Okay. Well, welcome to Math Modeling. My name is Rauro Cascaval. I'm faculty in the Math Department, and I'm glad to see some of you that I know, and I'm anxious to see you to learn to meet everybody else. So, let's see. I'm going to start with a few things about the course, general things, and then hopefully quickly start talking about what Math Modeling is and why do we learn it. I have a website that I'm going to post everything pertinent to the course. There's also going to be a lecture archive, so the video of the course, as well as the notes. So, hopefully you're going to have everything in your hands to succeed. I want to say a few words about the syllabus. So, everybody got a copy. So, there's going to be a required textbook. I want to make this clear. That is the third edition of Meershard. In addition, I list, I think, two other or maybe three other courses, three other books, actually, two only, that I will use during the semester to bring more examples or more problems. Now, they're not required in the sense that you can actually download them for free, chapter by chapter, and I don't know if you're familiar with this Springer website that you can download. You have to be on the campus network. But if you are or if you're at home and you're VPN, then I think you can access these. So, the first one is called mathematical modeling case studies and projects. Again, if you don't see this recognized as, it means you're not on the campus network. So, if you're in Honolulu in Spring Break, make sure you need a chapter of this book. Hopefully, you won't, but make sure you get to the VPN. So, what you do here is you can actually download individual chapters. So, for instance, and one thing that I should say is that you shouldn't rush immediately and download everything because I think this is here to stay for the semester. But regardless, you can go and kind of browse. We're going to start talking today about optimization problems, but these problems do not actually apply yet. So, we're not going to use it, but I just wanted to show you. You can download these and I don't know why this happens, but because my browser doesn't like this. Anyway, second time it works, I don't know why. But basically, you have the chapter in your hand, print it, keep it on your computer. If you print it, I recommend you take all the trees. So, you print only like double-sided, two pages or four pages probably too small. So, that's about these books that I list here. I specifically look for books that won't cost anything, but the funny thing is about this first one is actually, if you look through the format, I think it's identical. The authors must have talked to each other with the book that we use or what's more likely is these people use this book and then they came up with more examples. So, anyway, it will be almost identical. The second book is, again, it's also free downloadable. You can also buy a copy. The nice thing about this second book is you can, if you go here, some of these books on Springer Link, you can actually buy a print copy for $25, $24.95, including shipping. Anyway, so that's for convenience. This is not advertisement for Springer Link, but I think it's extremely useful, but you can print again chapter by chapter. Okay? I should say the second one contains some things that we're going to be talking about. Maybe more. Graddy students will use some of the chapters. So, we'll talk about this later. But anyway, so the important thing is we're going to use this extensively, so make sure you have a copy. And this is not free downloadable but anywhere. If you find it, lucky you. Okay. So, any questions about the textbook? Okay. Now, even on the front page, I kind of make this clear that we're going to be using computer software for solving this problem. So, you probably know already. I mean, my preference is to use MATLAB. So, I'm going to be using MATLAB. I don't expect that you guys have had exposure to MATLAB. So, we'll talk about a little bit about what it does and how you can use it. But it won't be the focus of this course. It won't be to become experts in MATLAB. Okay. I'm going to show you basically the way we're going to use it is we're going to learn three examples. So, I will post things on the website. So, here's one. I already posted like a first exercise, I mean, an example in the book. So, I give you basically, I give you the code. What you need to learn is how to use it, how to modify it. I mean, you have to learn what it does and how to modify it. Okay. Never seen MATLAB before. This might look strange. Okay. But that's how you, you know, make the computer do what you want it to do. So, I'll talk about the format. Keep in mind, all it is is a text file, the text. But it has an extension dot m. Okay. And so, anyway, so we'll learn how to run it, how to, you know, modify it and get the output. I want to say from the beginning, so that once you write a code or you use my code or you use a code, a MATLAB code, you run it, you can actually write a report or you can write a code in a way that it gives you a report. So, a report is in HTML format or it can, well, then you can PDF it or whatever. But that's sort of how I would expect the part of the homework to be turned in. Okay. And again, it's, it will be really quick to explain this thing. So, I just wanted to show you, okay. Now, here I talk about basically what it is and why we use it. It is available for free in the computer labs. In fact, I think in all, throughout campus now, we have a side license. So, it should be installing the library when the new computers come, which should be convenient. You can also access it remotely. How many of you have heard of remote access to, okay? So, if you, if you have not, there is, there are some instructions here how to get access to MATLAB remotely.  Well, you, for convenience, if you need it at home, you can, you can purchase it on your laptops. You can purchase a student version, but for most part, you can do it on remotely or, well, you can do it remotely period, or you can do it in a lab. Okay, so I'm going to make a plug for a course here that's kind of shameless advertisement, passes around. So, this is a syllabus for another course, which is not a required course. There's not a prerequisite to this course. But it is, it is a course that we offer. It's a one-carat hour course, Math 265. And you've probably got an email about this. So, the only thing I want to say is, is got a quote from a student that took it last, last year together, you know, at the same time as Math 448. And that's, that's what it is. So, if I could read it, it says, I found the MATLAB course invaluable in taking modeling last year. There are only a few of us from the modeling class at Tuke, the MATLAB course, and we became the go-to individuals in the modeling class. For providing help to those that do not know MATLAB. Mathematical modeling is B, and I would highly recommend it, that if a student does not know MATLAB, they take Math 265. The fact that it's a challenging course, I live, this is a personal opinion. So, well, everything is a personal opinion of this particular student. And, but the, there is sort of a truth to this. And I wanted to mention it here is that if you, if you have never seen MATLAB, or if maybe you've seen it, but you'd really like something. Thank you. More systematic, we offer this course. And it is surely before this class. So anyway, end of, end of, end of advertisement. Regardless, I think the point, the point that I want to make sort of from the beginning is, it may not, this class may not be the, how you've, you know, done calculus, or if you've done ODE's, you know, differential equations, or lean algebra, or what not. Because it really requires that you use a computer.  Okay? So, if you're very proficient maybe in a different language, you know, you can, and say, I'm totally against this, this, you know, software. Okay? Maybe you can go by, you know, the first few assignments. But then it gets to a point where, you know, what I show you in MATLAB may not be, you know, easily doable in another language. Okay? And then it becomes, it becomes kind of difficult to communicate with each other, and it, and that's, you know, or maybe at some point you decide, oh, I can use three of them at the same time. That's fine. That's fine. But the point is you want to make sure that you can communicate the outcome of your work to me. And I cannot use five different languages to explain the same concept. Okay? The book actually has somehow, if you read through the book, it has an example in Mathematica, an example in Maple, and then an example in, but not something derived, which I honestly don't know much about it. Okay? You will, you will very soon, I mean, unless you are proficient in all of them, you will soon realize that, okay, well now, what am I using to, you know, to solve a problem? Okay? So please keep that in mind. If you have doubts and, you know, feel free to come talk to me or about this, this aspect of the course. Okay?  I mean, or use your graphing calculator for this. Okay? Now, that being said, the choice that I made for MATLAB is because MATLAB is sort of the standard software language in this field. Okay? It's, it has evolved over the years. I mean, it was sort of started by mathematicians. Then the engineers picked it up and they developed it a lot. And in the past 10 years, it came back with a lot of capabilities that we need as, you know, in mathematics, one of them being symbolic computations. Okay? So we'll talk about those. But MATLAB is primarily used for numerical computations that is with numbers rather than with symbols. Okay? So that kind of distinguishes different computer algebra systems. Is it really powerful in a symbolic computation world? By symbolic, I mean, what's the derivative of x squared? Well, a symbolic software with symbolic capabilities would tell you it's 2x, right? And numerically, it's, well, you tell me the point where you want to take the derivative and I'll tell you the number, right? So it just takes a little bit of, it makes this distinction. And for most of what we need is numerical computations are essential. Certainly symbolic are useful, too. So anyway, so that's sort of a reason behind MATLAB. Don't just say anything else. So you have everything printed there. One thing on the home page here I made a link to a MATLAB resource page, which lists a bunch of things you can explore. I mean, you can do everything nowadays pretty much. You can find lots of resources, free resources on the web. There are whole books. There are two books by actually the inventor of MATLAB that he made available online. Lots of codes. The best way to learn MATLAB is look at the code, see what it does, modify it, okay? Use the help. So I'll show you in a second.  Maybe one that I found, again, the best way to learn is take the math to 65. Okay, you'll hear me say this first two weeks a lot. But short of that, again, there are lots of them. MathWorks, who's the company behind MATLAB has lots, a list of tons of tutorials, tons of video. I don't know how efficient they are. I mean, certainly it depends on the personal taste, personal learning style. You can take advantage of one or the other. But the one I found kind of useful is almost like a cheat sheet. I must say that no single tutorial will actually cover what you need, okay? That is to say, if you've done it, okay, you invested time, you spend an hour, two, three, go through what the tutorial says, and then, yes, I know it, right? So every time you kind of run into a math problem and you need to use something, there's probably something you need to learn about the computer function or some, okay? But just to give you this example is it goes through sort of how to start, you know, how to operate with MATLAB and other things. I will show you a little bit of this myself without a formal tutorial. But again, if you need, we actually have even the UCCS website has a few tutorials down here. The web is full of tutorials. I wouldn't recommend that you go and start hunting for the one that works for you. I mean, to spend days and days and then get frustrated. There is a huge resource this semester, a MATLAB tutor. His name is Terry Spence. You might not know him, a graduate student. He will be available nine to one every day, actually. So if you need questions about MATLAB and assuming he's available, he'll answer them to you.   I would say, see how it works. If you need, you know, if he's extremely busy with other things, maybe we can block some of his time. But, okay. So, again, lots of resources. At the end of the day, halfway in the course, if you, I mean, I'll just tell you this from experience of other students, is if you feel like, oh my gosh, it takes me, you know, 50 hours a week to just do things in this course, something's not right. Okay. I mean, we're not, as I said, I will give you kind of the sample codes. I'll give you the, you know, the codes that solve the problems we're talking about.  You can, I mean, you should be able to just modify it and do it and report and go forward. Okay. The goal here is not to learn everything in MATLAB. Okay. And again, I'm repeating myself, but the goal is to solve math problems and math modeling problems. And use it at some stage in that process, use MATLAB in that process. Okay. Let me say anything. I will post the homework here. So the first homework, I say it's going to be due next week from today. So that means we have to start talking about something fairly soon in chapter one. And I mentioned the exams, so there's going to be a midterm and a final. So that's, and the graduate students, I think, will have some sort of projects on top of that. So I think it's all in the syllabus. The lectures are going to be available on the website here. If you're not familiar with this, first time you visit the lecture page, you might be asked to do something, but, well, okay, we know who to blame this, right? Anyway, you're probably familiar about the video archive page. And it should be also an iTunes, so anybody knows iTunes? If you, yeah, you can play with me. I mean, just, no, but I mean, the point is that you can subscribe to the feed, sort of, so you get, it downloads automatically on the computer. It's not perfect, but anyway. All right, so finally, so here you just register if you've never done it before. Otherwise, just sign in with your name and email address, okay? All right, I'm really done, I think. Any questions? Yes, no, none? I have a tentative schedule here. It's kind of on the conservative side, but meaning that we might actually, we hopefully will be ahead of it, but if not, hopefully won't be too much behind it. But the important thing is to almost forget about that print copy of the syllabus and always refer to the website, okay? All right, so let's, no questions? Yeah, that's, as long as you don't do other things with it, that's fine. Yeah. Any other questions? Yeah, okay, I said it's not perfect. It's going to happen in a week or two, yeah. Yeah, I actually had it before spring break, but then it's kind of set. There might be an in-class and a take-home portion, so I'm saying, you know, the in-class should be set, okay? And so don't plan on not coming back from spring break. Okay. Anything else? Yeah. Considering this is done, what's the difference in work-like homework? Homework is the same project. So it's going to be a project that the grad students will have to do. And I did not, I talked about it in the syllabus. I haven't given the details yet. I will talk about this in the next two weeks, two weeks. Yeah, I don't think so. I think you have to be enrolled in, yeah. But yeah, you're welcome to. So again, this is, okay. So let me start talking a little bit about nature of this course. And then one thing that's nice about modeling is that it appeals to lots and lots of fields. I mean, it is sort of what math can do in all the science and all the fields, right? So probably some of you are not necessarily math majors. And everywhere you go, you see, oh, I want a math model, right? So you can be very powerful. Not at the end of the course, but if you become, if you have an expertise in modeling, you can have a career in it, right? Now, a course is not going to give you the full expertise, right? In fact, it's going to actually just prepare you or expose you to what it takes when you are in an environment where math modeling is required to actually do something, okay? So even though here we are working on baby models, baby, I mean, in examples, textbook examples, right? That's how they say it, right? We're not solving a problem that the company in Woodland Park would like us to solve, right? Or some very extremely concrete problem that if you solve it, whether you solve it or not, it depends on the existence of that company, right? So we're going to learn about aspects of what it takes to set up a model, what it takes to validate a model, what it takes to solve it, you know, and actually what's extremely important is what it takes to communicate what you've done in the model with the people that have no clue about mathematics, okay? So those are sort of the main goals. The examples we're going to cover, I mean, are by no means exhaustive. So these are the two kind of resources that I gave, two other books, just complement, you know, add to those list of examples, but even those are not going to be comprehensive. So if you have an interest in some whatever, right, it would be actually nice, you know, certainly come talk to me, see if we have the tools, okay, or if we'll ever learn the tools for that particular situation, we may not, right? So one other thing that I should say, like, in both the books that I mentioned, not the required one, there are a lot of models that require partial differential equations.  So the more math you know, the sort of the broader the coverage of your, you know, expertise can be in terms of math modeling, okay? So I'm not saying anything fancy here, I'm just pointing, you know, sort of, if you have an interest in a certain direction or a certain, you know, maybe you work in some company or maybe you will work in some company, I'd like to hear about it, okay? And I'll be happy to, you know, look at other references, you know, other things. You might be doing a project, you know, even if you're not grad students. And all I want is that you have a rewarding experience. At the end of the day is you finish the course, not because you had to take it, but because you really, you know, fit your interests, okay? So there are three main kind of motives that we're going to be touching in this course. So sorry for my handwriting, but it's going to get better hopefully. So the first kind of big pool of problems are going to be label optimization problems. Because they're in practice, you end up with many questions that where you want to optimize some, you want to maximize some profit, you want to minimize some cost, you know, the things going on in different fields. In all the fields, you can actually set up a problem where you need to, you can set it up so it's an optimization problem. So we'll start with those, and that's going to, you know, lead us to a lot of the applications. They're going to talk about dynamical systems, models, problems, and as a subset sort of of those, we're going to be talking about control problems, and sort of the last one, sorry for the, it's actually here, the last kind of class would be probability models. Now, if we had all the time in the world and we would really go into details in all of them, I will probably talk least about, I mean, spend least amount of time on the probability models simply because, you know, you can spend a whole course on those. There's a, of course, we offer another course, a casting model, modeling that really, you know, discusses those, but we'll talk about some of this. Okay, so, and by the way, I should say, I like when the class is very quiet, but if you really have, you know, if you have any questions, just don't be shy, just interrupt and ask because, you know, I mean, then that's pretty much how you learn. I mean, being active, not just passively listening to somebody talk about. It would be ideal if you all had computers or if we were in a computer lab, but, you know, that is not the main, you know, as I said, that's not everything that we'll do, so there will be some paper and pencil part in each of the problems. So, let me talk about optimization a little bit. Start talking about what is optimization? Well, in one dimensions, so, what do I mean by one dimensions? Basically, I mean that I'm looking at a function, you know, some variable that depends on another variable, right, just one. One variable, you know, real numbers, X, and I have a function that depends on that X. And what I want is I want to maximize that, right? I want to find the maximum. So, this is Y equals F of X. Okay, then you graph it and you look at it and say, oh, I see maximum, that's the maximum, right? Well, sort of, in practice, what do you, you know, typically what you do is you have, you know, you don't just have a function, I mean that's not the starting point, right? The first part of the problem is find the function that, you know, has an expression that you can deal with, right? Well, graphing may not be too difficult once you have that function, right? But graphing is not the end of it because you may have a maximum that you don't really see on a graph, right? It could be, the scale could be so huge that you may, you know, you may not see a maximum or you may see lots of maximum and so forth. So, of course, theoretically on paper, what do you do? Today's derivative and the first thing is see the critical points, right? So, you say that we're equal to zero and then, hopefully, then you can decide, you know, is it maximum, is it minimum, is it inflection, is it neither or so forth, right? So, that's calculus one. In reality, coming, you know, problems coming from, or functions coming from models from mathematical models of a realistic problem is taking the derivative maybe impossible, right? Let's say you're lucky that you have a function that you can just write down very symbolically. Then, okay, maybe you can take the derivative. The next hurdle is finding the solution of f' equals zero, right? That's not always possible to rule it explicitly, right? So, you really need a computer for every single step of this and you have to deal with these situations where you may not get an exact answer for each, right? So, you probably know, I mean, you know that even if you have some, I don't know, some function like this, I don't know if this is a maximum or not, but I don't know, let me put a minus here or something. Then, the derivative, so this isn't the case where you have the function. You can take the derivative by hand, but now you are facing the task of setting this equal to zero, right? And what do you do? You need a calculator, right? Okay, so you can do this with a graphing calculator. No big deal. But because of the nature of the things, it's probably better now to use one of these computer algebra systems. So, I will show you very, very briefly how to solve this in MATLAB. And then we're going to move to a baby problem that actually you have to start from the very beginning to even say what X is, what is F, and so forth, right? So, set up a model. So, we're going to set up a model. Let me just open MATLAB since I've talked so much about it. I'll show you really quick how to use this to solve this. No, I do have it locally on my machine. But if I don't have it on my local machine, I can remote desktop to what's called RADS, R-A-T-S, dot-E-S, dot-U-C-C-S-I-T-D-U, and use your U-F-P credentials. And what you do is you just go on this remote machine that you have access to lots of software, not just MATLAB, just lots of software, okay? I don't know how long it's going to take. But anyway, so I have access to... I get MATLAB, and I've never seen it before. And what you're probably going to see and the first time you open it is kind of cluttered, have all this kind of stuff, right? So, for the most part, I'm not going to be using the folder. I'm not going to be using the command history. Let me leave this what's called a workspace. I have these two windows, which I can play with. I have some garbage there. I'm going to clear it. CLC clears it. Okay, so this is how you start fresh, okay? So I simply want to solve that optimization problem, right? Okay, so how do I do? Well, many ways you can do it. But the one way I want to start with this is do it symbolically, okay? Remember, that's not the strength of MATLAB. Okay, but it's convenient that it has this capability. And by the way, if those of you that have used RATS before to connect remotely, now, even remotely, you can do symbolic computations. In the past, you were not able to do it because of, I don't know, 64-bit compatibility and so forth. But anyway, so right now, everything that I show you, you can do it remotely as well. Okay, so the first thing that I do is... And this is kind of unusual for MATLAB to have to define that I'm going to work with X, okay? But again, we're living in this symbolic, you know, we're working with the symbolic objects. So, I mean, that's the price of prey, which have to define, we have to say, we're going to work with X, okay? All right, the next thing is I'm going to define the function, okay? And you can see it, I mean, it's obvious, right? The way you define it is just equal, okay? It's not like other software, it's just simply equal, okay? Now, this is a command window, and MATLAB is just waiting for your next command, okay? Yeah, is that what it was? X squared is the derivative, yeah, yeah. Right, so when I take the derivative, it's going to be 2X, let's see. All right, now, let me clear this. I'm going to start fresh again. I mean, I'm not really starting fresh. If you look in the workspace, you can see those two objects are already defined there, right? So X and F. And they're symbolic, right? So that's what it says, it's symbolic, and it's a one by one. So the big thing you have to know about MATLAB is MATLAB thinks of everything, every thing that it works with is a matrix. So if it's just a one thing, I mean, if it's just a one scalar or not one number or one object, well, object is wrong, it's just a one by one, right? So number three would be thought as a matrix, but a one by one matrix, right? So here it's a one by one symbolic. So you can see it can make a two by two matrix with each entry a symbolic variable. Okay, but anyway, so I've defined X. I didn't have to do it again, but I'm just trying. And the next thing I'm doing is a semicolon, meaning it goes through that command, but it doesn't display something as a result, okay? Just to keep it kind of short. Okay, so that's that's that. What's the next thing to do? You can differentiate, you know, and there's going to be commands that you probably don't know if you haven't worked with MATLAB. And the best way to do it is, well, I want to say most of all the commands, well, all the commands, I want to say all, but probably it's not true. All the commands that you will ever need in this course, you would have seen prior to you having to work on the problem. But if you ever kind of need something, you can always go to help. In fact, this FX here has a list of all the functions categorized, so you can, I don't know, probably mathematics. Actually, yeah, they can go mathematics or it can go to, one thing I should say here is one peculiar feature of MATLAB is it has a core set of functions, and then it has functions that are very specialized for, let's say, control systems or image processing, right? So each of these has a very specialized set of functions. Now, the one where you have symbolic capabilities is called symbolic math toolbox. So if you don't have this listed, you cannot do symbolic computations, and you would get an error when you type SYMS, okay? Would you be able to get all those to rats? Yes, no. Okay. Which is a big, okay. So anyway, I don't want to go through much of this. I just want to show you how it works. So you can find things like that there. It does display the answer, right? Symbolically, right? And if you ask me how I did it, I don't know. It's just magic, right? Just took a Calc 1. This computer took a Calc 1 class. You recall, right? When you learn about derivatives, you just know the rules, right? So I imagine that these rules were kind of embedded in this, but anyway. But notice that I have a new variable called ANS, which I didn't call it that way, right? So one thing that you can always do just to make sure that you keep track of what you've computed is to call it somehow, right?  You can give it a name, right? You can Fx, or I don't know. Let's call it Fx, okay? So now it has created the Fx, and it kept it there, right? And it's this function. It's still symbolic. Well, okay. So we're wondering how do you... I keep deleting so you don't have to scroll. I guess you can do it. You can see on the bottom there, too. But anyway, everything's still there, right? I just cleared the screen here, but... So let me plot this function. Easy plot, Fx, okay? So I'm just showing you the real basic commands. Sorry if you're familiar with this. But all right, so now you see it, okay? But it's hard, right? It's hard to say if you have a minimum or a maximum, right? Well, it's not hard to see. I mean, in this, by the way, why negative 6 to 6? Well, easy plot uses negative 2pi to 2pi as by default. So it's 6.28, right? But you don't really want that. Now, here's one thing that's going to happen. You see this window here that pop up here? Now if I want to go and do something else, the window disappears. Okay, it's kind of frustrating, okay? Don't spend hours to find that, okay? Just listen to me here to find that figure, right? So where did it go? Well, it didn't go anywhere. It's just somewhere here. Okay, and this is window 7, which is a great thing that I can find it, right? But I, you know, I didn't have to wait for window 7 to show up to find this figure. What I can do is I can actually, what we call dock, right? So I can dock this. So I still have everything on full screen, and I just want to keep it, right? So I've docked it. Dock is this thing here. I want to have every single window to be on the same screen. Okay, so, okay? So hopefully everything is going to stay there. And now, let's say our x is only positive, 0 to, I don't know, you see, 6 is kind of big, right? Let's do 4. Now, if you put, instead of square parenthesis, if you put, you know, just parenthesis, I think it's going to give an error. So there's going to be stuff that you're going to be frustrated initially. Okay, what do I do, you know? Don't spend too much time on this. Just kind of look at the help, or whatever, right? Gosh, so hard to see. Do I have a minimum? Oh, I have to go. Well, I can see that between 0 and 1, if there is a minimum, that's going to be the minimum, right? Hey, and there's the minimum, right? I have to say I'm very lucky, because I just picked that at random, but... Okay, so, you know, it's a big issue here. How do you get to the thing that you want to conclude, right? Well, plotting has a lot of limitations, okay? Because you don't know what the window size should be, and so forth, okay? And this is an easy example. We're doing the calc 1 stuff, okay? So, we have not a maximum but a minimum. Okay, so, well... Oh, thank you so much. We're dealing with a derivative. Huh, I'm not plotting... Yeah, I'm plotting the derivative. Thanks. I should have looked at... Well, okay, so I'm not so lucky then. Let's go back. Okay. All right, so what should I do? Let me go back to 0 and 1 here, right? Well, so, I'm not looking at a maximum, thank you. But I'm looking at what? Zeroes of this function. All right. Okay, so the zero of this function is... It doesn't look like it's in this interval, right? It doesn't look... But it looks like there is somewhere. That's the other thing. You should keep things in perspective, right? Don't change the problem. I've changed the problem, right? I was looking at other things, right? I'm looking at the maximum or minimum of the function. So I'm looking at zeroes of the derivative. Okay, so, well, being a cubic function, I know there is a zero, right? Okay, so that wasn't random, but where the zero is is still not very clear, right? So I have to ask the computer, how does... Okay, so I have to solve fx equals zero. And what do you know about cubic functions? The difficult to solve, it's not impossible, but you're going to get cubic roots, all kinds of stuff. There are some formulas, but you don't even want to know. I see some complex numbers here. So, in fact, it's a big mess. In fact, if you look at the answer, I didn't call it anything. You see it's three by one, so I have three solutions, right? It found all three solutions, but they're not all real, right? So they found one and two complex. Where are those complex roots on the graph? So there's only one x-intersect, right? Of f prime with x-axis. So it's not easy. Well, okay. But first of all, let's... Let me give it a name here, x-crit. I don't know, x... This is the... Believe me, this becomes challenging. How should you call something? X-crit, take all whatever, okay? All right, well, now, at least I don't have that ANS, but I have this. It's too long. I should have called something shorter. But anyway... Now, here's where Matlab comes in handy. You can actually, of course, see the same but in a better way, right? Not symbolically. This is almost like... It's a symbol, yes. You could almost see the square roots or something, right? I think you can... Well, you don't see them here, but you can... Well, okay. I just want to see the solutions. So I use this double command, double, and it converts. You see the answer now? It's something you can visualize, right? Almost negative one, but not quite. This double command... Does anybody know what it does? Yeah, but not just that. Right, double precision. But the one thing that everybody has to understand is we were doing our computation in a symbolic world, right? Double brings it into the numerical world, okay? It's a big... Okay, so now it's like a... It's a huge change, okay? You may not show like this, but it is... Now it's a number that Matlab is really happy to work with, okay? These complex numbers are... Matlab is very comfortable with, okay? All right. What else should I say? Of course, I didn't give any name to this, so I should call it somehow, right? I don't know. You can even call it the same thing, as long as you didn't... Well, right? You can call it... If I use this name, right? I made a conversion, but it's... It just changed that nature of the... Yeah. Right, so if... Yeah, so that's a computer science question, and I only know a little, but I know that the variables that are stored, so the things that are in this workspace have some memory allocated, right? And as long as the size of that variable doesn't increase, it just used the same memory allocation. Sometimes what will happen is that we will increase the size of... You know, we could call the same variable, but increase its size, then it becomes... There are some flags that show up. They say it's not very optimal. Anyway, so optimizing the memory usage and so forth is an interesting thing, but not really mathematical. Okay, so final thing. Remember, I told you that MATLAB comes, has this... Everything MATLAB deals with is a matrix. Okay? So this thing now is a matrix. It's a three-by-one matrix, right? But you don't care about those two last two ones, right? So you can just extract only the one you need. So that's... Let me change... Well, let me change the name. And you extract it by saying... By putting this in parenthesis is a one, you know, the first entry in that matrix, right? Well, the matrix is three-by-one, so it's clear what the first entry is that, right? If it were a two-by-two matrix, you would better say it's a first row, first column, right? But here it doesn't make any difference, right? So you've... Give it a different name. Of course you could... It doesn't matter. Names is something... You have lots of choices, right? So you can... If this is a little bit confusing to you, always give it a new name, okay? All right? Anyway, so that's the answer. Well, okay, that's the... Max or minimum? We still don't know if it's a max or minimum, right? The derivative was negative and then positive, so the function was decreasing and increasing, so it is a minimum for the function f. And you can see it if you plot f, not fx, and you... Minus one... One, let's say... So it's right here, right? Right down here. Okay. All right, so thanks again for pointing that out. I mean, it is important, right? And if you do this in your homework, I'll say, you know... Don't do it. So I'll say it now. You know, every time you have to keep things in perspective. The one thing that modeling helps is actually... When you get to the end of your computation, of your model, of your solving the model, of your using the computer to solve the model, you have to translate everything into words and say, you know, again, tell your brother or sister, mother or father, something that has, you know, scared of math, say what you've found, okay? And that's a check that helps you catch, hopefully, most of this, you know, possible errors that are done in the process. Okay? Let's... Well, let me say two more things before I close this. This way of doing business with Matlab is not efficient because it asks for a command at a time, right? And yes, you can go back and recall a command, but that's not very efficient. Most efficient is to use what's called a script. Okay? And notice that I've opened what's called an editor. And in this editor, you can actually... And now it's gone, right? Where'd it go? Window 7 is good. I found it. So now, before I lose it again, I'm going to dock it. Now, it went above the figure. I don't really like that. I want that to be like, you know, window here, right? And you can play with this. Okay? And let's say I want to redo everything that I've done but now in one stroke. So what I do is I go to... Well, I go to command window history just because I'm lazy to rewrite everything. Wait. Okay. I think I needed to do something else to record this as a diary. But since I haven't done it, let me just say the following. That you can... Oh, that's another thing. You can click this little thing here. So this is not on docking. Well, this is on docking, right? This just takes it a separate window, which you may lose again. So instead of on docking, you can do... Maximize the error. So it just kind of goes on top of everything else but it's not on dock, right? You can put it back in and find the other. Okay. So I'm just going to focus on this for now. So what did I say f was? x4 minus x squared plus x. fx was different. The derivative of f. By the way, derivative, you don't have in this case to say with respect to x, but some other times will be also useful. And the last thing is solve. xc solve f. No, x, right? fx, right? Remember? Yeah. You know, you may be able to, in the newer versions, I don't know the answer. The point is we're not really doing the most efficient coding, okay? We just want to do some coding that gives us the answer. Then we can, that's a separate process, right? Optimizing the code itself, right? But I don't know. It's possible. A lot of the things that I do are either redundant or really slow or something, right? But we're not looking at speed at this point, okay? So remember we did this. What was the last thing we did? And the one thing that we didn't do is solve it f at this value, right? And this is going to be fmin. Well, it's of course a minimum in whatever interval it is, right? So now you have this nothing but what's called a text file that you just wrote, right? I wrote it fairly quick. How did I know to write all of this? Well, I've kind of went one step and I saw what it does, right? So if you, right? The first time you write it, you're not going to know how to do this. So what you're going to do? Well, I'll tell you. Practice, I mean experiment. Okay, so let me just do this. Well, you can run this thing. If it wasn't saved, it will ask you to save. So let's save it as the first one. It has to be .m to be recognized. Cool, already exists. I don't care, okay? So now it not only saved but it also run, but nothing happened. Well, because I wasn't watching the command window. So that was, again, that was just a focus on that, but of course you can do it here and it gave the value, right? In fact, let me do it again. So I'm going to clear this. I'm going to run this and you see the answer, right? Now, you only see this because everything else was commented out, not commented out, but suppressed. The display was suppressed, right? Okay, of course you can do and see everything, every single thing, but then it's going to be painful. Okay, so then you have to kind of scroll up and down, right? So that's not, and I think you can control Z to undo things. Okay, so it is a text editor, nothing else, okay? Which is good because you're going to go and take my codes or any codes. So, look, we're going to talk about this problem, specific problem in class, but if you have no idea what it is, but you want to see what it does, you just copy this text, right? There's no special formatting. Just text, right? And you're going to open a new one, paste it here. You can save it and then run it. You know, let's save it pig1. So we're talking about some pigs here, which is kind of funny, but that's the first example. And then you run it, right?  Which I just closed because it becomes, again, it becomes quite clever, right? So you don't know what it did. That's why I'm saying, well, you can see some of these numbers, right? But again, it's an ugly thing to scroll up and down, right? So when you're done with a code, again, I haven't showed you how to develop the code, but when you're done with this code, you want to just run it. There are two things to do. One thing is go and do one at a time. See what the code does one at a time. And that's done with this double percentages. So in your code, everything that has this percentage is ignored by Matlab. So it's just for you to see, right? So with one single percentage, what has two percentages is what's called a cell. So I don't know if you can see, but it gives a different color. If you're in this cell, this cell is from here to here, right? And you can run it one at a time. And that's done up here, if you can see my cursor. So you can run the cell and stay in that cell. So let me clear this so you can see. So if I run this, the first cell, well, it did it, but of course, there's nothing to display. Just define that variable, right? Therefore, I should go either to an Excel, or this is more useful, of course. So now I'm in the next cell. Well, take a look at this. I have this new function, which is a function of x. And now I can just evaluate this. And what's going to happen? It's going to plot something, which I don't see. Why do I don't see? Because it's... No, but it's hidden here. Actually, you know what? So my column for plotting is not... It doesn't have any effect. Yeah. But it was somewhere in a figure in a place where I couldn't see it, right? But it did. It did something, right? So this is the function that you have to maximize, right? Forget what it comes from. It comes from a maximization problem of profit. But now I can go forward and see, well, the next thing is find the maximum, find the derivative, but don't show me the derivative, right? Of course, you can see, but it will be ugly. The next thing is solve the derivative equal to zero. And you see I doubled... Immediately, I want to get into numeric format. Compute the maximum of... Well, x max was found that I showed. And now you can see what happens. I'm sorry if this is too small, but it found the maximum. It even plotted. It's kind of nice visually. OK. And then it goes into other things, which we'll have to talk about theoretically, OK? All right? And the last thing is when you're done with this code, what do you do with it? OK, you cannot... So this is one way to kind of see what it does step by step. Of course, it's also useful for debugging. Like if something is not right, you can go in that cell and modify what you need. When everything's working nice and fine, you can publish this. So this is another feature which is very useful. It just gives you a report of everything. And first, it goes through the computation. And you have an HTML file, which is already on your computer that is nicely organized. Of course, the formatting, we should worry about this later. The important thing is there is text, which is comments. There is commands, which are MATLAB commands. And there is output, which is graphs and values, OK? So you don't have to look and scroll up and down and look in different... OK? This thing you print and give it to me. But, of course, OK? So Monday we're going to talk about how we start with simple models and get to a code like this and then interpret. Thank you.


Live from Orlando, Florida Extracting the signal from the noise. It's the cue covering Pentaho World 2015 Now your host Dave Vellante and George Gilbert Welcome back to Pentaho World everybody. I'm hanging in there George. I know my voice is gone. I apologize for that But I'm gonna be with you guys for the bulk of the day if I can James Dixon is here as the CTO of Pentaho Or as his card says the Lord of ones and zeros This is binary James. Welcome to the queue. Thank you. Thank you very much Tell us about your perspective on Pentaho Pentaho World and we want to get into the architecture and your role. Sure the event is is Super it's it's always fun to see Our customers partners what what they're doing with the the platform the ways that they're extending it and and expanding it So that's that's always a lot of fun to see this many people in in in one place that you can talk to and and you know Exchange ideas with The focus for for me at the moment within Pentaho is on our IOT initiative So not just in Pentaho, but all across Hitachi You know Hitachi makes a lot of things it's over nine hundred and fifty companies make up the the whole Hitachi group They make a lot of sensors. They make a lot of devices trains power stations So they're it's actually very good at at the things and you know, obviously with the the connectivity the the internet of things becomes Something that's interesting Particularly from a form and analysis and visualization perspective. How do you handle all of that data? What do you? What do you need in place to? to orchestrate and manage the the control of all those of all those things and how do you how do you Get the timely events Processed in the right order quickly enough. So for instance if I'm driving my car and All of us I got something in my tire and so I've got a flat that's about to become a blowout If I'm notified in time to pull over two lanes and stop That's a five hundred dollar problem I have if I get a blowout hit the rating in the median hit three cars on the way over and then upside upside down in a ditch That's no longer a five hundred dollar problem And if you look a lot of the catastrophes in the oil industry a lot of those could have been avoided by incredibly rapid automated detection and Two to stop a chain of events And it's complicated because let's say a pump explodes The pump can't tell me that it's exploded because it's exploded But the pressure sensors either side maybe one of them, you know the pressure drops to zero the one on the other side The pressure goes through the roof Those are the the devices that can tell me about the problem of the pump in the middle So it's not just a case of looking at the data coming from one device. You have to infer things Sometimes from other devices that that give you information about what the actual what the actual problem is so what kind of infrastructure change has to occur For that vision to become a reality. It sounds like Pentaho is ready for it is the world It's the the stack is that a lot of layers in that IOT stack There's 10 or 12 different layers of things that you need in there One of the things that that I'm working on the moment is is a thing that I'm calling state analytics Which is the analysis of state, you know exactly how our things right now in the if you look at the classic applications HR ERP CRM for my technical perspective that they're called state machines. They basically they store the current state The system knows my address So the HR system knows my address it knows my name my phone number It knows all of those things and it's actually redundant because I know those things So it's storing that information about me In a central system so that people can access it easily so they can report on it But it's essentially it's redundant because I know that information But it's good that the system knows it because people don't call me all the time asking me for those pieces of information The the problem with those those systems is that they only remember The current state of everything they don't remember the history So if you can ask a CRM system, how many customers do you have it can tell you immediately? If you want to know how many customers you had yesterday, it has no idea you have to go back through these things called change logs Where okay, we added a customer. We lost a customer. We lost another one. We added three customers You have to go back through this log adding and we're moving you know to the the count to find out the number of of customers and so The the analytics industry has been focused on time series analysis because time series analysis was really hard Because the systems didn't understand their own history So just to bump that up a little bit because Dave's suggesting I I like to talk it I like to draw the most technical conversations out of our guests and in it Attempt to make it perhaps more digestible for for a larger segment. It sounded to me like you're saying the Analytics industry sort of had a backfill for what these old legacy systems of record could do in that They didn't the legacy systems didn't really keep track of history. So we had to build up new systems that did yes Yeah, and so we now have those we now have those systems for doing history What we what we haven't realized in the IOT space yet is that the Your device like an iPhone has there's a lot of information on here. That's only stored on my phone So how much what my battery level is how much? Space I have left That's only stored on my phone. It's not stored Centrally redundantly like an old HR system would be so in other words now we have a new set of systems devices devices that have some amount of history on them, but the Systems that are keeping track of them that are managing them. They don't have that same notion of Stuff that's happening over time is yeah So the the the stuff that's happening over time is for quite easy because that's what you put into the data lake So part of the IOT architecture is a data lake where you take all the all the Information you get from the devices as they're running you pour those into the data lake so you can do history and trending The the thing that's missing is let's say You've got smart cars. They continue to send you their location Until someone turns off the engine and gets out Let's say you have a question of how many how many vehicles do I have with enough gasoline to get to Baltimore in the next two Hours well if the car has been sitting in the parking lot for three days without being on We don't know where it is anymore the car knows where it is and it will tell you that as soon as someone You know turns the ignition back on but the the central system has no idea where that car is It out we would have to go back into the data lake and look at the history of that vehicle to work out where it is right now So a practical application would be let's say I've got a Predictive model of when a pump will fail and let's say the the two main indicators of pump failure are pressure and temperature We can deal with high pressures. We can deal with high temperatures. We can't deal with high pressure and high temperature And when these devices are running they only send the information that's changing So let's say the the temperature is fairly constant, but the pressure changes frequently So we'll get pressure changes every couple of seconds. We'll get the current pressure But the temperature might be constant for days And let's say so the let's say the pressure ticks up a little bit We now need to the mathematical model needs to know the current temperature We might have to go back through a billion records to find out when that pump last told us what the temperature is And if we're getting a thousand events a second, we can't a thousand times a second We can't go back through a billion records trying to piece the parts together so tie this back to how we use Pentaho and sort of traditional systems of record today As Dave was asking it sounds like something that's very different because to understand, you know Pressure and temperature, but the temperature we didn't we haven't seen any results from for ten billion Intervals, yeah, so how does how does Pentaho have to change to accommodate this type of application? So the I see the the the the system that's necessary for IOT Being there's a architecture called the Lambda architecture, which is basically a data lake and a real-time system Okay, and then so we're now adding real time bump that one up a little bit Yeah, so you've got these three main systems You've got the data lake for the history You've got a real-time system for handling the streaming events and then you've got this the state repository for knowing exactly How it how is each device right now? So the challenge for Pentaho is that we have to work with all three of those data sources Be able to query them be able to join the the results together As questions are being asked. We've also got to handle Blending so if I've got a subscription service, I don't really care how many devices I'm selling because I sell a subscription I'm giving the devices away I'm actually losing money when I when I gain a customer because I'm giving the device away because it's a subscription So what I care is are people using my service? So now I want to look at how many devices did I sell that's in my cell system and How much is my service being used that's in my data lake and my real-time system? so I need to blend those two data sets together in a In a reliable accurate accurate and and in a government way So blending becomes very important Of the blending these different data sources together making sure that that's accurate security metadata all these things play heavily into the Into the complexity of the system. So Pentaho basically it's the orchestration and the joining of all these different data source So James you think about this stuff all the time. I could tell you live it Think about it at night think about day while you're eating breakfast. I'm sure What is your role specifically and what's with the titles? the So it was so with the title first. I was originally the the title. I gave myself a CTO was Chief Geek And I'd had that title for six or seven years without a promotion And so I just decided to give myself a promotion from Chief Alpha Geek from Chief Geek to all of the ones and zeros I'm not sure what I'm going with next actually have my email That it's the stupidest feature in outlook you can have you can create multiple email signatures in outlook and Tell it to randomly put one of those in as your email signature So I have on my email signature. I've got Chief Geek. I got a lot of the ones and zeros I've got Duke of Earl you are URL Baron Von Tech. Oh Duke of Earl URL. That's great Baron Von Tech I've got a big data ninja So I've got a collection of so no one really knows if you get an email from you Don't really know what my title is changes the next time I reply to you So that's the you know the the story behind the behind the name So really what you know what I do is? You know when we started looking at big data That's when I came up with the whole idea of the data lake, you know the data lake concept was something I came up with six or seven years ago when I started looking at the It's a big data technologies and I was with our CEO now chief strategy officer Richard Daly we drove up and down Silicon Valley up and down 101 Talking to the Hadoop early adopters What they were doing with it? What were they trying to achieve? You know, what was the business purpose? What were the technical hurdles and then I tried to take all of those use cases and distill a common What are the common elements? Most of them were structured data But then I came I tried to come up with an analogy to help explain to people, you know There's a set of use cases that can be looked at one way And I tried a number of different analogies before settling on the the data lake It's not an ocean because the lake gives you a an idea that it's confined in some way. It's constrained. It's bounded But you know lake water is not clean water, so this is this is raw It's not Process it's not filtered. It's not distilled So I compare the data lake to say a data warehouse which is highly structured. You've got aisles and and pallets So it's like getting bottled water out of a out of a warehouse. It's highly organized The water is cleansed and purified in bottles. Yeah, so it's it's made it's Managed in the way that it's easily accessible and easily to navigate. Yeah, and so but the day like is complete opposite It's raw. It's unstructured. It's just an enormous amount of raw data. So how does your vision of IOT? affect Architecture product, how does it get translated into something that I can buy so we have so first we go look at the There's the technical aspects of what the platform needs to do There's the business purpose or some business purpose of this platform Is it something that we sell is it an enabling technology for all of Hitachi's many businesses? Is this an open source thing that we're making available to everyone? So we need to decide what the What is the business purpose of this platform? And then we get to the the technical nature of what are all the different pieces in there? And it gets coming if you consider something like do should this be cloud-based and or should this be on-premise? There are some people that will want this on-premise. There are some people that want it on the cloud So now we got something that needs to be to run in two environments and you know when it comes to the database some people will want to use Hadoops some people want to use you know vertical or green one. So the the platform needs to be very flexible So really what my job is with Several other groups in Hitachi is to define what this architecture looks like and then we'll go off and and and build it So, you know when when you talked about driving up and down 101 and looking at the early use cases of Hadoop I think many of them were I mean the earliest of course was the web crawl But like yahoo talked very specifically about making it easy to sort of change a data warehouse, you know pipeline If we were to say because there's you know now we've got buzz around internet of things But we always have clear use cases in mind Have you seen a couple early use cases that have things in common the same way the ETL off-load did? Or yes data warehouse off-load Yeah, absolutely. So you've got the So some of it you know you look at smart buildings and smart cars So there the the exercise is around Optimization of resources so reducing electricity Reducing fuel costs working with one of our customers and their goal is basically to save five million dollars a year in In gasoline costs for pumps. They're not they don't know Sometimes they leave pumps running longer than they need to and they estimate they can save five million dollars a year Just by shutting pumps down sooner, but they need mathematical models to work out exactly when to shut those pumps down So you've got the you've got the optimization. That's one use case Capacity planning is another one. So you're looking at I've got all these devices as people buy more and more devices. I need more and more infrastructure to handle Serving up the the data that those applications need So there's the capacity planning aspect and then there's the failure prediction the failure what failure prediction? Oh, yeah So and failure prediction or something like a fraud detection where you're basically running a As as each event comes in you run a mathematical model to determine whether there's a problem or not so for those with those three examples have sort of common elements among them or would each have its own sort of Optimal way of You know configuring Pentaho and some additional technologies if any. Yeah, so there There's a large amount of overlap in technology wise in all three use cases So for instance in the failure prediction, you need a mathematical model You cannot build the mathematical model without looking at all of the history in the data lake So you need the data lake there for the modeling purpose But at runtime the the mathematical model is running as the events come in and you don't need the data lake anymore, okay? So there's some some phases. So this is the classic. I build my prediction batch mode Put it into production on near real-time or real-time data. Yes. That's that simple. Yes. Yep with that same model work for Capacity planning so capacity planning is looking purely just at the at the data lake basically looking at history and time series With a capacity planning you very seldom needs Access to the real-time data because you're looking at looking at trends over Over weeks or months and you don't need the real-time aspect as much as that's really clear So then what about the I would I would guess then smart buildings and cars where you're optimizing Resources that sounds like another one where you need both Yes, that is so you need to look at the history. So you might have example where Okay for the next few hours I only have one meeting booked on this floor if we move that meeting to another floor now I can shut down that entire floor every light bulb the AC I can shut off that floor just by moving a meeting So it's that kind of Optimization looking at all the different resources saving lectures the saving power Yes, there's definitely an element to to analyzing the history But then also it's it again comes down to the the real-time of you know What what at which devices are on and which ones can I turn off? Oh James? We have to leave it there. Thanks very much for coming on the Cube and sharing your vision of IOT. It was great to have you on Yeah, thank you very much. All right. Keep right there, buddy We'll be back with our next guest right after this. This is the Cube we're live from Pentaho World 2015 right back


Hello, everyone. Welcome to groundwater hydrology and management. This is NPTEL course week six, lecture two. In the previous weeks, we looked at the importance of groundwater and most importantly, the key parameters for groundwater. In this week, we are looking at why groundwater level would fluctuate and in particular, we are looking at groundwater recharge and discharge. In the last class, we looked at the key functions or processes that influence groundwater levels. Let's move on and look at groundwater recharge in this particular lecture. So groundwater recharge can happen through multiple processes. However, it is important to distinguish between groundwater recharge and discharge. What we saw in the previous class is that one in the hydrological cycle that one process can lead to recharge and also discharge in the same process. The flow of water from the high aquifers into the rivers and lakes is an example. Yes, it is discharging, but on the way it is recharging. So for that, we are going to look at what are the common methods in which these are assessed. We looked at the processes. Now look at how they are assessed. It could be different for recharge and discharge, but there are some processes or some methods that can capture both. For example, the water balance method. Here, you put in parameters for your water balance and then you can estimate where the recharge is happening and discharge is happening or both are happening simultaneously. For which there is a lot of monitoring needed and or understanding of your properties of the soil, the material and water rainfall, hydroclimate, etc. Water balance method can also be done like back of the envelope calculation people do. You have a surface runoff coefficient and then you have rainfall. We say that whatever is not runoff is going into the ground and into the ground means it is grown water recharge. So there are some simplified models, but we will look into very specific models and methods that are used for recharge and discharge in the coming lectures. The other method is monitoring method. There's a lot of sensors that can capture the parameters to assess the fluctuations in the water level. For example, monitors or meters and sensors that can help in the water balance method, which we explained using this hydrological cycle. You have multiple components and you can put values for each component based on the recordings of these meters and sensors. Then you have groundwater recharge monitoring, specifically for groundwater recharge monitoring, which is done by wells and the well level recorder or meters you use to record the well levels. For see pitch, there is a different method. For example, you have water coming, you can put a meter inside and then calculate the groundwater recharge or fluctuation or discharge using a water meter. On the other hand, the water can go and get into the ocean and rivers and lakes, which is called see pitch. That see pitch can be estimated using a see pitch flux meter, which is a meter placed on the banks of the rivers and oceans and seas to monitor how much water is coming out. It may be easier for estimates in the oceans because there is a density difference in the water. However, it could be more difficult in the rivers and freshwater bodies. So monitoring can help in establishing the water balance components or specifically only the groundwater wells or the see pitch. The third point is estimates, the lots and lots of estimates that are made. And these estimates, as I said, are based on the back of the envelope calculations, very simplified calculations, which are coming because of a prior understanding of the system. Let's take this example. Your change in groundwater is nothing but del G, change in groundwater level is equal to precipitation minus rainfall minus runoff. As I told the parameter variable differs, you can put rainfall as R or P, etc., etc., but it's all safe. How you define it is very important.  So if I extract the runoff, if I subtract the runoff volume, whatever volume remains is going in the ground. Remember, there's no ET. There's no evapotranspiration. There's no other losses because I'm taking a very specific case study where I don't have all these. Let's take a barren land, for example. In that barren land, there's no plans. There's no evaporation also happening. It's just going in because there's no sunlight, for example. The rainfall only happens in the night. And in the night, there is runoff happening and most of the water will go down the remaining water and reach as a groundwater. These are the estimates that you can put with the back side. And even the R, which is your rainfall, which you need data, or every month you have a statistical model to predict the data. But Q can be, most probably, they do estimates. If you know, for example, it is a cement road. If you know, for example, it is a forest, you know that 80% of the water will runoff. The remaining 20% will go in. So those kind of percentages are estimates based on previous field work from different locations. Then your models, like this model you have here, which is the SWAT model, very complex hydrological models, which if you give all the parameters ranging from the top water meter models, water balance data, et cetera, et cetera, you feed it into these models and the models give you the output of groundwater recharge or discharge based on your calculations and based on your estimates of these parameters. So for example, you give all these parameters in the model, the model will spit out a groundwater recharge value and a groundwater discharge value. It also is based on the climate, the land, the land use, which is your trees, plants, et cetera, growing and your slope of the land, how the land is tilted and stuff. Let's look at some of these estimates, especially the recharge estimates. So now we're going to shift gears in just looking the recharge volumes for India and also only India. The first is our own Central Groundwater Board, where it says annual reprehensible groundwater resources are 433 billion cubic meters. The net annual groundwater availability is 398 billion cubic meters and your annual groundwater draft for irrigation, domestic and industry uses 245 billion cubic meters. So this 433 is based on annual data of how much water can be used to recharge. The net groundwater availability is the water that is remaining to be used because not all 433 can be consumed. Part of it is going to be held in the soil and the rocks and other materials. It is not going to be taken out, which is here, it is approximately 35 billion cubic meters. It's a big amount, but it's still, think about Pan India. This data is for Pan India. So I will say that this is data for a whole of India, CTW estimate. And then you have your annual groundwater draft for irrigation, domestic and industry use. Basically these are three different uses and if you understand what is the draft or pumping or use for irrigation because of the crop type, crop area, you know how much water is required for irrigation. Domestic, you know how many people are there through population census and from the census data, you can estimate what is the number of households and each household how much water they get for estimating domestic water use. Then you have your industrial use. Industrial use is the trickiest here because it is closed. Let's take a bottling company for example, where they make fruit juices, drinks, soda, etc. It is a big industry which takes a lot of water. We don't know how much water they use. They have pay per use system and or lease system. They will say, okay, 100 years I will pay this much money or 10 years, 30 years. And the pumps efficiency only they know. You cannot estimate it just by power supply and all because they can keep fine tuning the efficiency of these pumps. So what happens industrial use is still a big estimate where irrigation is all kind of monitored and measured because you know satellites can take pictures of crop types and domestic use you can take it from census which is a survey based data. So all this data is available. Industrial is kind of really tight but you still you can manage you can estimate as CGWB has done and it is same to 45 billion cubic meters. This is kind of an outdated number now it is to 65 billion cubic meters. So what is the stage of groundwater development? Now you know the draft. You know the recharge which is around 433 million cubic meters recharging after which 398 can only be used and out of the 390 only 245 was used which is 62 percent. So 62 percent is nothing but the percentage of 245 in the 433 almost around 50 plus. So it's 62 percentage which means that it's still safe. India is safe in groundwater reuse as per the CGWB estimate. It may or may not be the same by other estimates. Let's look at some other estimates. This is the estimate done by your team in Banja et al paper 2019 where they use explicitly lot of wells groundwater well data and they measure the recharge happening and also the precipitation happening per year. Okay so millimeters is a thickness not a volume but a thickness of recharge and thickness of rainfall happening in a year and note that they only do it for India and because of the data they have and there are multiple transboundary rivers also here like your Indus, Ganges and Brahmaputra could be multiple transboundary Ganges goes from Tibet, China, Nepal and India. Indus can be Pakistan and India part. So there are differences Brahmaputra and the Bangladesh et cetera. So here only the India part is spoken and what you could see is the number of wells helped in estimating the recharge for sure and there is differences in groundwater recharge. The differences is led by the groundwater parameters which we saw earlier in the class of the importance which is basically your aquifer type the soil material the rock material present in that basin which allows the groundwater to flow the ease of groundwater to flow and recharge. Not only that the area should have a good rainfall you might have the best groundwater aquifer but if you don't have rainfall water doesn't go in so water is important and after water the water from rainfall the rainfall should go into the aquifer so the availability and readiness of the aquifer to recharge is also important and in that aspect you could see that the recharge ranges from 143 to 264. Barak and other basins are 94 to 960 whereas I'm sorry the Brahmaputra is anywhere 94, 960. Barak is 77 to 802. So mostly your alluvial aquifers which are given in this first couple of things most of these basins I'm saying where the alluvial aquifers are more you could see a very healthy groundwater recharge compared to the other regions. Actually all of them are basins all of them have a river and stuff so you will see some part of alluvial in it but what is the major discussion in this slide is that you have multiple wells that can give you accurate data for estimating recharge and the recharge is not the same across again this is the driving factor. It could be 960 in the Brahmaputra whereas it is only 131 in the Fenar basin in the south and this is where I say it is also based on the rainfall which is 2300 in the Brahmaputra compared to 779 almost arid semi arid condition in the south of India Fenar and you also have the aquifer type the geology which is allowing the recharge amount. So recharge is a good combination of your rainfall availability your physical processes the aquifer properties that allow the recharge and the availability of water inside the aquifer if the water is already there recharge won't happen right. So this study beautifully quantifies across India through wells the recharge rates and also compares them with the rainfall rate and most importantly they establish the range. So the range could why is there a range difference for example you have the Brahmaputra let's say this is the Brahmaputra again just looks somewhere like this. So you have 143 to 264 why is there a range difference because the rainfall also varies even though they give only one rainfall here okay let me erase some of it. So then you have multiple wells in different locations the rainfall is not the same but let's say on average this is a rainfall but there is very very important change in the groundwater recharge because of the location aquifer type and the slope and the rainfall also differs along the ganges it is not the same okay. So this study is very important to quantify the differences one can expect because of the placement of the basin in a particular aquifer system or a geology type and also the rainfall all of this is driven by your well record. So different estimates are there this is the other confusing part this may not agree with the CGWB's estimate the differences can occur because of the well type maybe they're using more deep wells to establish the aquifer recharge conditions and also the region in the previous slide we just saw 245 433 as a recharge annual but where is it placed where is that 433 million cubic meters happening we don't know it is a combination but which regions have more and which regions have less we don't know this gives a good picture of where in data where it happens more okay. So as I said more recharge is happening in the Brahmaputra compared to the other regions and then the Benar and the south have very very less recharge. Let's come back to the book that we're using for the class which is the hydrology principles and analysis designed by Raghunath professor Raghunath and what you see here is water is taken as rainfall and then an estimate see here's the estimate at one third so this estimate is given it is not or it need not be a calculator monitored it would sensibly acquire data it is a one third based on literature review so they say the rainfall is 370 million hectare meters it's a volume okay hectare meter is a volume see how the units change so it's not readily comparable the previous slide was millimeters per year in the previous slide it was billion cubic meters per year so in the CGW basement it was a volume in the next slide the banjai at all paper it is a thickness here it is a volume okay so in evaporation at one third 123 runoff from rainfall and rivers is 167 as I said they'll just estimate how much we have runoff seepage into soil by balance okay so how much is seepage seepage happening you just subtract one which is your rainfall and then 123 and 167 so if you know one quantity in your water balance you can estimate the other components by a simple addition or subtraction okay so here they've added two and three and subtracted excuse me to get at 80 so this is the groundwater recharge see how the language is seepage is used here which is basically your recharge into the subsoil into the soil water observed in topsoil contribution to a soil measure this is also an estimate okay he is put for 43 and 43 is from the 80 okay so what is the recharge for the deeper aquifers so recharge into groundwater from rain for the net recharge is going into the aquifers after the water is observed or in the soil moisture is only 37 so seepage is here is just the infiltration water infiltrates part of the water stays in the soil which is 43 the remaining goes down as recharge which is 37 so 43 plus 37 is 80 okay then your annual groundwater recharge from rainfall and seepage from other canals and approximate they've put it very clearly date and which is good if you don't have the data read some books and papers and put a number and say it is an estimate do not say it is actual value so these are actual rainfall is actual you cannot say that you can just say approximate then groundwater that can economically share from the present drilling technology at 60 percent so 60 percent is again a number they put that on seven and then take 27 present utilization of groundwater at 50 percent in the previous cgwb slide it was saying 62 percent here they are using 50 percent maybe when they did the book in 2006 it was a cgwb estimate okay hours was 2000 10 past so there is some difference in the percentage so let's say 50 percent of eight of 50 percent 27 13.5 so available groundwater for future exploitation which is the remaining 50 percent okay 50 percent is utilized 50 percent is remaining so that is 13.5 so you see here how a water balance equation is set up in the mind or and then they've written it down identified which are the key parameters and throw it out the negligible parameters like ET capture water captured in the canopy those kind of things through rainfall etc they lift it up we don't know we don't want to and then they put estimates for each and every parameter one third 50 percent 60 percent and then arrive at recharge so this is another way of estimating groundwater recharge so this is 37 it could be also be done with the equation i gave you which is del g is equals to just rainfall minus q so if i if i assume there's no evaporation i say rainfall is happening 370 minus runoff 167 is a net recharge in my very simplistic case it is approximate please read in between the lines is it an actual data if it's an actual data they'll give you the data source otherwise it is approximate and there are differences okay they've identified only parameters that they want to be sure of the others they give it very blatantly it is an approximate so driving home here is there are multiple methods for estimation of groundwater recharge and it can be based on multiple physical or data intensive or modeling perspectives let's look at some of them the very very important as per the recent review by Sajil Kumar in 2021 and also as defended by the freeze and cherries uh groundwater book which has identified the most important groundwater recharge estimation methods so now all estimates is important like you saw that different estimates are there not one method is important there are multiple methods depending on the data depending on the cost depending on the time for the research project let's look at some physical methods this needs a lot of physical data okay the soil water balance method by dawn twight is an example where you construct hydrological water balance only for the soil because you don't care about the evaporation you don't care about how much is left in the rainfall etc you only care about how much water comes in and out of that what is the real location to plants animals etc and how much water goes in so this is a soil water balance method which is developed by dawn twight nothing else but a water balance which is focused on the soil water so you have the groundwater surface you have a water table and dash lines and then you have multiple instruments that can collect data at different different depths for understanding groundwater recharge understand that the first set of tensiometers here will only look at infiltration slow infiltration of water and then you have a rainfall gauge to look at how much rainfall is happening so you have an input to the system you have the first seepage infiltration into the system and then you start slowly monitoring your groundwater wells the soil electrical resistance is a device that is used to measure the soil moisture once the soil moisture is full 100 percent then water goes down if soil moisture is not 100 percent water still stays in the soil slowly recharging the soil moisture not the groundwater we are here looking at groundwater recharge not soil moisture recharge then you have observation wells which is your wells with a meter in it and all but piezometers which are deep deep aquifer wells so these two are just wells but the difference is the depth you can see here how deep it is it is a broken x axis sorry y axis so it is not going in tens and hundreds it goes different units okay depth and feed then you have zero flux plane is that fp based on Darcy remember Darcy's is a saturated column and how water flows through this plane is determined by Darcy's flow so Darcy's flow if it is kept only in this soil profile gives you the groundwater recharge after that you can use a Darcy's flow here to look at groundwater flow remember your class notes that we use Darcy to estimate groundwater flow but Darcy's principle can also be used as a recharge all you're doing is shifting from the confined aquifer and unconfined aquifer into the zone where water is coming into the soil it is recharging and then comes out which is recharge again recharge is also is a flow it happens from top to bottom it goes down in the soil profile so there is a groundwater level fluctuation method which is one of the most important methods used worldwide including USGS including CGWB there always people use this groundwater level fluctuation method for which there is a need of groundwater data from these wells and then you have the groundwater balance method which is another soil water balance type of a water balance but only kept for the groundwater we've already seen these water balance equations in the previous class all of these need extensive data that is the driving point then you have tracer techniques here comes the kind of an invasive way of testing groundwater because you are now getting into contact with the water here you're just measuring the water that's it here you are putting something in the water to measure it okay please understand here it is need of not data alone but need of chemicals you're going to put a chloride you're going to put a chloride to see how the chloride signal travels or traces like environmentally friendly traces inks you can put an ink to see how groundwater recharge happens but then there are tritium method and stable isotope method which are water signature methods which are based on the chemical property of the water okay so traces not only include the inks and biological or chemical traces that you add in the water it can be also done by analyzing the water chemicals components or the isotopes that are present in fact the isotopes are very useful for understanding the age of the water then finally we have the numerical methods which are based on pure modeling there are softwares which actually ask you for a lot of data and then it is a data heavy but there are models which can also estimate for you you just have to tell this is the type of soil this is the rainfall this is the crop i'm growing it automatically tells you the groundwater recharge okay and within the groundwater model you have multiple dimensions there can be a 1d which is just looking at one dimensional moment of water there can be a 3d where kx alone is not only there but also we have kz ky and kx so three dimensions how groundwater moves and the net groundwater flow is going to be modeled hydros is a good model for 1d whereas mod flow is a very good model for 3d and then you have inverse modeling which is also based on lot of data so here we have seen that establishing these connections on how recharge happens like the physical establishments you can have different estimates based on different methods there is no one method that is being promoted across the world it depends on your region it depends on the data you have the time and the resources for example for numerical methods it is very important to have a very sophisticated computer otherwise the model will crash for traces you need a good environmental tracer or a clearance from the government to test these traces most importantly the stable isotopes and tritium would need a radioactive lab it is not easy to do all these the physical methods are more easier you have to put data collecting monitoring sensors collect the data come back do the calculations by hand or by computer and then you estimate so there is given taken each method and what method is suitable for you you could use it for the long one okay so we have looked at the different methods we will look into one or two methods for this class and then we'll jump into the discharge methods with this I will see you in the next class thank you


Pirates at Cubs, top of the sixth inning. The Cubs manager Ross is out with COVID, so Andy Green is the acting manager. You got a runner on first and second, one out. Cubs have a three run lead. This is in play, double play ball.  That's gonna score a run, pro long the inning, and the manager for the Cubs, Andy Green, ain't happy about it. He wants to go ask for a review. He thinks the slide may have not been, you know, a nice slide. Only problem is, he asked for a review earlier in the game. It did not get overturned, so he doesn't have any more reviews, and it's not the eighth inning yet. So basically, he just has to ask the umpire, like, hey, can you review that for me? Can you go to replay for me? And Tom Hallingham says, no, no, no, I can't, I can't do it, I'm not gonna do it. It was a good slide, and it was a good slide. I mean, he touches the base with his back foot there. He's in the vicinity of the base. He doesn't even touch the guy throwing the ball until after it's out of his hand, so it is a good slide. But he's asking him, can we just review it? Can we check? Can we see if this is cool? Because my guy threw the ball like he got hit. He had to have get hit, because the ball was so poorly thrown. But the umpire says, no, I'm not going to review. And then he tells them as they're talking, he says, I'm done listening. And he's like, okay, well that's two now.   What are you doing? You know what I'm doing. I told you, there's no way. There's no way. I'm walking away. You gotta be shitting me.  Don't care at all. Walk home.     You know it was wrong. You blew it and you won't accept that you're wrong.  I don't know.  That's what I'm telling you.  That's right. Well, what do you know about the foot on the back? Really, you know that foot's on the back? You think you know that? What happens to me if I told you what you just said? What happens to me if I told you I said that? Well, he was over there, his clear path. He starts explaining, no, get out of here. I love that. I love it. He starts going back down the rabbit hole. He's like, he was going there. He was going there. The foot's on the back. You know what? Then he's like, no, no, no. Done. Enough. Get out of here. You're done. Phil Cuzzy steps in as a little middleman bouncer, starts escorting him out. He keeps yelling. He keeps yelling. Tom Helen says, I know more than you know. You have to know this. Andy Green's like, wait, what? You know more than me? Yep.  You don't have to treat me like that. You don't have to treat me like that. Geez. That's not umping. He's going to have to realize that.  And then in the inning that they wanted over because of the double play, a home run happens and now it is a tie game and uh-oh. Maybe all that yelling was worthwhile. Look.


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