest are the ones who are satisfied in life as we go through we find that very very rich people who have everything they want are always or sometimes they're found to be disappointed the reason being that they do not have satisfaction in their hearts they're not content with what's around them with that I wish to bid you farewell but before I do I want to remind you once again if you follow us on social media you can catch the details at the bottom of the screen please also don't forget to send us your videos most importantly on these nights I would ask you humbly to please remember myself and the whole of the Imam Hussain TV team in your du'as and please most importantly don't forget to make a du'a for the reappearance of the awaited Imam, alayhi salam with that I bid you farewell and say wassalamu alaykum jami'an warahmatullahi wabarakatuh


So for those of you who don't know, I'm a big fan of LARPing and I try to go at least once a month. The idea of being able to live out an experience that I'd usually be resigned to talking about over a pen and paper makes LARPing one of the most fun experiences that I have in my life right now. And while it's cold and wintery here in my home state of Michigan, I'm stuck indoors with my LARP closed until March. So I've decided to talk about my very first experience at my very first LARP to both quell my inner LARPer for a period of time as well as potentially influence other people to maybe give LARPing a try and maybe find themselves an amazing hobby to be a part of. Names and situations may be altered to protect anonymity or because it makes a better story. So there I was. Me and my four friends had just gotten on the field for the very first time. I was playing a half-elf bard. One guy was a human rogue and my other three friends were all playing orcs, two warriors and a shaman. It was my first event, so I was in awe of everything. I saw people practicing swordplay on the trail, selling drinks in a tavern. I even overheard a couple people trading items, one of them mentioning, thanks, this is gonna break the greater curse on me. Now, I know a lot of people are gonna hear that and think that it's hella nerdy, but to be in a fantasy world and seriously, like, live it, it was crazy. After taking in all the sights, we pitched a tent, had some grab bread, and then went off to complete a quest that some vendor guy had given us, talking about clearing out an abandoned keep that had been recently taken over by some squatting cobalds. My whole shtick was that I shot arrows at people, so when we got to the old keep, we kicked open the door and I let loose my very first arrow. It flew through the air, whistling in the breeze. And then I shot a female NPC right in the tit. She took it and stride, and I'm sure that her response of yeeting a throwing dagger in my chest was more of a welcome to the game yeet full of friendliness and wet blood. At that point, all the orcs started swinging and our first fight got pretty crazy. Every once in a while, a cobald would notice me alone, firing arrows, and it would turn into a game of knife tag where we would see who could run the fastest. Unfortunately, the cobalds never expected it when I would pull a knife out of my bag and start shanking everybody that got near me. Sure enough, after about a minute, all the cobalds had been stab-murdered and the keep was clear of its creepy critters. But all was not well, for deep in the keep was an old trail that ran deep into the forest, beyond the keep. At the end of the trail lay a grove, clearly magical and druidic, as noted by the fact that there was a big ball of light that was floating in the middle of it. This wispy thing flew up to our shaman and was all like, Yo dawg, I need a druid. I've been abandoned, shit's not right. And it was at that point that we realized that, in our search for a one-off mission to gain money and notoriety, we had accidentally unlocked an entire side quest. So we returned to town and involved ourselves in the second half of what LARPING's all about, interacting with other players. The group splits up and searches for clues as to where to find a druid, and there were actually quite a few different paths to go down. There was a druid among the triblans, full of barbarians, that you would have to prove a show of strength to if you sought their aid. There was a practicing druid on the far side of the field, that you could get help from if you managed to find her relatively secluded grove, but the druid that we landed on ended up being an even more interesting choice. The last druid was a member of a major elven presence on the field, and she hated orcs.  And only assisted us because it was her druidic teacher that had once owned the grove that we were looking to help. As it turned out, she had been tending to it while he was gone, but due to an accident, she had broken her leg, and couldn't safely travel all the way to the grove in the previous month, leading the grove to apparently panic and attract all manner of creatures so that it could find a new druid to keep it safe. Clearly, she was the druid that we needed for our quest, but her leg was still broken, and she couldn't get to the grove, but she wasn't about to let a dirty green skin just go back to the grove and tell it that everything was gonna be alright, so instead, she sent with us an elven assassin, one of the strongest players on the field. His reputation sort of preceded him, since we had heard from other players not to get tangled up with him specifically. Like, hey, don't listen to that guy. That guy smells.   Needless to say, he seemed like a great guy, and we were happy to have him. We made our way back to the grove. Stab murder, McNifeers, and Toe, and the grove just looked at us with a grovy visage, like, what, where's the druid? Upon telling it that the druid had taken a long fall off a short sloop, the grove decided, well, beggars can't be choosers, and declared our shaman companion as its new caretaker. However, this did not sit well with the assassin, who, as it turned out, had came along as insurance against this exact scenario, and so he handled it the way all assassins like to handle things. In just a few blinding quick motions, he silently killed everyone but our shaman, who had entered the grove's circle already, and so no one without permission could enter, like it was nature's dirty VIP room. Of course, being completely new to the game, our shaman player didn't fully grasp that concept, and so the assassin capitalized on this by challenging the shaman, which the shaman accepted. Immediately, the assassin yeeted his way into the circle, and struck down our shaman, TPK'ing the party and doing the Fortnite dance over our graves. Afterwards, the assassin decided that if his people couldn't have the grove, no one could, and he buried our bodies within the circle as a sacrifice, so that he could perform a ritual to dismiss the grove and have it go back from whence it came.  In one last show of total bro-iness, the grove decided that we were way too high in saturated fats, and spat us back out into the forest, reviving us in the process and leaving our mouths filled with dirt like we had just filleted a molehill. We got up, unanimously decided, well, that was weird, and walked off into the sunset to return to the town, ready to continue our LARP adventures wherever they may take us. So, yeah, that was my very first experience at a LARP. There was drama, romance, bloodshed, and everything I love about D&D, but in real life. I now LARP whenever I get the chance, usually at least once a month, and it's honestly my favorite thing right now. I'm always looking forward to my next event. I'm even planning on, in the future, maybe making a small series covering the in-and-outs of LARPing. I hope this influences you to maybe, I don't know, give LARPing a try, but yeah, to have you out.


Hello students, I am Deepak Maslaker working as an assistant professor in the Department of Mechanical Engineering at WIT, Solapur. In this session we are going to look at the solution of differential equation by weighted residual method. Here are the learning outcomes of this session. So at the end of this session students will understand what is weighted residual method, what are the steps involved in it and we will try to solve one example problem by using weighted residual method. So weighted residual method is a method, weighted residual method is a numerical method which is used to find out the approximate solution of a boundary value problem. Here is a problem statement. So here you can see the problem, the differential equation is given d square y by dx square plus y plus x equal to 0 and the domain is 0 to 1 and these are the boundary conditions y of 0 equal to y of 1 equal to 0. So we are going to find out the approximate solution of this differential equation by using Galerkin's weighted residual method. The first step involved in the solution is assumption of trial solution. So let us assume a trial solution. Here is our trial solution y of x equal to a0 plus a1x plus a2x square. So the thumb rule is that number of constants involved in the trial solution should be more in number than the order of differential equation. So we are trying to solve second order differential equation and I have chosen three constants here a0 plus a1 a0 a1 and a2. Let us apply the boundary condition over this trial solution. So first boundary condition is at x equal to 0 y is 0 and if I put these values in equation number 1 I get the value of a0 a0 equal to 0. So please remember I have assumed trial solution and this trial solution contains number of constants which are one more in number than the order of differential equation. That is the order of differential equation is 2. So the trial solution contains three constants. If the order of differential equation is 4 then you have to incorporate five constants in the trial solution. After applying first boundary condition let us apply second boundary condition and the second boundary condition is at x equal to 1 y is 0. If I put these values in equation number 1 I will get a1 plus a2 equal to 0 because here a0 is a0 that already we have determined and I can simplify this as a1 equal to minus a2. So till this moment we got two values a0 equal to 0 and a1 equal to minus a2. Now putting the values of a0 and a1 in equation number 1. So after substituting values of a0 and a1 in equation number 1 what we get y of x equal to a0 that is 0 plus a1x but a1 equal to minus a2 minus a2x plus a2x square. So after taking a2 common I will get y of x equal to x square minus x equation number 2. Please remember equation number 2 is the approximate solution of differential equation and this is called one parameter solution because this equation contains only one unknown that is a2 therefore this solution is called one parameter solution. Now in the second step I am defining weighting function and this weighting function or weight function is w of x equal to dou y by dou a2 that is partial derivative of y with respect to a2. So if I differentiate equation 2 partially with respect to a2 I will get w of x that is equal to x square minus x. So in the second step I have calculated weighting function or weight function and how to calculate it just by differentiating the trial solution with respect to the unknown parameter. Once we get the weighting function we have tried to find out domain residual and this domain residual is nothing but the left hand side of the differential equation that is rd of x equal to d square y by dx square plus y plus x. This is our left hand side of differential equation. Now substituting the value of y from equation 2. So from equation 2 we have y equal to a2 into x square minus x plus y and here is the value of y y equal to a2 into x square minus x plus x. So after taking the second derivative of this quantity I get 2 into a2 plus a2 into x square minus x plus x. So here is the value of domain residual and the fourth step is minimization of domain residual. So in order to minimize the domain residual in overall sense I integrate the domain residual multiplied by weighting function over the entire domain and this integral should be zero that means in overall sense the error should be zero over the domain. So substituting the values of wx and rdx here is the value of wx here is the value of domain residual. Now expanding these brackets I have expanded these brackets x square minus x into first term plus a2 into x square minus x into second term it becomes x square minus x whole squared plus x into x square minus x dx. So I expanded this bracket. Now after expansion let us carry out the integration and if I carry out the integration I will get like this 2 a2 into x cube by 3 minus x square by 2 plus a2 into x raise to 5 by 5 minus 2 x raise to 4 by 4 plus x cube by 3 between the limit 0 to 1 plus x raise to 4 by 4 minus x cube by 3 between the limit 0 to 1 equal to 0. Now imposing upper and lower limit x equal to 1 and x equal to 0. So if I substitute these values I will get 2 a2 into minus 5 by 6 plus a2 into 1 by 30 minus 1 by 12 equal to 0 and adding the terms of a2 a2 is taken common and if I add these 2 quantities minus 5 by 3 plus 1 by 30 I will get minus 49 by 30 into a2 minus 1 by 12 equal to 0. If I simplify this expression and extract the value of a2 I will get a2 equal to minus 1 by 12 into 30 by 49. After solving this after simplifying this I will get a2 equal to minus 5 divided by 2 into 49 and a2 equal to minus 5 by 98. Now putting the value of a2 in equation number 2 y of x equal to minus 5 by 98 into x square minus x or we can write y of x equal to 5 by 98 into x minus x square. This negative sign is absorbed inside the bracket. So in this way we can find out the approximate solution of a differential equation by using Galerkin's Wetter residual method. So please remember the steps and please try to recall the steps. The first step is assumption of trial solution and once we assume the trial solution we apply boundary conditions and find out the constants. The second step is finding the value of wetting function. Wetting function is the partial derivative of trial solution with respect to unknown parameter. In the third step we find out domain residual and in the fourth step we go for the minimization of domain residual. By operating these four steps we can obtain the approximate solution of a boundary value problem. Thank you.


Good morning and welcome to the 11th meeting of the criminal justice committee. There are no apologies this morning, and the first agenda item is to agree whether to take items 2 and 3 and any subsequent draft reports from the committee's recent ground table evidence sessions in private at future meetings. Are we all agreed? Thank you. We now move into private session, and our next meeting will be announced in the business bulletin in due course.


I grew up in the South, so I'm attached to Southern themes. I love the idea of redemption. And I figured I'd write about an old cowboy type character who played guitar and sang on stage, and something happened to him that he had to redeem himself for it. That was the original idea. And there was a Hank Williams senior sort of theme floating around in my head. I'm a big Hank Williams senior fan and follow his story. It's pretty amazing. And then I realized I can't play guitar and I really can't sing. So let's figure this out.


On Tuesday, October 17th, the East Kentucky Strong Forum was held at the Appalachian Wireless Arena. The goal was to teach high school girls about self-worth and the opportunities they have here in the region before going to college. Mountaintop News spoke with East Kentucky Strong committee member Patricia Collins for more details. Patricia Collins – We want the girls to know and to get from this event that they are strong and that there's no more glass ceilings, that they can do and anything they want to do when they look in the mirror. We want them to see someone who is strong looking back at them. They can be whatever they want to be. We want to instill confidence in them. We try to find guest speakers and presenters from all areas of life that can give them examples that they might could find a role model. Appalachian Wireless is making it so easy and affordable to stay connected to friends, family and the world. With the Forward Pay Unlimited or Unlimited Plus Plan, get $50 off any Forward Pay device. And don't forget, with Forward Pay, there are no credit checks or long term contracts. It's Forward Pay on the region's premier network, Appalachian Wireless.  We are Appalachian Wireless. Activation fee required, just kind of apply that point of sale. Numerous guest speakers and presenters were invited to share their experiences. The students were also able to learn about potential career paths during the event. It was great to see some of the post secondary schools here showing them that electricians and stuff that you would normally think would be a man's job. Those lines have been blurred and a woman can do anything that she sets her mind to, whether it's coal mining or electrician or climbing the electricity poles. What it is that a woman wants to do now, we want to encourage these young women to set their goals and work to achieve them. I tell the girls, you know, life is hard and there's a lot of times it sucks, but it's up to us to make the best of that and overcome and get stronger. And that's the whole thing, no matter what we go through in life, emerging stronger on the other side. Reporting from Outantop News, I'm Nick Colum.