So now, boy, that board is already full of formulas. So here we go with b_k*sin(kx). So the rule for derivatives, the whole point about Fourier is, it connects perfectly with calculus. And then I have b_2-- Now, here's the one that's going to live through the integration. Interesting and famous. And everything is depending on this answer. Availability. I can do one one-dimensional projection at a time. And project that onto this guy, so the projections are there? We're going less smooth as we take more derivatives. Right? Nov 24, 2020 - Binomial theorem Engineering Mathematics Video | EduRev is made by best teachers of Engineering Mathematics . No. So how is it possible to find those coefficients? Between zero and pi. You're just matching terms. Odd means that S(-x) is -S(x). So b_k, b_2 or b_k, yeah tell me the formula for b_k. So the boundary conditions, let me just say, periodic would be great. But I'm really interested to know what happens as both of these increase. That's as close as sin(x) can get, 4/pi is the optimal number. A step function, a square-- And if I repeat it, of course, it would go down, up, down, up, so on. Right? You're given the right side. It's so easy, it jumps at you. I'm not seeing quite why. We're not dealing with vectors now. And one important question is, is the Fourier series quickly convergent? Additional costs. Lec : 1; Modules / Lectures. And beautifully really means zero. So I have net minus minus one, I get a two. Was it really possible to represent other functions, maybe even including a step function, in terms of sines or maybe cosines? Welcome! So that's b_2 times pi here, and I just divide by the pi. FE. This module is a 20-credit, year-long module which covers the mathematics you will need for the first year of your degree. And at the beginning it doesn't look too easy, right? Introduction; Basic Ideas of Applied Linear Algebra; Systems of Linear Equations; Square Non-Singular Systems; Ill-Conditioned and Ill-Posed Systems; Module II. So this is a typical nice example, an important example. Our application, we started this course with equations like -u''(x) = delta(x-a). What does that mean? The most important point. And so it's got a whole infinity of coefficients. We'll see it over and over that like for a delta function, which is not smooth at all, we'll see no decay at all. May 27, 2020 - Explore our online course catalog of degree courses, competitive exams, professional courses and skill-based specializations. In this application, which, by the way I had no intention to do this. You see the ripples moving over there, but their height doesn't change. » cos(k*pi). My N from the graph? Lec : 1; Modules / Lectures. And what do I get from k=5? I hope you'll see some new aspects here. Oh yeah, rules for the derivative. Lectures by Prof. S.K.Ray Department of Mathematics and Statistics IIT Kanpur. Could I have a c(x) in here? Which makes everything possible. At k=1, the cosine of pi is? OK, so what do we do about Fourier series? Chris Tisdell UNSW Sydney, 17.Gradient and directional derivative. And when does it work? We're lucky in this course, u = [1, 1, 1, 1] is the guilty main vector many times. If I add that one to this one I'm way out here somewhere. It's not as bad as usual. Free Video Lectures – more than 700 (excluding Khan Academy’s which they also listed) videos. This knowledge and understanding may be evidenced by possession of the HN Unit Engineering Mathematics 1 or Higher Mathematics. Fee waivers or funding may apply. I have to figure out what is cos(kx) at zero, no problem, it's one. This 4/pi*sin(x) is the best, the closest I can get to one. If k=l, what is it? Courses > Engineering Mathematics - I. The healthy snack company Graze is a start-up of an University of Bristol Engineering Mathematics graduate. Write the right-hand side as a Fourier series. Now, what's b_2, the coefficient for k=2? It's just terrific. So that's one good reason to look at the complex form. Right? And what's the result? So, a step function. Department: Mathematics Faculty: Science; Tags. How do I find b_2? What did b_2 come out to be? That's what I've got with sin(3x), and of course odd on the other side. What happens? In practice, in computing practice, we're close to computing practice here. And then you've got the answer, but you're still in Fourier space, you're still in frequency space. If I plug in x=0 on the right-hand side I get zero, certainly. We know that video is important to many learners. You can see the rule. And nor have we really got that. Project there. Let me just with put these formulas down. The optimal coefficient. The first ripple gets thinner, the first ripple gets thinner. Well, fixed-fixed was where we started. Fixed-free will have some sines or cosines. Now I do have some sin(3x)'s, how much do I have? So a little bit to fix, still. So there are two numbers there, we had N points on a ray, out from the center. k=4, what do I get? OK. Now, well, you might say wait a minute how are we going to expand this function in sines. And a lot of examples fit in one or the other of those, and it's easy to see them. What would the graph of sine squared x look like, from minus pi to pi? The most important, interesting function. Contact Us . The integral of sin(kx) is not minus cos(kx). Excellent course helped me understand topic that i couldn't while attendinfg my college. Toggle navigation An-Najah Lectures. Get to know the methods of measurement, classification of … Chris Tisdell UNSW Sydney, 27.Leibniz rule Integration via differentiation under integral sign, 28.Evaluating challenging integrals via differentiation Leibniz rule, 29.Critical points of functions. A particular S(x). An-Najah Videos. In other words, if you're computing shock. 5000 free math, physics, and engineering video tutorials and lectures. Solution of Linear Systems. So I googled for free online engineering subjects and found the Ekeeda app. Do you know whose name is associated with that, in that phenomenon? You know, when does he raise his hand, say yes I can solve that problem? And we get something highly interesting. So what's up? Mathematical Methods in Engineering and Science (Video) Syllabus; Co-ordinated by : IIT Kanpur; Available from : 2012-07-04. Everybody knows what odd means? And now I'm taking two derivatives, so I bring down ik twice. So, this is the standard Fourier series, which I couldn't get onto one line, but it has all the cosines including this slightly different cos(0), and all the sines. But I don't know if you can see from my picture, I'm actually proud of that picture. At the end of the interval? So we want, it works perfectly when it's constant coefficients. In GATE it is very easy to score in mathematics there is nothing required like lectures for maths. That's b_k. So those will have only cosines. Engineering Mathematics II. So this is b_2, and multiplying, right? no.2) Vector calculus, 48.Line integrals. What is it if sine, if k=l so I'm integrating sine squared of kx, then it's certainly not zero. Just one. Engineering Mathematics – I Dr. V. Lokesha 10 MAT11 1 2011 Engineering Mathematics – I (10 MAT11) LECTURE NOTES (FOR I SEMESTER B E OF VTU) VTU-EDUSAT Programme-15 Dr. V. Lokesha Professor and Head DEPARTMENT OF MATHEMATICS ACHARYA INSTITUTE OF … But over here, with 90 degrees, these are the two projections, project there. And with physical variable x, position. Instructor: Mohammad Omran . Engineering Mathematics provides the strong foundation of concepts like Advanced matrix, increases the analytical ability in solving mathematical problems, and many other advantages to engineering students. Step function. And I agreed with you, but we haven't computed it. Now, so that's one integral better. I would take the Fourier series of both sides. The final step is, now you know the right coefficients, add them back up. Don't forget that it's four on the right-hand side and not one, so if you get an answer near 1/4 at the center of the circle, that's the reason. So now b_3, I have 1-cos(3pi). Then one more integral, one over k fourth would be a cubic spline. Well, not so little, but it's a saving. But it jumped into my head and I thought why not just do it. And that again makes exactly the same point about the decay rate or the opposite, the non-decay rate. And I'll call its coefficient c_k, and now they multiply e^(ikx), so we have to get used to e^(ikx). This is one of over 2,200 courses on OCW. Watch Next | Lecture 2 Lecture 1. In GATE it is very easy to score in mathematics there is nothing required like lectures for maths. So let me take a 2/pi out here. Can I project that onto this guy? By Prof. Jitendra Kumar | IIT Kharagpur This course is about the basic mathematics that is fundamental and essential component in all streams of undergraduate studies in sciences and engineering. They're orthogonal to each other. The point is, the point of this 90 degree angle there is, that I can split this S(x), whatever it might be, I can find its sin(x) piece directly. I'll need that one. So what's the formula for c_k? Now we're getting better. Chris Tisdell UNSW Sydney, 44.Divergence of a vector field Vector Calculus, 45.What is the curl? In fact, when Fourier proposed this idea, Fourier series, there was a lot of doubters. So we would have the sum of k squared c_k e^(ikx). Polar form and de Moivre's theorem. Let me write that word down. LinkedIn 23. Enroll now! So and of course, the second derivative would bring down ik squared. They involve integrals. Always interesting. dF/dx. I think of k here, I'll use the word frequency for k. So high frequency means high k, far up the Fourier series, and the question is, are the coefficients staying up there big, and we have to worry about them? Again, I'm looking for b_2. Here, in applying Fourier, the first step is always find the coefficients. And here's a point that's highly interesting. Oh, I can tell you even at a start. Gibbs noticed that the ripple height as you add more and more terms, you're closer and closer to the function over more and more of the interval. We're in function space. Tell me what these numbers are for-- Let me put the k in here because that's part of it. Its derivative is continuous, that gives us a one over k cubed. Freely browse and use OCW materials at your own pace. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. ), Learn more at Get Started with MIT OpenCourseWare, MIT OpenCourseWare makes the materials used in the teaching of almost all of MIT's subjects available on the Web, free of charge. When does it work? Chris Tisdell UNSW Sydney, 21.Gradient & directional derivative tutorial. Because all those series are series of orthogonal functions. And now I take its derivative. Course information; Full-class lectures; Notes and exercises; Video lectures; Problem classes; Contacts; Exam matters; Interesting extras; Course Information. Watch Next | Lecture 2 Lecture 1. Sine of what? The whole interval is of length 2pi, and we're taking the area under sine squared. OK, let me do the key example now. The sines are orthogonal. In some way, the work is only half as much. It's gone. But then there will be a 4/pi sine, what's the next term now? And now let me take Fourier transforms. This course involves an additional SQA fee. I would look at, I'd jump into what people would call the frequency domain. But there is a sin(4x), we're in infinite dimensions. So I'll pick the 2pi interval to be minus pi to pi here. Also, Coaching is too expensive with Rs 7000 per subject. Well, linear equation, right? The derivative brings down a factor ik. We don't offer credit or certification for using OCW. Chris Tisdell UNSW Sydney, 23.Partial derivatives and error estimation, 24.Multivariable Taylor Polynomials. This sin(2x) squared? Because there's just one formula. So I have 4/pi 1-cos(5pi), I have no sin(2x), forget that. 4/pi times sin(x), sine(3x)/3, sin(5x)/5, it's a beautiful example of an odd function. It's just so great you have to let the computer draw it a couple of times. And let me chose a particular S(x). One is, I am going to get closer and closer to one. If I have a function that's a step function, I'll have decay at rate is 1/k.. So what am I getting, then? At k=1? So when we do these examples, so I've sort of moved on to examples, so these are two basic examples. So it's going to have coefficients, and I use b for sine, so it's going to have b_1*sin(x), and b_2*sin(2x), and so on. I'm getting 2/pi-- no, 2/(pi*k). So that's the sort of functions that have Fourier series. You see, it goes up here. And the whole point is that that calculation didn't involve b_2 and b_3 and all the other b's. Everybody see what happens when I take the derivative of that typical term in the Fourier series? 2/3. So, let me just get organized. I have 1-cos(2pi), what's cos(2pi)? To see why that's zero. So let me draw two orthogonal directions. Engineering Mathematics I.Instructor: Prof. Jitendra Kumar, Department of Mathematics, IIT Kharagpur. That's the model. This section contains videos of Professor Strang's lectures, recorded at MIT's Lincoln Laboratory in the Spring of 2001. What have I forgotten? A review of vectors for those beginning vector calculus and several variable calculus. If you want to familiarize with all concepts of engineering maths and enhance your problem-solving ability and time … no.1) Vector Calculus, 47.Curl of a vector field (ex. Mathematics as a subject is vast and with these online tutorials, we have tried to segregate some major topics into distinct lectures. Right, same as the cosine of pi. And you might keep the two proportional as you increase them. Instruction Year: 2012 (First Semester) Views: 994 Tought In. And then there's no 4x's, no sin(4x)'s. And double it. OK. If I could just close with one more word. This is a series of lectures for "Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. With taking derivatives. Because the derivative just brings a factor ik, so its high frequencies are more present. Do you see what's happening there? OK, so now how do I use that? Zero, because the cosine of 4pi has come back to one. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. Well, yeah, or maybe a hat next. Now, what do I mean by two functions being orthogonal? 1-cos(5pi), which is? Match the coefficients of these eigenvectors. Trimesterised qualifications have courses available to enrol in and study over set periods, three times a year - Trimester 1, 2 or 3.; Open qualifications have courses available to enrol in and study every month throughout the year. But now when I put in sin(3x), I think it'll do something more like this. Have larger coefficients. You'll have to deal with Gibbs. So it's good to see complex numbers first and then we can just translate the formulas from-- And these are also almost always written with complex numbers. NPTEL Video Lectures, IIT Video Lectures Online, NPTEL Youtube Lectures, Free Video Lectures, NPTEL Online Courses, Youtube IIT Videos NPTEL Courses. I'll just use this formula. Facebook 50. Do you see that everything is disappearing, except b_2. Such problems involving vectors are seen in first year university mathematics, physics and engineering. So I divide by pi and I get the integral from minus pi to pi of my function times my sine. Videos include single variable calculus, multivariable calculus, vector calculus, probability and statistics, algebraic topology and more. $x$, 13.Chain rule identity involving partial derivatives, 16.Multivariable chain rule tutorial. A hat function might be the next, yeah, a ramp, exactly. Toggle navigation. NPTEL Online Videos, Courses - IIT Video Lectures Well Organized! And I want it to be simple, because it's going to be an important example that I can actually compute. You'd have to compute that integral. I can see, what's my formula, what should c_k be if I know the d_k? cos(5pi) is back to negative one, so one minus negative one is a two. But it's always interesting, the delta function. It has cosines and it has sines, it's just the sum of the two pieces. So ready to go on that MATLAB. This is b_2, and then this is some number. Chris Tisdell UNSW Sydney, 11.Multivariable chain rule and differentiability Chris Tisdell UNSW Sydney, 12.Chain rule partial derivative of $arctan (yx)$ w.r.t. In recent years, OCW has substantially increased its video content. What is this integral, the integral of sin(3x) times sin(2x)? Chris Tisdell UNSW Sydney. Use OCW to guide your own life-long learning, or to teach others. Shall we call those d? You see the pattern. If k is equal to l then I have to figure that one out. Lecture 1 - Real Number. This S(x) is, let's see. Studying Engineering Mathematics at MSc level will give you fantastic career opportunities. So you could say the length of the sine function is square root of pi. I get a two over a one. We get Fourier coefficients of the deltas. It's got this right-hand side. Fees. No . Svetlana Mateeva Engineering. So I'm looking. Very nice. We're asking a lot. Because, I mean it's fantastic when it works. But what's the requirement for Fourier to work perfectly? Well, not easily, anyway. However, the high cost of video production means we can only provide video for select courses. Right? So I'm not interested in doing more and more complicated integrals and finding Fourier coefficients of weird functions. About us; Courses; Contact us; Courses; Computer Science and Engineering; Discrete Mathematical Structures (Video) Syllabus; Co-ordinated by : IIT Madras; Available from : 2009-12-31. Now, what boundary conditions do we think about here? OK. 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Vector functions tutorial chris Tisdell UNSW Sydney, 42.What is the sine coordinate. Fact and it makes the crucial point, two, and this might be, you the... Me what these numbers are for -- let me draw enough so you say. Yeah tell me the correct decay rate or the opposite, the number mesh. Function times my sine we integrate again, that would be something like that such problems vectors! Graduates are highly important integrals that just involve sine 'm trying to find the coefficient for k=2 through Web! One formula for these coefficients ) at zero, I can see, you might say wait a how... Comes the b_3 guy, would be something like that on that coordinate ;...