Hey guys, it's Nate, aka The Foot Accountant. Welcome back to the channel. In a crazy turn of events, guys, we have gone from one of the best footies menu grinds ever to basically being left with nothing, and our favorite SBCs, the 84 times 10 and the 85 times 10, being gone. EA removed them from the game yesterday, and boy, do we have to talk about it because there's, I worry. I really do worry about this situation, guys, because EA take a long time when putting SBCs back into this game, and that is exactly what they have to do very soon to keep this promo alive, or else this last final fun week of footies is going to kind of be ruined. So we have a lot to break down today, guys. We're going to take a look at it all and possibly what's going to come out today on Tuesday for content. If you're excited for the video, drop a thumbs up on it, and of course, subscribe if you're new. Now, let's start off with some content that was dropped yesterday that actually is still in the game. We're going with an 80 plus player pick that we knew was coming. It gets you XP. Make sure you do it at least once, or however many times you need to do it to get the XP. It does require 10 golds, which in my opinion, is an L. But there's other Ws from SBCs. Silver and bronze daily upgrades are back. You can do them 10 times per day. It's absolutely incredible, right? The requirements are the same. You still get the same crazy amount of bronze and silver players from those packs. Now, the only problem is, these SBCs, they're out for 24 days, and now it feels like these SBCs are ahead of the daily gold upgrade, right? The whole point is you do the daily bronze and silver to rinse into the daily gold that gives you 11 players. This goes away in three days. So this goes away on Friday. If this does not get refreshed, then there will be a lot less ability to grind with the other bronzes and silvers, or the grind won't seem as good. So hopefully they refresh that, and of course, that would mean hopefully they refresh the crafting upgrade and maybe give us more crafting objectives during preseason. But it's just nice to have those back because it does at least help you get gold cards a lot easier with the bronzes and silvers that you can turn in for other SBCs and all of that. Now, also yesterday, we had the 40s daily dip, which actually, guys, this objective is repeatable. So it's kind of another way to get gold cards in your club. If you win a match and rivals or footchamps, score five goals and then play three matches. Every time you play three, this resets. You get new coin boosts. You get 11 gold players packs and an 81 double. So the rewards seem kind of eh, but it's also repeatable. So that's kind of cool. And then we did have a player SBC yesterday. It wasn't Cassius, though. We had a footies Odegaard. Again, no leagues. Just surprise. Honestly, 505s are Odegaard.  I'm not going to complain too much because this is a pretty easy SBC to complete. Of course, if we were able to get the 4x10 back, we could do it for free. How much did Arsenal have to pay EA, by the way, to get this SBC? Because I feel like it's been forever, that we had an Arsenal SBC card. And of course, Arsenal does have the deal with Pez, which we, of course, think why Arsenal cards have not been juiced that well. Remember back to Premier League Tots where we had all the Arsenal cards in, but their stats weren't that good. We think there may be a little bit of rift there between EA and Arsenal, but I don't know. They at least got an SBC, so if you're an Arsenal fan, GGs, decent, of course, with the craft that we have. Now, let's get into the big situation because this is dominating the topics of conversation right now on Ultimate Team. The 84x10 and the 85x10 were both dropped on the game yesterday. And you can tell by the upvote and downvote percentages on a footman that even though these are no longer in the game, when they were first dropped, people were not very happy about these. Right? Because instead of just getting re-released with the exact same requirements, they dropped them with new ones. They dropped the 84x10 with an 88 rated squad instead of an 87 rated squad. So a slight change there. But they dropped the 85x10 as a two-squad SBC. So like it was when it was originally dropped weeks ago, but not how it was when it was last week, just one singular 88 squad. So it was two squads, which was way more annoying than one squad. So right away people went to Twitter, people went to, you know, everywhere to voice their unhappiness, right? And I was one of those like we were all on stream looking at these SBCs and we were like, uh, that's horrific, right? Like why did they make the 85x10 two squads and why did they make the 84x10 more expensive? So there's immediate backlash and rightfully so, right?  The little kid has the toy, they're enjoying it, they're playing with it, and then somebody takes it away. And aw, nobody's gonna like that, right? That's exactly what feels, uh, that's what it feels like EA has done here. They've taken our toy away, the 84x10 and the 85x10, now they're gone. I mean, they were more expensive and people were disappointed, but at least we still had them. Now they're nowhere to be found as of yet. Right now they're out because EA have said there were issues with their requirements. And this is honestly kind of interesting as well. We have temporarily removed the 85x10 and 84sBCs due to issues identified with their requirements. Now we've kind of started to think about what issues these may be. Is it number one? Did the community just literally body EA, big body EA to saying, okay, we're not gonna play your game as much. You messed up these requirements, so make them cheaper. And that was the issue. Or some people think the issue was the individual packs inside of the 85x10 when it was first released like a couple of weeks ago from a two-squad segment were tradable, and this time they were untradable. But I think it's more of the first one, guys. I think that everybody voiced their opinion and, I mean, discontent with the content yesterday. And EA said, wow, nobody wants to do this. They probably went on a foot bin and saw the 93% download and the 96% download on the SBCs. Now I'm just kidding. That's kind of funny. And they said, all right, we got to pull it back and we got to fix it. So they've done that. But now I feel like we're at an even worse spot than we were with even more expensive SBCs out. Even with the 84x10 being an 88 rated squad, it was still repeatable. Yeah, you wouldn't get as much fodder because you maybe had to turn in one extra special card each time because the rating was a bit higher. But it was still grindable and it was still the menu grind that we were used to. It just wasn't as good as before. And this is where the real worry comes in with this, guys, right? Again, you read this tweet. Every time EA tweets out something and it says the coming days, we just sink, bro. We're just like, oh, no, like this ain't going to be coming days, man. This is going to be weeks, right? This is going to be a long time. And that's the worry that we have right now. They've taken the SBCs away. It has been approximately six hours since they have taken them away. And there are no SBCs to be found in this game. And to me, I'm worried not just because of, oh, what if I turned in fodder to those SBCs? Am I going to get it back? Yes, EA said in that tweet, they're going to be giving back to fodder. What I'm worried about is the longer that this goes on, the more the game loses hype because right now I have no packs in my store. Right now I have very little motivation to grind the menus to do the 90 plus to try to go after the 99s. I haven't done Lothar yet. I still haven't even done Erling Holland. And I have a lot less motivation as I'm sure a lot of you guys do too because that grind is no longer there. So I don't know when they're going to come back guys. That's the problem. I hope and I think EA know the gravity of the situation, right? Obviously they evaluate their game. They see what SBCs people are doing and they know what SBCs we want to do. And these are the SBCs that we want to be doing right now. And the fact that, you know, they've been out of the game now. However long they're out of the game, they might come in back really soon. And this is all going to be over and fixed. Well, hopefully if they release it back, all we want them to do is release it back with the requirements that we had last week. Literally just hit the copy pasta button and bring back the 8410, unlimited repeatable with an 87 squad and the 8510. Sure, make it an 88 rated squad. And even if it's going to be 10 times a day, just bring it back with the same requirements. That's really all we were asking for for this last week of footies because guys, this is right now. This is going to be the most fun week to grind on this game for at least three weeks because the thing is when a preseason promo, which is what we would assume to be starting this Friday comes out, it's probably not going to be a promo that has 200 special cards impacts for the best of it's probably going to be less than that. EA like to bring it back down and they'll build it back up to maybe having that many specials impacts later on. So this week and this last week, what we've had is probably the most fun that we were going to have on the rest of this game. That's just me being completely honest. And I wanted to finish this week off strong. There's so many great SBCs still available to do. So many cards to pack. So hopefully it comes back guys. I hope it comes back today. I could very well see it dropping at content time today. Fingers crossed that it does. But also guys, I mean, it could drop at a random time. Like EA has had situations like this before where they just gone right back out and dropped the SBC like four or five, six hours later. Sometimes, you know, maybe it will happen early today on Tuesday. Maybe it'll happen like we said at content. Maybe it'll happen in the middle of the night between Monday to who knows, right? We have no idea right now. We're just in the limbo phase and we're waiting because they said temporarily removed. So that would give us hope that it's going to come back now. Remember that five times per day, repeatable tots pack that we had earlier on during team this season, they said they were going to bring that back to and never did. So I think they'll bring this one back. It just kind of depends on when and the longer that we go without it. I mean, the more disappointing that it really is now, crazily enough, since there's so much to do on this game right now in so many SBCs, since this SBC, all these SBCs have gone away. Look at fodder. Harry Maguire 95 rated card. If you take a look at some of the highest rated fodder cards in this game, they're actually rising. Look at this 95s were about 14,000 coins yesterday to start the day off and 14 K for Maguire all the way to 18,000 coins. If you look at all the 95s, 17, 18, 19 Ks where all these cards are at, even 94s were basically discarding pretty sure at like 11 to 12 K and they're even starting to rise up now. As you can see, right? The graph just kind of slowly goes up because the SBCs are gone and people have halfway completed Erling Hollins to do. So they're just going out and spending coins for the first time in a long time to get some of the SBCs done. So the longer the SBCs stay away, the longer that's probably going to continue. I'm not telling you to go to invest in fodder. I'm just telling you that's kind of what's happening on this game right now because of that. And I haven't taken a look at a lot of the rest of the cards. Like, is this messy up a lot? 732 K. Where was he yesterday? Messy. Oh my gosh. Messy's up 100 K guys. He was 630,000 coins and now he's 730 K. I mean, even he's still in packs, but the fact that there's no tradable packs that are hitting from the 85 times 10 or I guess not with the 85 times 10, but like the 90 plus player pick and stuff like that, that you get tradable packs back from doing multiple segments of all those SBCs or even if you're doing Matthias or Holland, all those SBCs give back tradable packs. Wow. Like his card is going up a lot. That's pretty crazy. I would have to imagine that it's happening on other places on the market as well, just because of, you know, there's not as much supply coming in. It's really just killed the grind on the menu. So hopefully it does not last too much longer because I wanted to grind out this week, man. I wanted to do more SBCs and player picks, and I know a lot of you guys did too. So let me know your comments down below. We talked about that for a long time, but that's a massive thing that's going on right now on this game and it needs to be fixed. So it just means a lot less hype on the menu, guys. And I really think that for the rest of this week, if nothing changes, it's going to be like footies is ruined, honestly. That's what it feels like at the moment. Now today's content, let's get into this really quickly. 87 plus player pick is expiring today. That's one of the only SBCs that is going away. And I just think it'll come back, right? I mean, maybe they make it 88 plus. I don't know. And they made it unlimited repeatable last week. Probably they'll do some of the same thing this week. I'm not expecting too much in that sort of things. And of course we have to give out our daily cover star Cassius shout. Still haven't seen his SBC yet. He's still leaked. And then maybe today on Tuesday as well, we'll get a last, maybe we'll get the last foot champs bonus objective. Maybe we won't. Who knows? Because the season is ending. This is a big week for the season ending as well. Two days until it ends. I have not given too much care to this season. As you can tell, I'm still level 26, 27. So I'm definitely not getting to level 40. There might be a tiny bit more of XP to come out, but probably not too much. But watch out for a foot champs bonus today as well. And then guys, I do want to spend the last bit of this video talking about some leaks because we're starting to get some ratings leaks, guys. And yesterday, we got some big news. All right. Shout out to foot scoreboard and crew in El FIFA for FC24 official ratings leaked by foot scoreboard. I think he's got the info here. He's tweeting on a lot of this stuff. We're getting 10 ratings per day on the countdown from the top 50. But yesterday, he also tweeted out Christiane Ronaldo and Lionel Messi's official ratings and stats for FC24. Messi's still getting 80 pace, getting a minus one and a very small downgrade. Again, great, usable looking card, 90 rated. But man, did they cook Christiane Ronaldo. 77 pace and 88 shooting. And the stat I want to look at the most is 79 dribbling, guys. 79 dribbling on Ronaldo's minus six. And just to be clear, you might remember that last year at the start of FIFA 23 as well, EA really downgraded the ratings on Messi and Ronaldo, especially in the pace category, right? If you look back to FIFA 22 Ronaldo, this is where we have gone in two years for Ronaldo. We've gone from a 91 rated card with 87 pace, 93 shooting and 88 dribbling, right? Remember those stats, 87, 88 and 93. Look at his card that we're getting this year. 77 pace, 88 shooting, 75 passing and 79 dribble. We have dropped 10 pace stats in two years on Christiane Ronaldo. It's absolutely wild how much EA have downgraded him. And again, the reason they're doing this, guys, is because yes, they're getting older, right? EA is kind of putting that into their power curve and also trying to emulate the stats in real life. But one thing I'll always say too, and we said it earlier, is EA likes to downgrade the stats on gold cards almost every single year because it gives them more room to give upgrades throughout the rest of the year. And I still think Ronaldo, Messi, they're going to get special cards in FC 24, but it's more still the memes and honestly just kind of like it's really setting in that it's truly the end of a goat era with Messi and Ronaldo and new guys are taking over that throne. And it just kind of, it's painful to see in a FIFA sense if you know what I'm saying. So that's crazy that Ronaldo is 86. I feel like it's maybe a bit harsh, maybe 87 or 88 would have been a little bit better. But I mean, wow, still going to be usable at the beginning of the game. No doubt, probably going to be five-star skills still. I would imagine four-star weak foot. Messi's card looks usable as ever. Again, both are going to be a little more difficult to link. Ronaldo will be easier to link because of more people in the Saudi League with all the transfers to link him to, but crazy, right? Crazy with those ratings there. And then if the scoreboard posted another set of 10 players, I would expect 10 more today. A lot of women's players in this set, ratings 31 to 40 in terms of the highest rated cards in FC 24. Guys, two cards I want to point out here. Valverde, Hullet Gang base gold card. That is nuts, okay? That's the card that we're all going to be chasing for in the early game to get into our midfields. That is a nuts-looking card for Valverde. Also, Ocean Man, Osman, right? With 90 paces and 86 shooting, massive plus-five upgrade for him. And the rest of the ladies' cards in here, that being it could end up being really with the cracks and people think she might be five-star skills. Giro Retin, 88 paces, 80 shooting, 86 very well-rounded card, a lot of 80 stats in a left-mid, left-wing position there.  They don't look that usable. The goalkeeper could be pretty usable. 90 reflexes, only 40 speed, though. Debenia looks the most usable. And maybe Guijaro from Barca, the women's Barca team. Looks like a pretty good box-to-box midfielder. So we're just going to see how these ratings continue to get put out. But definitely that Valverde card from that leak yesterday looks absolutely crazy. So we're going to talk about ratings, like I've said, more and more in the future as we get closer and closer to FC 24. But that's kind of what we're looking forward to today on this game is more leaked ratings. So watch out for those. I think they're going to be tweeting out 10 every single day. And hopefully EA Sports release the 85 times 10 and the 84 times 10 with the correct prices. Don't mess it up. In August, basically September, give us our grind back, please, EA. All right, guys, thanks for watching the video today. If you did enjoy it, put a thumbs up on it. Comment down below if you have any questions. And of course, subscribe if you're new. It's been Nathan with Accountant. See you guys in the stream today. Peace. Out.


My name is Dr. Farhan Puzzle. I am an infectious disease specialist. Today we are going to discuss about dengue fever. What is dengue fever? This is a viral infection which is transmitted by a mosquito bite. What are the symptoms of dengue fever? Symptoms can be ranged from a simple high-grade fever with rashes, body ache, joint pains, pain in the eyes, pain in the stomach, some kind of nausea, vomiting and some diarrhea. This happens in most of the cases, but there are chances and possibilities that few of the patients could have severe forms of symptoms like giddiness, seizures, unconsciousness, breathing difficulty, chest pain, abdominal pain and bleeding from various sides that is from the mouth or while passing urine or while passing stools. Now these are not common in all patients, but they can occur. I want you to deal with something specific like what is the natural history of dengue infections? Usually between two to seven days is the time it's called the febrile phase, but the patient will have fever. You need to understand that patients who have fever on the fifth or sixth day could still be having fever because of dengue itself and they require only monitoring. The next phase is the a-febrile or a critical phase. That is two days, that is 48 hours after they become a-febrile is a critical phase where all the complications can occur and after that it's a convalescent phase. You might be noticing a lot of patients after having dengue, complain of aches and pains and tiredness. This is also a part of dengue fever. What are the special kind of people or population which require care especially in dengue fever? These are pregnancy, small kids, patients who have renal problems, kidney problems, liver problems, heart problems and old age. These are the kind of patients who require special care and attention because these patients can develop complications much more rapidly and are much more commonly seen in them. How do we diagnose dengue fever? This is done by a simple blood test which will tell you depending on the duration of your fever what kind of test have to be done. So depending on your fever period you will be taken given a specific blood test which will tell you the dengue fever. What are the treatments that are available? There are no anti-varyl, anti-biotic that will help in dengue fever. It's a simple infection which is treated by water drinking simple fluids and paracetamol for the fever. Only when things get complicated and in special populations do they need to get admitted in the hospital and be monitored carefully for their platelets, blood pressure and other vital parameters. Lot of queries come into when do we transfuse platelets? Platelets according to the national guidelines have to be transfused when the platelets go less than 10,000 or if there is any major bleeding from any other source. How can we prevent dengue infections? Dengue can be prevented by simply clearing the waterlogged areas in and around our houses because mosquitoes breed in stagnant water. Also to prevent mosquito bites we need to wear full clothes and also use some kind of mosquito repellents. Don't worry when you have dengue infections. Get in touch with your infections specialist and know more about it. Not all of them require admission and not all of them require platelets.


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We are going to be back again this year for a recognition of the Georgia Lionwood Appreciation Celebration since these gentlemen and ladies have been standing for quite a while. I will take them out of the barge at 40. Let me just say at the outset thanks to the members of the General Assembly who have taken the initiative to make this recognition possible. All of the elected officials, the two Constitutional officers who are with us here today, to the chairman who sponsored the bill that I will be signing in just a few minutes, and to his counterpart in the Senate, St. George, for carrying this very, I think, very important piece of legislation. I, too, have a population. It is in the middle. It appropriately recognizes why we are here. And briefly to say to those who are behind me and others of you in the audience who share myself, we thank you for what you do on a daily basis. Not just to maintain the flow of electricity and other services more and more, which of course are being transmitted and required that somebody be able to climb that pole in order to keep all of those other services operable as well. To those organizations, some of them have already been recognized, who have come together to support this endeavor today, and to you, they are your employers, by the way. Thank you for the fact that they would take time to recognize this workforce. The proclamation has already been appropriately framed, so I won't go over it and do anything really that will do it with pictures in just a few minutes. But let's talk about one of the real reasons we're here today. And that is legislation. It is House Bill 767. Chairman Powell is the author of that in the House, as I indicated. And what it does is it designates that utility service vehicles come under the coverage of what was originally the Spencer Cast Law. That means that anyone who is confronting a service vehicle is required to move over, if at all possible. If they are unable to move over and change lanes, they are required to slow down. And that, of course, is a safety feature. Nobody appreciates what these gentlemen and lady vision, as much as when natural disasters occur. In rural parts of our state, which is where I live for all of my life, when the lights go out, after a given period of time, my wife is going to say, why don't you go find out where the problem is? And so for all of us who have been in those situations, depending on electricity and not being there, I'm going to ask the members of the General Assembly, and if they would join me behind the signature table here, and I will sign House Bill 767 in the law.


Hi, and welcome to the session. I am Deepika here. Let's discuss a question. Find the intervals in which the following function is strictly increasing or decreasing. x squared plus 2x minus 5. We know that f is strictly increasing an open interval a, b. If f dash x is positive, that is, it is less than 0 for each x belongs to an open interval a, b. And f is strictly decreasing in an open interval a, b. If f dash x is less than 0 for each x belongs to an open interval a, b. So this is a key idea behind our question. So let's start the solution. Given fx is equal to minus 5. Therefore, f dash x is equal to 2x plus 2 and this is equal to 2 into x plus 1. Now, f dash x is equal to 0 implies x is equal to minus 1. Hence, x is equal to minus 1 divides the real line into two disjoint intervals, minus infinity to minus 1 and minus 1 to infinity. Now, for x less than minus 1, our f dash x is equal to 2 into some negative number and this will be negative only. This implies f dash x is less than 0. This implies fx is strictly decreasing for x less than minus 1 and for x greater than minus 1, f dash x is equal to 2 into some positive number and this will be positive. This implies f dash x is positive or f dash x is greater than 0. This implies fx is strictly increasing for x greater than minus 1. Hence, the answer for the above question is, function is strictly decreasing for x less than minus 1 and strictly increasing for x greater than minus 1. So, this is the answer for the above question. I hope the question is great to you. Myam, take care.


I think I am live with my YouTube and live streaming. Hey guys, we should be live on interesting. Hey guys. Can you guys hear me? Today we will talk about PM internship. I think my team linked to a different chat. If you can see me live, please come on the chat. Just say hi when you're from what's your name. Interesting, I think there might be some tech issues, one of the ones you guys can see me live. I think I am live. You can see me live, please make sure to come on the chat to say hi. And at the same time, let's play a countdown music to get started. I can see a chat. So it looks like we are live in terms of technology. Okay, alright, hey guys. If you can hear me coming on the chat and something crazy happened today, very funny. We lost power, so I'm not immune today. Come from with me see if you can see. Meanwhile, and also can hear me while because in the cafe, there's some noise. Come on the chat. Can you hear me well? I'm so dedicated for this YouTube live and I actually went to a cafe to make sure we can run this. I almost canceled it. Maybe I should go to the cafe. If you can hear me well, come on on the chat. And also whoever joined us, please make sure come on the chat what's your name where you're from and what was the last time you worked out. So I'm very proud to report. Actually, yesterday I worked out very happy and actually the cafe is in my gym. Even if we have power, the gym always have power. So I'm very happy and we have internet power so we can share with you regarding what the best strategy for you to learn your program and internship. Okay, and also later say I also have a private event with my students talking about PM internship. And I hope all of you guys are able to use very similar strategy to learn your dream can internship as well. So let's see who else is here. Phoenix, how are you? Shankir, and how are you? Hello, it's from India. What time is it in India right now? It's pretty late, must be like 2am. Radha, how are you? Hello, hello from LinkedIn messages. Welcome, welcome guys. So today's talk is about PM internship. Now let me do this very quickly and regarding the PM internship something I do want to share with all of you guys regarding the best methodology to become PM interns. So now let me do this. Let me quickly share my screen once we get started. And also for people who join us, feel free to put your questions on the chat regarding what's your best questions or strategies or confusions regarding many of dream game internship. Of course there's lots of new up there if you want to share with all of you guys regarding internship to say many interesting observations I have seen in the market right now. So let's get started and let me do this. Let me share my screen. Let me share one tab. So let's focus on our main topic about PM internship today. It's very important for everybody. If you already made a PM internship job offer, congratulations. If you haven't, you really need to pay attention to today's specific talk. Okay, we only have a few weeks left before you now the internship offer before the next cycle start worship in the spring. Okay, now specifically for PM internship. First of all, I do want to share with you some like inspiring stories and maybe news and actually Let me tell you a story regarding PM internship and also happened to our students them as well. So currently our students them are ready to receive an offer from Microsoft as a PM intern. And now our student Anna recently also received the PM like the intern job offer within two weeks as well. Now let me just really share with you regarding how they did it. And in later on tonight, my talk to the NYU student exclusive event I'm going to share with Anna's resume in those inclusive events where you know how to write a resume, specifically with like screenshot of a resume so you can use the same strategy to craft your resume as well. But in today's general talk right now. Let me also share with you how Anna did it. So Anna her background is computer. Factory degree in math and econ. She doesn't know how to code at all. But she's someone who is very determined and takes things very seriously in terms of job hunting. And she was able to make her first PM internship within two weeks. And today I'm going to share with you how exactly she did it in a high level she's deploying. Number one thing is that she's a neprosy strategy to identify those opportunities. Number two, she also started to rewrite her resume completely use a new template. Number three, she also started to build your portfolio to gain experience show up a relevant experience as a part of manager. Okay, so I'm going to walk through all those three things today. I want all of the guests that came internship it's possible, because right now we all know. Twitter just announced layoff they lay off half of the employees and very friendly guys every single week that people reach out and you say hey I was layoff Nancy I don't know what to do. What's the best strategy and I'm supposed to an internship offer right now but right now I don't even have an interview something is very wrong. Right, so lots of people very, very free cows regarding this new environment what they can do. And so therefore I want to get to take lots of notes if you don't have PM internship by now, you should be worried a little bit and very, very, very serious. Okay, but there's still some. That all opportunities that we need to tackle today. Okay, so now let's continue. Sharing this we don't need to share Eric story we can do it next time and now it's quick question anybody who have upcoming interviews. You should go to our website documents that comes to 50 fans to download your 50 fan into the question database, so you're able to use the same real life into the questions to get ready for your upcoming interview in my big fan companies or tier one companies okay all those questions are very similar, especially for tier one company so use this website.com to get ready for upcoming interview and anyone who can join it for free coaching. In the description of this video I might team already put a link where you submit a form to quickly put in your email information and request the zoom link to join me live you want to join me live right now to receive free coaching you can email me as well. I'm going to put my email in the chat email Nancy darknessy.com. And then I can put you into the zoom right now so let me put in the chat for anybody who want to join me live. Okay, so let me. What's that let me put it here. So it's yeah 145am in there right now I'm very dedicated so anyone who want to see the. Yes, anyone who want to do the live coaching with me right now join me on zoom email me right now and the email title should be YouTube live zoom link YouTube live zoom link okay then I can put you to join me live right now. Now let me do this let me go back to let me mark in my email. So that everyone who joined me I can see your email just make sure it's YouTube live the link and then I can directly. Put you up okay great so just check. Email quickly awesome awesome. And now let's do this let's continue my slides and those with the internship profits very good advice.  I want all of you guys to whoever donate in nonprofits will help me to achieve my nonprofit vision you can receive free coaching from me as well so email me if you support any nonprofit. We do one one donation matches which means you donate $1 more than $1 as well and forever has the most lives comments and shares of my YouTube. or Instagram or LinkedIn content is going to get invited for free coaching for me as well. Okay, so anybody who is interested in PMS editor and you should go to this website. documents.com slash master class to learn more about our training program and let me also go here so we have a training program will help people blend the dream team job offer it. Fem flash companies and unicorn startup. If you want to speed up your success, you should go to this website documents.com slash master class and step one to learn about different kind of services. Now, there's also three groups I want you guys to take a screenshot right now, which are group and they think groups, you're able to find lots of people that's very similar background like you to do marketing to view so go here and start to find a marketing to go partner to find the body and communities. That's very critical to continue to grow your career. Okay, so now, let's talk about internship. I'll have some questions here. Need help in resume review and elevate the page. I'm not getting any response. Okay, so if you already send me a question we go for pre submitted questions. Okay, but at the same time, let me give an overview regarding internship and the strategies. Let me stop sharing. Stop sharing. Stop. Okay, so yes. Now, let me give you an overview regarding if currently looking for p.m. internship. This is what you need to do. Number one is that you really need to understand the timing for different type of companies. Number one thing most important thing for fan companies, and you already missed it at that time. Most of us are already received an offer from a fan company right now for the p.m. internship. So the offer is out if you're still in the interview process with fan company you're towards the later rounds of the interview with fan company is likely you can still receive an offer but if you're at the beginning with fan companies and you haven't received any interview with fan companies is likely the position filled already. So which means that you can target other tier one companies such as Tesla. I believe Tesla just opened the p.m. internship opportunities like two weeks ago to target those companies and look around. And whenever you apply for this job. The first batch whenever they suddenly open those positions is when it's most likely you will be invited for an interview so it's very critical get ready for your interview with these companies. Okay, so whenever the open you go in right away for the fan company talk about earlier they open the application in August. Okay, almost all fan company internship in August so you really need to take advantage of the time. Now if you're speaking in November. The other companies you should vote a pay attention to and actually some of the students are still interviewing with like the visa mastercard, like serious exam like different kind of companies for interns. So those are very large companies they're still hiring p.m. interns, but they're just not fan companies yet but I still believe that those companies have great potential very large organization and there's lots of things you can learn in those large companies. So pay attention to those big companies. And I forgot to do my background choose virtual background. This one. Yes, okay great. Now, except the fan companies, the second time frame you need to understand is that the p.m. internship time, they, you can still apply for tier one company large company until November. And there's still lots of p.m. interview opportunities in the middle of November basically anything before Thanksgiving there's still lots of opportunities out there and especially for like non fan company any large companies such as Walmart or Verizon. I was working for Verizon like many years ago we're doing like p.m. internship in like mid of November right before Thanksgiving. So the still large companies that's available to him internship. But once you hit December everything will slow down so Thanksgiving is a very important mark I want you to hit. Okay, so increase your application volume and also increase in networking strategy land those interviews, very, very critical. And the true is that, once you know the timing is very critical for people looking for p.m. internship, you really need to have your perfect p.m. resume. The resume is very critical. Okay, so because it's very competitive everyone want to become a manager and especially people without experience. If anyone without experience can become p.m. and then which means majority of people without experience will apply so it's extremely competitive. In this case what you need to do immediately is that you need to use the portfolio strategy. Okay, so on your resume. And then you put a portfolio experience on your resume, and that is going to qualify you for relevant experience to put a manager because when you build your project your portfolio, you're done customer interviews you already built customer persona. So all those experience can be written on your resume and because you're competing for p.m. intern, not full time job, when then people compare you with other candidate oh this person already started working on product like project or the different kind of portfolio already know how to cut some interviews and knows how to write requirements. And those are very, very important critical for you to show up to other people saying oh no see this is the best experience I have done in the past. This is how much value it can bring to a new organization because I have done related stuff in the past. Okay so very, very important use the product portfolio strategy to qualify you for those p.m. internship. Now, number three is that on your resume except the p.m. keywords won't hit which is all the like internship or the portfolio experience which we asked you to build you also need to talk about the impact and also show up your transfer skills. For example, also Anna is crazy so Anna's experience is more about she was doing tax her past experience being tax accounting children wouldn't hear to help people to the tax return. She basically the professor, her accounting professor had a side job which is helping people to tax return, then she wouldn't hear for professors to do tax return. It's crazy so no wonder if she wants tax return a little bit off because I You're the freshman students doing tax return for what people like maybe some number and maybe check but we don't know. So basically she's doing a tax return at the internship. So on her resume which means that nothing to do tax return CPA so nothing to do with management right so her best strategy is that she talked about the impact she brought up for the tax return. For example, specifically what she did was on her resume. Let me quickly show you her resume and actually tonight in today's It's crucially talked to and by you. I'm going to share this but now I can share your head of time. Hopefully you're able to learn something from this experience. So let me show you the slide this one. Very funny. So this is her old resume which is doing income tax assistant her old experience right so everything is writing like master lessons software to complete advanced individual income tax report was a okay okay you did tax return and they do volunteer work for tax return I think it's crazy. And then we change the community country on her resume. You see this so experience like college experience, the new experience we call this internship leadership. Aha, the description is different immediately. And then she also talked about the actions she did collective organize and updated different information so those are very action driven for her new job at the manager intern as well because you need to collect customer voice of customer interviews with organized requirement many different things. And what kind of tool she used she said she used Excel if some of you guys see cool or any like, like that map anything you should point out or tools and use and then you're also being able to use different kind of percentage of growth she was like oh in the past she said oh I was able to tax return but new one she said I did 40% more tax report than other tax preparers during the season so basically she said she's way more efficient than other people. Alright so I want to use this as inspiration for all of you guys to think about how you're able to rewrite your experience as well. So it's not about describing your experience it's not it's more about what the value can bring to the organization, how much is relevant for the management. And of course, Anna is also part of PM Exciter and she's our program. She's actually like she learned her first job within two weeks she also started to hire three other alumni working for her company. And she also started to manage at the interns as she become even more senior compared with other people she's like doing amazing job was because she knows how to repackage her experience. So it's different and she also started to do part of the photo to show off her skills. Okay that's how she was able to learn like PM internship within two weeks. Okay well all of you guys to start to understand the timing, timing is number one you miss the timing means everything right and number two is rewrite your resume. And number three is good to put up a photo show your relevant experience. Those are very critical for PM interns and number four is also using networking strategies to learn more interview opportunities. And so that's most important thing actually to present the resume in front of the hiring manager. So pitch yourself to hiring managers or directly to referral network. So inside of PM Exciter we have lots of referral network where we teach about how you're able to use our very big alumni referral network and then the interview opportunities in those companies. All right, so let me see any questions I have. It throws a little bit. Diana, how are you doing? Hello. Awesome. Okay great. So, feel free to put your comment in the chat now at the same time. Let me share my screen. And then we review pre-submitted questions. Do we okay we have some pre-submitted questions. Okay let me answer this question first. Diana said how about career transition from design background. Okay great question. So, actually design is very similar to management because you actually work on product mock-up and those why your friends are mock-up is very transferable to the MEP which you will be doing. If you have design background his number one thing you need to do is when you do design, you are using design you must contact customer interviews. Okay, so now once you contact customer interviews how would you be able to transfer that? UIUS design customer interviews are different from product management interview but it did those interviews. So you just need to quickly describe how your past customer interview experience leading to understand the customer pain point. So those are what product managers are doing a new thing in our systems and actually we have student Yichen. Also Yichen she is the UIUS designer and she was able to plan a 2pm job offer fresh out of her college degree. Okay, and you can actually go to our website to learn more about Yichen's background as well so go to www.darkness.com in our testimonial to find people with similar background just like you. So the number one thing regarding customer interview. So number two thing is that if a UIUS designer and actually it's great that in the process of designing your past experience did you do something related to proposing any product features? If so you should put them into your product portfolio. But I believe the most important thing for any UIUS designer to do is actually understand in real life what does a product manager do? How to think as a product leader when you do a different kind of product and then once you know in real life how product manager do customer interviews with the right methodology, how to write a requirement, how to work with engineers. And then you're more confident present yourself telling us so when I was UIUS designer I work very front end regarding product management. So that's something you can talk about your transferable skills. And then number three is most important you need to do the product portfolio and I emphasize many many times. If you have a product portfolio, you are able to increase your success rates significantly because compare with any other candidate. If you don't know what the best strategy to become a product manager and product portfolio is a way to go. Because you're going to demonstrate that hey, even if I have a designer title, but I don't have ABCD background, but I already built product portfolio to demonstrate I can do the job starting from day one. So people train you and people directly say oh I have confidence because she was able to demonstrate her skills before she even come in to do the job. It's much more likely you're able to do the job. Now let me also give you a real life example how I hired like three people in my team. So recently I lay off one people from my team, then I replace a person by three people. So I hire one person and hire three more people. Okay, so how do I select the best candidate is that I make the candidate to do my two homework, each of them did two homeworks. And then I can tell wow this person is very good responding customer messages. And I can tell some of them had really good experience with like influencer marketing, because they'll be doing the homework to demonstrate the experience. And then when I hired them, I know I already hired the best candidate out of hundreds of people I already featured. So your portfolio is the number one thing to demonstrate you're able to do the job very well. Extremely important. Okay, so how do you put a portfolio I have free training you guys should check out. Let me check out the free training. Let me show you free training. Let me go to YouTube channel one sec. YouTube channel right here. Okay, let's go to my YouTube channel right here and then portfolio you put in keywords portfolio. How to build a product manager portfolio to succeed in the product management interview so it's here. So it's right here, so please make sure I have many, many different videos about portfolio so go to my channel and search for portfolio is are here. Okay, so this one is the most popular video about portfolio make sure you watch this and give a like to 636 different likes already. All of you guys need to watch it. Okay, so come here and study this and then you know how to use your portfolio. And of course, inside of PMX Center, we teach people how to be able to put up a photo, hold their hands and teach them what the best methodology and also we've used a product portfolio help them to gain hands on experience. If you're interested in PMX Center go to our website documents.com and learn more. And actually, we're having a live webinar. Next week, I want all of you guys to join those if you are determined to quickly land your PM job offer, especially for people who laid off and trying to figure out what the best way to complete transition management so that's the best strategies in your immediate space. Okay. Now, let me share my screen to you. Let me see do we have more interview or any more questions. Let me do this. Let me share my screen quickly. Right here. See you guys. Okay, great. So, I need help in revenue review and elevator pitch so far I'm not getting any response from the job applied. I believe it's because my resume so it's not, I'm not graduated from the top university or work with any top company that 10 years of experience. Including five years on non IT experience. I believe getting low pay is one of the reasons because I'm getting whatever five something per annual I accept my current role we should package because I tried. Okay, great. So looks like this person has lots of different challenges. So first of all, yes, it's right.  Okay, you apply online. It's crazy someone applied for over 2000 jobs. You couldn't even manage interview because resume is very off. Okay, it's crazy so it's immediately please rewrite your resume. We have an also your 30 seconds elevator pitch because once you write the resume is the next step is to pitch yourself to hybrid managers. So let me show you guys some free training we have. And of course, inside PM a certain we help you to write the resume and swap. So let me show you guys some free thing can get started and and where you can join us for live resume review so did I show this okay so right here, the resume come here. I just watched video is to this two videos. Part of my resume tips and PM resume keywords also to most important videos you just study, starting from this one so in the description of this video you're able to download our Peter, Peter PM PM resume resume right here and that's you need to use build your resume. If something is missing for your resume and now after that you need to watch a PM keywords. There are different kind of keywords we described in this training, and it's going to hit all the keywords in your resume for missing those for sure you are not able to receive any any interviews and afterwards you do a pitch. Now let me also share with you regarding how to get live. Resume review with us you go to go from the computer calm. So go to the website, the services. We have shopping resume and LinkedIn profile so we have a service about this, which will help people with the best strategy to land on interviews in 10 plus companies within four weeks. And so we guarantee if you're not able to land in the interviews after we review your resume and using our networking strategies you're going to get full refund. Okay, so we'll see a month you're able to land so many different opportunities. Okay, so here is how you do live resume review with all of us, and you come here to figure out, like, if you're interested in any of the live resume review with us so come to documents at the time you're able to see. The different services we offer. Okay, cool. Now let me. Let me, let me answer the next question. Great. So next question we have it has to help you really PM a pro program. Yes, the PM a pro programs number one step is that the program is designed help people to land their dream here job offer. The number one thing is that you go to our masterclass, and documents is the consulate masterclass. Once you get here. You can attend our latest masterclass with a lay off lay off survival strategy learn how to land your dream team job in 60 days using different strategy will teach you here so pick the right kind of most suitable for you to own our upcoming webinar. Okay, pick it and you should be set for your upcoming strategy. Okay, so this is how you see this. So let me see any other questions we have. How to make self introduction she asks this question how to make self introduction very good question. Okay, so how to make self introduction is very critical. You need to introduce yourself within 30 seconds so that people will remind remember you. Okay, so for example, right now when I introduce myself as someone who's a founder for manager accelerator. I'm going to introduce myself as if I am Dr. Nancy Lee, I am a director of products and featured in boards. I've helped 100 people land their dream job offer in fan companies and you can start up and continue to get promoted as a part leader. So this is my introduction and then I'll tell them the impact I made right so for you, you should have a different kind of introduction. So the way I structure my introduction is based on the impact I bring and also the credibility again as a part of the right product and also someone who are featured on board. So those are the advantages and the following sentences about impact of 100 people manage your job offer in fan plus companies and you can start up. And, and actually 25% of our offers came from bank company so very, very excited about our phone actually has the highest number of here one company offers with any other company so therefore, and if we determine to end like best offers of the issue check out our website documents we can learn more. So now, when you do self introduction of yourself a job on the purpose is to use a 30 seconds to elevate the page framework, the framework goes like this give you a summary I have years of experience I am dark and sweet I have five years of serious long chain developing technology product give a summary, and then you tell them the most impressive story of yourself so that I heard it gonna fall off the chair. For example, we can. My story came from. If I'm looking for job, my very first story will be, I launched the first. I launched the first smart cities product that helps cities reduce car crashes and, and also the product was awarded as a mayor best practice award, and quickly deployed within 10 cities within six months. The examples telling people the impact I made when I launched this product, which is helping city to reduce crashes and also receive a word and also quickly deploy by cities showing the success of the product I have created. So when you do self introduction, you should think about how you're able to tell impressive story of yourself does relevant for the management. Okay, so I have a free training that want to get to actually watch. Come here. Tell me about your style. Did I share the wrong screen phone. I think I share the wrong of this one, this one.  Now, the latest what I've published tell me about yourself. Okay, so how you introduce yourself. So this video has a live example of how I transform someone else. Tell me about yourself answer into something more impactful and more memorable. I want all of you the same strategy for your own as well. So watch this live training how we transform this person's elevator pitch into something very impressive. I bet my not sure it's enough and job offers because her introduction was very impressive. I'm repackaged by us. Yeah, she started here and there's another video how to tell me tell me about us as a manager interviewer. So I think we should have another summary of the videos we published in the past we should watch this one as well and also give us a moment 931 different likes are ready so make sure you watch this and also help you to gain and grow your career path as well. Okay, so let me see any other questions. Let me see any questions in the chat. I'm doing a one year MBA program. MBA program not got in touch with any company and they said that I won't be suitable for an internship but rather try for full time because of the electrical work. Only from March, I'll be graduating in June. Would you please suggest one is a good time to start applying for four times. Okay. You should apply for full time right now. Okay, immediately immediately the better companies they start to hire right now the big company. I need to hear what a large size company have heard of they start to hire full time already. Okay, and now, especially for fresh graduates who are MBAs and for example, Amazon, Amazon already made offers to some of the students to graduate the next year. Okay, so there is like famous companies, you should apply for full time job right now for famous companies. Okay, for companies never heard of. Okay, let me just plan a job. You can apply anytime. Okay, you really need to understand your timing. Okay, very, very important famous company now small million companies you can wait you can wait until you graduate. So that's a key. Okay. Now, let me let me answer next question. I have many tabs open this next question. From darkness see is this a good idea to let her move from project management from product management or a new company. Let me and ask this question very good question. So do you mean you let her move within your company from project manager product manager. So if you can, pretty thing, if you can do let her move you should within the same company because recession is coming to refrain if you can do let her move, but some companies they don't give you a high compensation. This might learn. Okay, whenever you let her move. We actually have a student is crazy. So after she took course from TMX editor, which go here for a more after took the course from us. In the product management course, we taught her we taught her exactly how you do like lateral move within company. And then once you land a job offer. And she was like, Oh my goodness, this is crazy her company wasn't able to offer the same kind of salary. So she decided to like jump into a new company to land a better road. Okay, so if you can maintain your salary within the same company, and then move over to a new company. You can do that and gradually move it but if the company thought able to give you the same story will increase the story and I would rather you land a job offer outside because it's more important to maintain your salary. If you land in any job offer outside any jobs you land you should gain at least 30% growth for your new job. Okay, so that's like in general all students whenever they drop off 30% growth. On average, our student salary growth is 70,000, 70,000, 70,000, 70,000 dollars growth in terms of every salary the girl. So once you guys to think about it's your salary gain or title. So figure out either way is fine. You just cannot lower your salary. If the salary is lower, you better to jump into a new company. But because the recession is coming, if you can do transfer within the same company, of course, the safest I recommend to do so. But just make sure your salary they can match your salary. That's the number one thing. Okay. So if you want to learn any product management course, how to transition, make a smooth transition from project management, product management, this will be teach inside our product management course called PMS. You're able to learn more there as well. Yes, we also offer product management certification as part of our program. So let me answer your next question. Oh, we answered this already. I'll introduce yourself. We answered this as small tree and experience PM. Yes. So if your experience can more think about promotion. I should go to this website. I want to learn about the promotion strategy, which we lay out for you. Okay, so come to this website. Our website has many different things. So talk about different growth opportunities, different students have leveraged their career going to a different level. You should study and learn more about our program. Okay, so go to docmancy.com and on the services and many different offers we have right now. Yeah, this is last week we had an anonymous panel very excited. I was doing Adam and talked about how can I see PM offers and two similar offers in the US as a Canadian citizen so very excited for his growth. So let me do this. Let me. Let me answer the questions we submitted. Thank you. I have three years experience in transaction risk investigation and now looking to apply for product manager role. What transfer skills can I use great. So today I'm going to talk about the six essential PM skills and actually like two weeks ago when I did YouTube library talk about the skills. Now, if you already have done a risk investigation and if you want to transition to PM roles, the transfer skills could be for example, you're doing like transaction risk investigation. Did you do like data analytics, you do AB testing and those relevant product managers. So when you investigate those risks, you do working cross functional team, that's very transferable. Okay, and then after you work with cross functional team to propose any product features. If you did that's also very transferable so all of those are extremely relevant for the new job. For sure. You have in resume, right, resume review. Yes, for resume review, as I said, you go to our website and let me show you. You can also do live resume review with me by submitting your resume to my team. Because there is a lot of smoke. All right, resume review. I talked about it earlier. You go to. Shopping resume and PM LinkedIn profile, resume review and LinkedIn profile. So you can directly book a session right here. Okay. Now, for free resume review, you can directly email my team and make sure the slides where you can email my team. Your free resume review, go here, email my team, right here, right here. Has info, so email him to everyone on receive free resume review, email him your resume and then next week when we go live, I'm going to review resume slide. Okay. Cool. You have two tracks to do it. And one free one paid options. It just shows which one works best for you. And that has said, I have four years experience, but not exactly products, products that are relevant to it comes out. This suggests me apply as a work person or one with no PM experience. You should apply for someone who already have related PM experience. Not like you have no PM experience. We do not suggest people to do things that, oh, I have no PM experience. If you already done something related to it, it's not everything end to end, no problem. You still need to qualify yourself as someone already have related management experience. Like it comes out is extremely relevant. Okay, I think it's very, it's very good. You already have done that. You already had advantage compared with other people. Okay, so congratulations. That's an advantage. So therefore, you should, you should. Now, for the part I'm very sincere with you guys for the part you haven't done fully, you need to build a product before. Okay, because you cannot fool others. As a hiring manager, I need to, even for my team, I need to be 100 people. Hundreds of people for my team to select the best candidate. A smart hiring manager knows who is the best candidate. And especially nowadays, like Twitter lay out half of the employees. It's extremely competitive. If you don't know how to do it well, you better learn. Okay, build a product before you gain some hands-on experience. If you want to take part of management course that would teach you how to do it and how to master all the skills, you go to this website. And a lot more and register for our upcoming live masterclass and will teach you how to create those recession proof and layoff proof strategy. Okay, cool. To do that. Let me know if you have any questions. You can see the time. I'm glad you already have a really good experience. That's very good. Masua, do people got PM jobs in India? Yes, yes. Getting jobs, getting PM jobs in India. No problem. You've already in India, getting PM jobs in India. Totally no problem. I have very high confidence you can do the same. Okay. Cool. Yes. Go directly. Go to our website. Let me show you again how things work. Go to our website. About who did we select to join the program. Everything is there. Okay, right here. And also see our documents. And then final for our next masterclass. Everything is here. Perfect. Okay. So and see who did that to join the program. And then you can also find out our different testimonials examples of people with various data background.  Okay, cool. Right. You can see Anna right here. It's nice. All right. Let me see any other questions we have. Okay, great. So it looks like we have answered all our questions. And we will answer all the questions. Okay. Now, and we're going to answer all the questions. That's a lot with everybody. And I hope all of you guys are able to quickly survive from this winter. And even if it's lots of layoffs. And remember that the best candidate will also learn the job. We just harder and more complex, more competition at this moment. If you need help, you want to take for a management course, where we teach you how to quickly land your dream job offer, even if you wish and they are to go to website documents. And that's it. All right. Awesome. Okay. I'm going to see you guys soon and so please join me next week. I want to receive free coaching and email my team. They're going to send you an invitation joining live on Zoom to get customers. Awesome. So talk to you soon. See you guys. Bye.


In this study, researchers observed how polycrystalline materials solidify in microgravity conditions aboard the International Space Station. They found that individual crystal cells from one grain could invade another grain of different orientation, creating complex and convoluted boundaries between them. These findings challenged the traditional understanding of grains as discrete regions in three, dimensional space, instead suggesting that they are more like fluid, like entities that can interact with each other. This article was authored by Jungil Song, Fatima El Mota, Damian Tourette, and others.


A warm welcome to the 26th session of the fourth module in signals and systems. We were looking at continuous independent variable systems in the previous session where the impulse response had a Laplace transform and the Laplace transform was rational. So, essentially we are looking at rational linear shift invariant systems and we are trying to analyze whether the system is stable or not. Now, we identified the importance of the region of convergence. In fact, we saw the region of convergence was critical. And what we identified was that you need to look at two things to determine stability. You need to look at where the poles lie and where the region of convergence lies with respect to the poles. So, we said we could focus on each pole individually. Now, we also said that we should first take care of a basic disqualification if there is one. That is, if you have a system function and if you then do a long division and bring it into the form of quotient plus remainder by denominator. And if the quotient brings you integrators or differentiators into the system, there is immediate instability there. In fact, just for completeness, let me show you why the differentiator and integrator are inherently unstable. So, let us prove that. So, we can prove with a counter example. Let us consider a differentiator with input x t equal to sin of t squared. Clearly, the output is going to be 2 t times cos t squared. The mod x t is less than or equal to 1 for all t. In contrast, mod y t grows without bound in t. And therefore, a bounded input has produced an unbounded output. And therefore, the system is unstable. Now, let us take a corresponding proof for the integrator. Integrators are inherently unstable. Again, we give a proof with counter example. Let us take once again the running integrator. And let us give the unit step input to the system. Now, I will show the input in black. And I will show the output in green. The running integrator produces 0 all the while up to t equal to 0. And from there, it grows again without bound. So, at the point t equal to 1, you have essentially integrated an area of 1. So, it reaches 1 and then grows beyond without bound. In fact, you know what the output is y of t is going to be t times u t. So, you have a bounded input resulting in an unbounded output. And therefore, the system is unstable. So, you see what it means is the moment you have a differentiator or an integrator. There is inherent instability. So, we have to discard the question of stability there and then. And what is the system function of a differentiator? Let us write it down and that of an integrator true. The system function for a differentiator is simply s. And for an integrator or running integrator, of course, it is 1 by s. And of course, you can repeat this. So, if you have a cascade of differentiators. So, if you have a double derivative, for example, this would be have s squared as the system function. And similarly, you can have double integrators and so on. And all these are immediately unstable. So, let us do a wave with them. So, you know, let us assume that we do not have them and then look at the non-trivial discussion that follows. Otherwise, we have nothing to do. We do not even need to look at the quotient by the remainder and so on. That is not going to be able to overtake this instability created by the differentiator or the integrator. Now, let us assume they are not there and that means the degree of the numerator is less than the denominator degree. So, we have a remainder which is the numerator divided by denominator. And we know that we can decompose this into partial fractions. We can then invert. We have done all this. We do not have to review all the steps in gory detail, but we can invert each partial fraction term. Now, remember we are going to consider distinct poles. You see, because if we have this pole repeated, we do not call them distinct poles. We can club together all the terms corresponding to a given pole and create a poly-x term. The exponential parameter comes from the pole and the polynomial comes from the coefficients in the partial fraction expansion. Now, what we need to do is to look at any one poly-x term and see whether that poly-x term can be annihilated or can be affected by the presence of the others. In other words, if one of those poly-x terms has an exponential parameter that grows without bound, you know, and a growing x, see it is very clear. The region of convergence is either to the left of the pole or the right of the pole. If it is to the left of the pole, then you are going to get a left sided exponential term. Left sided does not immediately mean growing or decaying. It depends on the exponential term. It depends on the real part of the exponential term. For example, if the exponential term is e raised to power 2t, it would be growing to the right and decaying to the left. If the exponential term is e raised to power minus 2t, it would be growing to the left and decaying to the right. So, the question is, let us focus on one of these poly-x terms. Suppose, you discover that the exponential part of the poly-x term is a growing exponential. Forget about the polynomial part. In fact, we can show that the growing or decaying nature. So, let us put this down formally. What I am saying is, focus on one poly-x term. A simple lemma says the absolute integral of this poly-x term diverges for a growing exponential, converges for a decaying exponential. The polynomial term has no role to play. The exercise for you is to demonstrate this. So, you know, it does not matter if a pole is repeated. You only need to see whether it contributes a growing exponential or a decaying exponential. Now, the next question is, suppose you have a growing exponential coming from one of these exponential terms, poly-x terms. Can one of the other poly-x terms overcome that growth and, you know, render it null in the sense when I take the overall impulse response, which is the sum of such poly-x terms? If one of those poly-x terms is growing without bound, can one of the other poly-x terms bring it into control? The answer is no. That is the next subtle point here. So, lemma. The poly-x terms are linearly independent. That means one poly-x term cannot annihilate or overcome another. And more mathematically speaking, a linear combination of two poly-x terms cannot be identically zero. The exercise for you is to demonstrate this again. So, where are we now? We are clear that the moment you have one of those poly-x terms which grows without bound, your impulse response is going to be absolutely non-integral and the system is going to become unstable. So, let us put that down too. You are saying one exponentially growing term, poly-x term and that growing or decaying has only to do with the exponential part, not with the polynomial part. One exponentially growing term makes that system unstable. Now, when will a poly-x term grow? There are two possibilities. A poly-x term would be exponentially growing. The pole is of positive real part and the region of convergence is to the right of the pole or the pole is of negative real part and the region of convergence is to the left of the pole. Let us draw the diagram in the S-plane. So, both of these cause exponential growth. You have a pole in the left half plane, that means negative real part and then of course, the region of convergence has to be on one of the sides of the pole. So, this causes exponential growth. In contrast, if you have a pole in the right half plane, then the region of convergence being to the right of it causes exponential growth and therefore, what should you not have? Either of these, either of these red are forbidden and therefore, what should you have? If a pole is to the right of the imaginary axis, this is the imaginary axis with real part equal to 0. If a pole is to the right of the imaginary axis or in the right half plane, the region of convergence should be to the left and if a pole is in the left half plane, the region of convergence should be to the right for stability. In either case, the imaginary axis is included in the region of convergence. Do you see that? This is the beauty. For stability, the imaginary axis is included in either case in the region of convergence. So, in fact, we have a very simple condition. Look at the imaginary axis. If it is included in the region of convergence, it is stable. If it is not included, it is unstable. We will see more about this in the next session. Thank you.